meta analysis research paper

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• Published: 30 January 2023

A systematic review and meta-analysis of the evidence on learning during the COVID-19 pandemic

• Bastian A. Betthäuser   ORCID: orcid.org/0000-0002-4544-4073 1 , 2 , 3 ,
• Anders M. Bach-Mortensen   ORCID: orcid.org/0000-0001-7804-7958 2 &
• Per Engzell   ORCID: orcid.org/0000-0002-2404-6308 3 , 4 , 5  

Nature Human Behaviour volume  7 ,  pages 375–385 ( 2023 ) Cite this article

70k Accesses

105 Citations

1963 Altmetric

Metrics details

• Social policy

To what extent has the learning progress of school-aged children slowed down during the COVID-19 pandemic? A growing number of studies address this question, but findings vary depending on context. Here we conduct a pre-registered systematic review, quality appraisal and meta-analysis of 42 studies across 15 countries to assess the magnitude of learning deficits during the pandemic. We find a substantial overall learning deficit (Cohen’s d  = −0.14, 95% confidence interval −0.17 to −0.10), which arose early in the pandemic and persists over time. Learning deficits are particularly large among children from low socio-economic backgrounds. They are also larger in maths than in reading and in middle-income countries relative to high-income countries. There is a lack of evidence on learning progress during the pandemic in low-income countries. Future research should address this evidence gap and avoid the common risks of bias that we identify.

Similar content being viewed by others

Elementary school teachers’ perspectives about learning during the COVID-19 pandemic

Measuring and forecasting progress in education: what about early childhood?

School-based health care: improving academic outcomes for inner-city children—a prospective cohort quasi-experimental study

The coronavirus disease 2019 (COVID-19) pandemic has led to one of the largest disruptions to learning in history. To a large extent, this is due to school closures, which are estimated to have affected 95% of the world’s student population 1 . But even when face-to-face teaching resumed, instruction has often been compromised by hybrid teaching, and by children or teachers having to quarantine and miss classes. The effect of limited face-to-face instruction is compounded by the pandemic’s consequences for children’s out-of-school learning environment, as well as their mental and physical health. Lockdowns have restricted children’s movement and their ability to play, meet other children and engage in extra-curricular activities. Children’s wellbeing and family relationships have also suffered due to economic uncertainties and conflicting demands of work, care and learning. These negative consequences can be expected to be most pronounced for children from low socio-economic family backgrounds, exacerbating pre-existing educational inequalities.

It is critical to understand the extent to which learning progress has changed since the onset of the COVID-19 pandemic. We use the term ‘learning deficit’ to encompass both a delay in expected learning progress, as well as a loss of skills and knowledge already gained. The COVID-19 learning deficit is likely to affect children’s life chances through their education and labour market prospects. At the societal level, it can have important implications for growth, prosperity and social cohesion. As policy-makers across the world are seeking to limit further learning deficits and to devise policies to recover learning deficits that have already been incurred, assessing the current state of learning is crucial. A careful assessment of the COVID-19 learning deficit is also necessary to weigh the true costs and benefits of school closures.

A number of narrative reviews have sought to summarize the emerging research on COVID-19 and learning, mostly focusing on learning progress relatively early in the pandemic 2 , 3 , 4 , 5 , 6 . Moreover, two reviews harmonized and synthesized existing estimates of learning deficits during the pandemic 7 , 8 . In line with the narrative reviews, these two reviews find a substantial reduction in learning progress during the pandemic. However, this finding is based on a relatively small number of studies (18 and 10 studies, respectively). The limited evidence that was available at the time these reviews were conducted also precluded them from meta-analysing variation in the magnitude of learning deficits over time and across subjects, different groups of students or country contexts.

In this Article, we conduct a systematic review and meta-analysis of the evidence on COVID-19 learning deficits 2.5 years into the pandemic. Our primary pre-registered research question was ‘What is the effect of the COVID-19 pandemic on learning progress amongst school-age children?’, and we address this question using evidence from studies examining changes in learning outcomes during the pandemic. Our second pre-registered research aim was ‘To examine whether the effect of the COVID-19 pandemic on learning differs across different social background groups, age groups, boys and girls, learning areas or subjects, national contexts’.

We contribute to the existing research in two ways. First, we describe and appraise the up-to-date body of evidence, including its geographic reach and quality. More specifically, we ask the following questions: (1) what is the state of the evidence, in terms of the available peer-reviewed research and grey literature, on learning progress of school-aged children during the COVID-19 pandemic?, (2) which countries are represented in the available evidence? and (3) what is the quality of the existing evidence?

Our second contribution is to harmonize, synthesize and meta-analyse the existing evidence, with special attention to variation across different subpopulations and country contexts. On the basis of the identified studies, we ask (4) to what extent has the learning progress of school-aged children changed since the onset of the pandemic?, (5) how has the magnitude of the learning deficit (if any) evolved since the beginning of the pandemic?, (6) to what extent has the pandemic reinforced inequalities between children from different socio-economic backgrounds?, (7) are there differences in the magnitude of learning deficits between subject domains (maths and reading) and between age groups (primary and secondary students)? and (8) to what extent does the magnitude of learning deficits vary across national contexts?

Below, we report our answers to each of these questions in turn. The questions correspond to the analysis plan set out in our pre-registered protocol ( https://www.crd.york.ac.uk/prospero/display_record.php?ID=CRD42021249944 ), but we have adjusted the order and wording to aid readability. We had planned to examine gender differences in learning progress during the pandemic, but found there to be insufficient evidence to conduct this subgroup analysis, as the large majority of the identified studies do not provide evidence on learning deficits separately by gender. We also planned to examine how the magnitude of learning deficits differs across groups of students with varying exposures to school closures. This was not possible as the available data on school closures lack sufficient depth with respect to variation of school closures within countries, across grade levels and with respect to different modes of instruction, to meaningfully examine this association.

The state of the evidence

Our systematic review identified 42 studies on learning progress during the COVID-19 pandemic that met our inclusion criteria. To be included in our systematic review and meta-analysis, studies had to use a measure of learning that can be standardized (using Cohen’s d ) and base their estimates on empirical data collected since the onset of the COVID-19 pandemic (rather than making projections based on pre-COVID-19 data). As shown in Fig. 1 , the initial literature search resulted in 5,153 hits after removal of duplicates. All studies were double screened by the first two authors. The formal database search process identified 15 eligible studies. We also hand searched relevant preprint repositories and policy databases. Further, to ensure that our study selection was as up to date as possible, we conducted two full forward and backward citation searches of all included studies on 15 February 2022, and on 8 August 2022. The citation and preprint hand searches allowed us to identify 27 additional eligible studies, resulting in a total of 42 studies. Most of these studies were published after the initial database search, which illustrates that the body of evidence continues to expand. Most studies provide multiple estimates of COVID-19 learning deficits, separately for maths and reading and for different school grades. The number of estimates ( n  = 291) is therefore larger than the number of included studies ( n  = 42).

Flow diagram of the study identification and selection process, following Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines.

The geographic reach of evidence is limited

Table 1 presents all included studies and estimates of COVID-19 learning deficits (in brackets), grouped by the 15 countries represented: Australia, Belgium, Brazil, Colombia, Denmark, Germany, Italy, Mexico, the Netherlands, South Africa, Spain, Sweden, Switzerland, the UK and the United States. About half of the estimates ( n  = 149) are from the United States, 58 are from the UK, a further 70 are from other European countries and the remaining 14 estimates are from Australia, Brazil, Colombia, Mexico and South Africa. As this list shows, there is a strong over-representation of studies from high-income countries, a dearth of studies from middle-income countries and no studies from low-income countries. This skewed representation should be kept in mind when interpreting our synthesis of the existing evidence on COVID-19 learning deficits.

The quality of evidence is mixed

We assessed the quality of the evidence using an adapted version of the Risk Of Bias In Non-randomized Studies of Interventions (ROBINS-I) tool 9 . More specifically, we analysed the risk of bias of each estimate from confounding, sample selection, classification of treatments, missing data, the measurement of outcomes and the selection of reported results. A.M.B.-M. and B.A.B. performed the risk-of-bias assessments, which were independently checked by the respective other author. We then assigned each study an overall risk-of-bias rating (low, moderate, serious or critical) based on the estimate and domain with the highest risk of bias.

Figure 2a shows the distribution of all studies of COVID-19 learning deficits according to their risk-of-bias rating separately for each domain (top six rows), as well as the distribution of studies according to their overall risk of bias rating (bottom row). The overall risk of bias was considered ‘low’ for 15% of studies, ‘moderate’ for 30% of studies, ‘serious’ for 25% of studies and ‘critical’ for 30% of studies.

a , Domain-specific and overall distribution of studies of COVID-19 learning deficits by risk of bias rating using ROBINS-I, including studies rated to be at critical risk of bias ( n  = 19 out of a total of n  = 61 studies shown in this figure). In line with ROBINS-I guidance, studies rated to be at critical risk of bias were excluded from all analyses and other figures in this article and in the Supplementary Information (including b ). b , z curve: distribution of the z scores of all estimates included in the meta-analysis ( n  = 291) to test for publication bias. The dotted line indicates z  = 1.96 ( P  = 0.050), the conventional threshold for statistical significance. The overlaid curve shows a normal distribution. The absence of a spike in the distribution of the z scores just above the threshold for statistical significance and the absence of a slump just below it indicate the absence of evidence for publication bias.

In line with ROBINS-I guidance, we excluded studies rated to be at critical risk of bias ( n  = 19) from all of our analyses and figures, except for Fig. 2a , which visualizes the distribution of studies according to their risk of bias 9 . These are thus not part of the 42 studies included in our meta-analysis. Supplementary Table 2 provides an overview of these studies as well as the main potential sources of risk of bias. Moreover, in Supplementary Figs. 3 – 6 , we replicate all our results excluding studies deemed to be at serious risk of bias.

As shown in Fig. 2a , common sources of potential bias were confounding, sample selection and missing data. Studies rated at risk of confounding typically compared only two timepoints, without accounting for longer time trends in learning progress. The main causes of selection bias were the use of convenience samples and insufficient consideration of self-selection by schools or students. Several studies found evidence of selection bias, often with students from a low socio-economic background or schools in deprived areas being under-represented after (as compared with before) the pandemic, but this was not always adjusted for. Some studies also reported a higher amount of missing data post-pandemic, again generally without adjustment, and several studies did not report any information on missing data. For an overview of the risk-of-bias ratings for each domain of each study, see Supplementary Fig. 1 and Supplementary Tables 1 and 2 .

No evidence of publication bias

Publication bias can occur if authors self-censor to conform to theoretical expectations, or if journals favour statistically significant results. To mitigate this concern, we include not only published papers, but also preprints, working papers and policy reports.

Moreover, Fig. 2b tests for publication bias by showing the distribution of z -statistics for the effect size estimates of all identified studies. The dotted line indicates z  = 1.96 ( P  = 0.050), the conventional threshold for statistical significance. The overlaid curve shows a normal distribution. If there was publication bias, we would expect a spike just above the threshold, and a slump just below it. There is no indication of this. Moreover, we do not find a left-skewed distribution of P values (see P curve in Supplementary Fig. 2a ), or an association between estimates of learning deficits and their standard errors (see funnel plot in Supplementary Fig. 2b ) that would suggest publication bias. Publication bias thus does not appear to be a major concern.

Having assessed the quality of the existing evidence, we now present the substantive results of our meta-analysis, focusing on the magnitude of COVID-19 learning deficits and on the variation in learning deficits over time, across different groups of students, and across country contexts.

Learning progress slowed substantially during the pandemic

Figure 3 shows the effect sizes that we extracted from each study (averaged across grades and learning subject) as well as the pooled effect size (red diamond). Effects are expressed in standard deviations, using Cohen’s d . Estimates are pooled using inverse variance weights. The pooled effect size across all studies is d  = −0.14, t (41) = −7.30, two-tailed P  = 0.000, 95% confidence interval (CI) −0.17 to −0.10. Under normal circumstances, students generally improve their performance by around 0.4 standard deviations per school year 10 , 11 , 12 . Thus, the overall effect of d  = −0.14 suggests that students lost out on 0.14/0.4, or about 35%, of a school year’s worth of learning. On average, the learning progress of school-aged children has slowed substantially during the pandemic.

Effect sizes are expressed in standard deviations, using Cohen’s d , with 95% CI, and are sorted by magnitude.

Learning deficits arose early in the pandemic and persist

One may expect that children were able to recover learning that was lost early in the pandemic, after teachers and families had time to adjust to the new learning conditions and after structures for online learning and for recovering early learning deficits were set up. However, existing research on teacher strikes in Belgium 13 and Argentina 14 , shortened school years in Germany 15 and disruptions to education during World War II 16 suggests that learning deficits are difficult to compensate and tend to persist in the long run.

Figure 4 plots the magnitude of estimated learning deficits (on the vertical axis) by the date of measurement (on the horizontal axis). The colour of the circles reflects the relevant country, the size of the circles indicates the sample size for a given estimate and the line displays a linear trend. The figure suggests that learning deficits opened up early in the pandemic and have neither closed nor substantially widened since then. We find no evidence that the slope coefficient is different from zero ( β months  = −0.00, t (41) = −7.30, two-tailed P  = 0.097, 95% CI −0.01 to 0.00). This implies that efforts by children, parents, teachers and policy-makers to adjust to the changed circumstance have been successful in preventing further learning deficits but so far have been unable to reverse them. As shown in Supplementary Fig. 8 , the pattern of persistent learning deficits also emerges within each of the three countries for which we have a relatively large number of estimates at different timepoints: the United States, the UK and the Netherlands. However, it is important to note that estimates of learning deficits are based on distinct samples of students. Future research should continue to follow the learning progress of cohorts of students in different countries to reveal how learning deficits of these cohorts have developed and continue to develop since the onset of the pandemic.

The horizontal axis displays the date on which learning progress was measured. The vertical axis displays estimated learning deficits, expressed in standard deviation (s.d.) using Cohen’s d . The colour of the circles reflects the respective country, the size of the circles indicates the sample size for a given estimate and the line displays a linear trend with a 95% CI. The trend line is estimated as a linear regression using ordinary least squares, with standard errors clustered at the study level ( n  = 42 clusters). β months  = −0.00, t (41) = −7.30, two-tailed P  = 0.097, 95% CI −0.01 to 0.00.

Socio-economic inequality in education increased

Existing research on the development of learning gaps during summer vacations 17 , 18 , disruptions to schooling during the Ebola outbreak in Sierra Leone and Guinea 19 , and the 2005 earthquake in Pakistan 20 shows that the suspension of face-to-face teaching can increase educational inequality between children from different socio-economic backgrounds. Learning deficits during the COVID-19 pandemic are likely to have been particularly pronounced for children from low socio-economic backgrounds. These children have been more affected by school closures than children from more advantaged backgrounds 21 . Moreover, they are likely to be disadvantaged with respect to their access and ability to use digital learning technology, the quality of their home learning environment, the learning support they receive from teachers and parents, and their ability to study autonomously 22 , 23 , 24 .

Most studies we identify examine changes in socio-economic inequality during the pandemic, attesting to the importance of the issue. As studies use different measures of socio-economic background (for example, parental income, parental education, free school meal eligibility or neighbourhood disadvantage), pooling the estimates is not possible. Instead, we code all estimates according to whether they indicate a reduction, no change or an increase in learning inequality during the pandemic. Figure 5 displays this information. Estimates that indicate an increase in inequality are shown on the right, those that indicate a decrease on the left and those that suggest no change in the middle. Squares represent estimates of changes in inequality during the pandemic in reading performance, and circles represent estimates of changes in inequality in maths performance. The shading represents when in the pandemic educational inequality was measured, differentiating between the first, second and third year of the pandemic. Estimates are also arranged horizontally by grade level. A large majority of estimates indicate an increase in educational inequality between children from different socio-economic backgrounds. This holds for both maths and reading, across primary and secondary education, at each stage of the pandemic, and independently of how socio-economic background is measured.

Each circle/square refers to one estimate of over-time change in inequality in maths/reading performance ( n  = 211). Estimates that find a decrease/no change/increase in inequality are grouped on the left/middle/right. Within these categories, estimates are ordered horizontally by school grade. The shading indicates when in the pandemic a given measure was taken.

Learning deficits are larger in maths than in reading

Available research on summer learning deficits 17 , 25 , student absenteeism 26 , 27 and extreme weather events 28 suggests that learning progress in mathematics is more dependent on formal instruction than in reading. This might be due to parents being better equipped to help their children with reading, and children advancing their reading skills (but not their maths skills) when reading for enjoyment outside of school. Figure 6a shows that, similarly to earlier disruptions to learning, the estimated learning deficits during the COVID-19 pandemic are larger for maths than for reading (mean difference δ  = −0.07, t (41) = −4.02, two-tailed P  = 0.000, 95% CI −0.11 to −0.04). This difference is statistically significant and robust to dropping estimates from individual countries (Supplementary Fig. 9 ).

Each plot shows the distribution of COVID-19 learning deficit estimates for the respective subgroup, with the box marking the interquartile range and the white circle denoting the median. Whiskers mark upper and lower adjacent values: the furthest observation within 1.5 interquartile range of either side of the box. a , Learning subject (reading versus maths). Median: reading −0.09, maths −0.18. Interquartile range: reading −0.15 to −0.02, maths −0.23 to −0.09. b , Level of education (primary versus secondary). Median: primary −0.12, secondary −0.12. Interquartile range: primary −0.19 to −0.05, secondary −0.21 to −0.06. c , Country income level (high versus middle). Median: high −0.12, middle −0.37. Interquartile range: high −0.20 to −0.05, middle −0.65 to −0.30.

No evidence of variation across grade levels

One may expect learning deficits to be smaller for older than for younger children, as older children may be more autonomous in their learning and better able to cope with a sudden change in their learning environment. However, older students were subject to longer school closures in some countries, such as Denmark 29 , based partly on the assumption that they would be better able to learn from home. This may have offset any advantage that older children would otherwise have had in learning remotely.

Figure 6b shows the distribution of estimates of learning deficits for students at the primary and secondary level, respectively. Our analysis yields no evidence of variation in learning deficits across grade levels (mean difference δ  = −0.01, t (41) = −0.59, two-tailed P  = 0.556, 95% CI −0.06 to 0.03). Due to the limited number of available estimates of learning deficits, we cannot be certain about whether learning deficits differ between primary and secondary students or not.

Learning deficits are larger in poorer countries

Low- and middle-income countries were already struggling with a learning crisis before the pandemic. Despite large expansions of the proportion of children in school, children in low- and middle-income countries still perform poorly by international standards, and inequality in learning remains high 30 , 31 , 32 . The pandemic is likely to deepen this learning crisis and to undo past progress. Schools in low- and middle-income countries have not only been closed for longer, but have also had fewer resources to facilitate remote learning 33 , 34 . Moreover, the economic resources, availability of digital learning equipment and ability of children, parents, teachers and governments to support learning from home are likely to be lower in low- and middle-income countries 35 .

As discussed above, most evidence on COVID-19 learning deficits comes from high-income countries. We found no studies on low-income countries that met our inclusion criteria, and evidence from middle-income countries is limited to Brazil, Colombia, Mexico and South Africa. Figure 6c groups the estimates of COVID-19 learning deficits in these four middle-income countries together (on the right) and compares them with estimates from high-income countries (on the left). The learning deficit is appreciably larger in middle-income countries than in high-income countries (mean difference δ  = −0.29, t (41) = −2.78, two-tailed P  = 0.008, 95% CI −0.50 to −0.08). In fact, the three largest estimates of learning deficits in our sample are from middle-income countries (Fig. 3 ) 36 , 37 , 38 .

Two years since the COVID-19 pandemic, there is a growing number of studies examining the learning progress of school-aged children during the pandemic. This paper first systematically reviews the existing literature on learning progress of school-aged children during the pandemic and appraises its geographic reach and quality. Second, it harmonizes, synthesizes and meta-analyses the existing evidence to examine the extent to which learning progress has changed since the onset of the pandemic, and how it varies across different groups of students and across country contexts.

Our meta-analysis suggests that learning progress has slowed substantially during the COVID-19 pandemic. The pooled effect size of d  = −0.14, implies that students lost out on about 35% of a normal school year’s worth of learning. This confirms initial concerns that substantial learning deficits would arise during the pandemic 10 , 39 , 40 . But our results also suggest that fears of an accumulation of learning deficits as the pandemic continues have not materialized 41 , 42 . On average, learning deficits emerged early in the pandemic and have neither closed nor widened substantially. Future research should continue to follow the learning progress of cohorts of students in different countries to reveal how learning deficits of these cohorts have developed and continue to develop since the onset of the pandemic.

Most studies that we identify find that learning deficits have been largest for children from disadvantaged socio-economic backgrounds. This holds across different timepoints during the pandemic, countries, grade levels and learning subjects, and independently of how socio-economic background is measured. It suggests that the pandemic has exacerbated educational inequalities between children from different socio-economic backgrounds, which were already large before the pandemic 43 , 44 . Policy initiatives to compensate learning deficits need to prioritize support for children from low socio-economic backgrounds in order to allow them to recover the learning they lost during the pandemic.

There is a need for future research to assess how the COVID-19 pandemic has affected gender inequality in education. So far, there is very little evidence on this issue. The large majority of the studies that we identify do not examine learning deficits separately by gender.

Comparing estimates of learning deficits across subjects, we find that learning deficits tend to be larger in maths than in reading. As noted above, this may be due to the fact that parents and children have been in a better position to compensate school-based learning in reading by reading at home. Accordingly, there are grounds for policy initiatives to prioritize the compensation of learning deficits in maths and other science subjects.

A limitation of this study and the existing body of evidence on learning progress during the COVID-19 pandemic is that the existing studies primarily focus on high-income countries, while there is a dearth of evidence from low- and middle-income countries. This is particularly concerning because the small number of existing studies from middle-income countries suggest that learning deficits have been particularly severe in these countries. Learning deficits are likely to be even larger in low-income countries, considering that these countries already faced a learning crisis before the pandemic, generally implemented longer school closures, and were under-resourced and ill-equipped to facilitate remote learning 32 , 33 , 34 , 35 , 45 . It is critical that this evidence gap on low- and middle-income countries is addressed swiftly, and that the infrastructure to collect and share data on educational performance in middle- and low-income countries is strengthened. Collecting and making available these data is a key prerequisite for fully understanding how learning progress and related outcomes have changed since the onset of the pandemic 46 .

A further limitation is that about half of the studies that we identify are rated as having a serious or critical risk of bias. We seek to limit the risk of bias in our results by excluding all studies rated to be at critical risk of bias from all of our analyses. Moreover, in Supplementary Figs. 3 – 6 , we show that our results are robust to further excluding studies deemed to be at serious risk of bias. Future studies should minimize risk of bias in estimating learning deficits by employing research designs that appropriately account for common sources of bias. These include a lack of accounting for secular time trends, non-representative samples and imbalances between treatment and comparison groups.

The persistence of learning deficits two and a half years into the pandemic highlights the need for well-designed, well-resourced and decisive policy initiatives to recover learning deficits. Policy-makers, schools and families will need to identify and realize opportunities to complement and expand on regular school-based learning. Experimental evidence from low- and middle-income countries suggests that even relatively low-tech and low-cost learning interventions can have substantial, positive effects on students’ learning progress in the context of remote learning. For example, sending SMS messages with numeracy problems accompanied by short phone calls was found to lead to substantial learning gains in numeracy in Botswana 47 . Sending motivational text messages successfully limited learning losses in maths and Portuguese in Brazil 48 .

More evidence is needed to assess the effectiveness of other interventions for limiting or recovering learning deficits. Potential avenues include the use of the often extensive summer holidays to offer summer schools and learning camps, extending school days and school weeks, and organizing and scaling up tutoring programmes. Further potential lies in developing, advertising and providing access to learning apps, online learning platforms or educational TV programmes that are free at the point of use. Many countries have already begun investing substantial resources to capitalize on some of these opportunities. If these interventions prove effective, and if the momentum of existing policy efforts is maintained and expanded, the disruptions to learning during the pandemic may be a window of opportunity to improve the education afforded to children.

Eligibility criteria

We consider all types of primary research, including peer-reviewed publications, preprints, working papers and reports, for inclusion. To be eligible for inclusion, studies have to measure learning progress using test scores that can be standardized across studies using Cohen’s d . Moreover, studies have to be in English, Danish, Dutch, French, German, Norwegian, Spanish or Swedish.

Search strategy and study identification

We identified relevant studies using the following steps. First, we developed a Boolean search string defining the population (school-aged children), exposure (the COVID-19 pandemic) and outcomes of interest (learning progress). The full search string can be found in Section 1.1 of Supplementary Information . Second, we used this string to search the following academic databases: Coronavirus Research Database, the Education Resources Information Centre, International Bibliography of the Social Sciences, Politics Collection (PAIS index, policy file index, political science database and worldwide political science abstracts), Social Science Database, Sociology Collection (applied social science index and abstracts, sociological abstracts and sociology database), Cumulative Index to Nursing and Allied Health Literature, and Web of Science. Second, we hand-searched multiple preprint and working paper repositories (Social Science Research Network, Munich Personal RePEc Archive, IZA, National Bureau of Economic Research, OSF Preprints, PsyArXiv, SocArXiv and EdArXiv) and relevant policy websites, including the websites of the Organization for Economic Co-operation and Development, the United Nations, the World Bank and the Education Endowment Foundation. Third, we periodically posted our protocol via Twitter in order to crowdsource additional relevant studies not identified through the search. All titles and abstracts identified in our search were double-screened using the Rayyan online application 49 . Our initial search was conducted on 27 April 2021, and we conducted two forward and backward citation searches of all eligible studies identified in the above steps, on 14 February 2022, and on 8 August 2022, to ensure that our analysis includes recent relevant research.

Data extraction

From the studies that meet our inclusion criteria we extracted all estimates of learning deficits during the pandemic, separately for maths and reading and for different school grades. We also extracted the corresponding sample size, standard error, date(s) of measurement, author name(s) and country. Last, we recorded whether studies differentiate between children’s socio-economic background, which measure is used to this end and whether studies find an increase, decrease or no change in learning inequality. We contacted study authors if any of the above information was missing in the study. Data extraction was performed by B.A.B. and validated independently by A.M.B.-M., with discrepancies resolved through discussion and by conferring with P.E.

Measurement and standardizationr

We standardize all estimates of learning deficits during the pandemic using Cohen’s d , which expresses effect sizes in terms of standard deviations. Cohen’s d is calculated as the difference in the mean learning gain in a given subject (maths or reading) over two comparable periods before and after the onset of the pandemic, divided by the pooled standard deviation of learning progress in this subject:

Effect sizes expressed as β coefficients are converted to Cohen’s d :

We use a binary indicator for whether the study outcome is maths or reading. One study does not differentiate the outcome but includes a composite of maths and reading scores 50 .

Level of education

We distinguish between primary and secondary education. We first consulted the original studies for this information. Where this was not stated in a given study, students’ age was used in conjunction with information about education systems from external sources to determine the level of education 51 .

Country income level

We follow the World Bank’s classification of countries into four income groups: low, lower-middle, upper-middle and high income. Four countries in our sample are in the upper-middle-income group: Brazil, Colombia, Mexico and South Africa. All other countries are in the high-income group.

Data synthesis

We synthesize our data using three synthesis techniques. First, we generate a forest plot, based on all available estimates of learning progress during the pandemic. We pool estimates using a random-effects restricted maximum likelihood model and inverse variance weights to calculate an overall effect size (Fig. 3 ) 52 . Second, we code all estimates of changes in educational inequality between children from different socio-economic backgrounds during the pandemic, according to whether they indicate an increase, a decrease or no change in educational inequality. We visualize the resulting distribution using a harvest plot (Fig. 5 ) 53 . Third, given that the limited amount of available evidence precludes multivariate or causal analyses, we examine the bivariate association between COVID-19 learning deficits and the months in which learning was measured using a scatter plot (Fig. 4 ), and the bivariate association between COVID-19 learning deficits and subject, grade level and countries’ income level, using a series of violin plots (Fig. 6 ). The reported estimates, CIs and statistical significance tests of these bivariate associations are based on common-effects models with standard errors clustered by study, and two-sided tests. With respect to statistical tests reported, the data distribution was assumed to be normal, but this was not formally tested. The distribution of estimates of learning deficits is shown separately for the different moderator categories in Fig. 6 .

Pre-registration

We prospectively registered a protocol of our systematic review and meta-analysis in the International Prospective Register of Systematic Reviews (CRD42021249944) on 19 April 2021 ( https://www.crd.york.ac.uk/prospero/display_record.php?ID=CRD42021249944 ).

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

The data used in the analyses for this manuscript were compiled by the authors based on the studies identified in the systematic review. The data are available on the Open Science Framework repository ( https://doi.org/10.17605/osf.io/u8gaz ). For our systematic review, we searched the following databases: Coronavirus Research Database ( https://proquest.libguides.com/covid19 ), Education Resources Information Centre database ( https://eric.ed.gov ), International Bibliography of the Social Sciences ( https://about.proquest.com/en/products-services/ibss-set-c/ ), Politics Collection ( https://about.proquest.com/en/products-services/ProQuest-Politics-Collection/ ), Social Science Database ( https://about.proquest.com/en/products-services/pq_social_science/ ), Sociology Collection ( https://about.proquest.com/en/products-services/ProQuest-Sociology-Collection/ ), Cumulative Index to Nursing and Allied Health Literature ( https://www.ebsco.com/products/research-databases/cinahl-database ) and Web of Science ( https://clarivate.com/webofsciencegroup/solutions/web-of-science/ ). We also searched the following preprint and working paper repositories: Social Science Research Network ( https://papers.ssrn.com/sol3/DisplayJournalBrowse.cfm ), Munich Personal RePEc Archive ( https://mpra.ub.uni-muenchen.de ), IZA ( https://www.iza.org/content/publications ), National Bureau of Economic Research ( https://www.nber.org/papers?page=1&perPage=50&sortBy=public_date ), OSF Preprints ( https://osf.io/preprints/ ), PsyArXiv ( https://psyarxiv.com ), SocArXiv ( https://osf.io/preprints/socarxiv ) and EdArXiv ( https://edarxiv.org ).

Code availability

All code needed to replicate our findings is available on the Open Science Framework repository ( https://doi.org/10.17605/osf.io/u8gaz ).

The Impact of COVID-19 on Children. UN Policy Briefs (United Nations, 2020).

Donnelly, R. & Patrinos, H. A. Learning loss during Covid-19: An early systematic review. Prospects (Paris) 51 , 601–609 (2022).

Hammerstein, S., König, C., Dreisörner, T. & Frey, A. Effects of COVID-19-related school closures on student achievement: a systematic review. Front. Psychol. https://doi.org/10.3389/fpsyg.2021.746289 (2021).

Panagouli, E. et al. School performance among children and adolescents during COVID-19 pandemic: a systematic review. Children 8 , 1134 (2021).

Article   PubMed   PubMed Central   Google Scholar  

Patrinos, H. A., Vegas, E. & Carter-Rau, R. An Analysis of COVID-19 Student Learning Loss (World Bank, 2022).

Zierer, K. Effects of pandemic-related school closures on pupils’ performance and learning in selected countries: a rapid review. Educ. Sci. 11 , 252 (2021).

Article   Google Scholar  

König, C. & Frey, A. The impact of COVID-19-related school closures on student achievement: a meta-analysis. Educ. Meas. Issues Pract. 41 , 16–22 (2022).

Storey, N. & Zhang, Q. A meta-analysis of COVID learning loss. Preprint at EdArXiv (2021).

Sterne, J. A. et al. ROBINS-I: a tool for assessing risk of bias in non-randomised studies of interventions. BMJ https://doi.org/10.1136/bmj.i4919 (2016).

Azevedo, J. P., Hasan, A., Goldemberg, D., Iqbal, S. A. & Geven, K. Simulating the Potential Impacts of COVID-19 School Closures on Schooling and Learning Outcomes: A Set of Global Estimates (World Bank, 2020).

Bloom, H. S., Hill, C. J., Black, A. R. & Lipsey, M. W. Performance trajectories and performance gaps as achievement effect-size benchmarks for educational interventions. J. Res. Educ. Effectiveness 1 , 289–328 (2008).

Hill, C. J., Bloom, H. S., Black, A. R. & Lipsey, M. W. Empirical benchmarks for interpreting effect sizes in research. Child Dev. Perspect. 2 , 172–177 (2008).

Belot, M. & Webbink, D. Do teacher strikes harm educational attainment of students? Labour 24 , 391–406 (2010).

Jaume, D. & Willén, A. The long-run effects of teacher strikes: evidence from Argentina. J. Labor Econ. 37 , 1097–1139 (2019).

Cygan-Rehm, K. Are there no wage returns to compulsory schooling in Germany? A reassessment. J. Appl. Econ. 37 , 218–223 (2022).

Ichino, A. & Winter-Ebmer, R. The long-run educational cost of World War II. J. Labor Econ. 22 , 57–87 (2004).

Cooper, H., Nye, B., Charlton, K., Lindsay, J. & Greathouse, S. The effects of summer vacation on achievement test scores: a narrative and meta-analytic review. Rev. Educ. Res. 66 , 227–268 (1996).

Allington, R. L. et al. Addressing summer reading setback among economically disadvantaged elementary students. Read. Psychol. 31 , 411–427 (2010).

Smith, W. C. Consequences of school closure on access to education: lessons from the 2013–2016 Ebola pandemic. Int. Rev. Educ. 67 , 53–78 (2021).

Andrabi, T., Daniels, B. & Das, J. Human capital accumulation and disasters: evidence from the Pakistan earthquake of 2005. J. Hum. Resour . https://doi.org/10.35489/BSG-RISE-WP_2020/039 (2021).

Parolin, Z. & Lee, E. K. Large socio-economic, geographic and demographic disparities exist in exposure to school closures. Nat. Hum. Behav. 5 , 522–528 (2021).

Goudeau, S., Sanrey, C., Stanczak, A., Manstead, A. & Darnon, C. Why lockdown and distance learning during the COVID-19 pandemic are likely to increase the social class achievement gap. Nat. Hum. Behav. 5 , 1273–1281 (2021).

Article   PubMed   Google Scholar  

Bailey, D. H., Duncan, G. J., Murnane, R. J. & Au Yeung, N. Achievement gaps in the wake of COVID-19. Educ. Researcher 50 , 266–275 (2021).

van de Werfhorst, H. G. Inequality in learning is a major concern after school closures. Proc. Natl Acad. Sci. USA https://doi.org/10.1073/pnas.2105243118 (2021).

Alexander, K. L., Entwisle, D. R. & Olson, L. S. Schools, achievement, and inequality: a seasonal perspective. Educ. Eval. Policy Anal. 23 , 171–191 (2001).

Aucejo, E. M. & Romano, T. F. Assessing the effect of school days and absences on test score performance. Econ. Educ. Rev. 55 , 70–87 (2016).

Gottfried, M. A. The detrimental effects of missing school: evidence from urban siblings. Am. J. Educ. 117 , 147–182 (2011).

Goodman, J. Flaking Out: Student Absences and Snow Days as Disruptions of Instructional Time (National Bureau of Economic Research, 2014).

Birkelund, J. F. & Karlson, K. B. No evidence of a major learning slide 14 months into the COVID-19 pandemic in Denmark. European Societies https://doi.org/10.1080/14616696.2022.2129085 (2022).

Angrist, N., Djankov, S., Goldberg, P. K. & Patrinos, H. A. Measuring human capital using global learning data. Nature 592 , 403–408 (2021).

Article   CAS   PubMed   PubMed Central   Google Scholar  

Torche, F. in Social Mobility in Developing Countries: Concepts, Methods, and Determinants (eds Iversen, V., Krishna, A. & Sen, K.) 139–171 (Oxford Univ. Press, 2021).

World Development Report 2018: Learning to Realize Education’s Promise (World Bank, 2018).

Policy Brief: Education during COVID-19 and Beyond (United Nations, 2020).

One Year into COVID-19 Education Disruption: Where Do We Stand? (UNESCO, 2021).

Azevedo, J. P., Hasan, A., Goldemberg, D., Geven, K. & Iqbal, S. A. Simulating the potential impacts of COVID-19 school closures on schooling and learning outcomes: a set of global estimates. World Bank Res. Observer 36 , 1–40 (2021).

Google Scholar  

Ardington, C., Wills, G. & Kotze, J. COVID-19 learning losses: early grade reading in South Africa. Int. J. Educ. Dev. 86 , 102480 (2021).

Hevia, F. J., Vergara-Lope, S., Velásquez-Durán, A. & Calderón, D. Estimation of the fundamental learning loss and learning poverty related to COVID-19 pandemic in Mexico. Int. J. Educ. Dev. 88 , 102515 (2022).

Lichand, G., Doria, C. A., Leal-Neto, O. & Fernandes, J. P. C. The impacts of remote learning in secondary education during the pandemic in Brazil. Nat. Hum. Behav. 6 , 1079–1086 (2022).

Major, L. E., Eyles, A., Machin, S. et al. Learning Loss since Lockdown: Variation across the Home Nations (Centre for Economic Performance, London School of Economics and Political Science, 2021).

Di Pietro, G., Biagi, F., Costa, P., Karpinski, Z. & Mazza, J. The Likely Impact of COVID-19 on Education: Reflections Based on the Existing Literature and Recent International Datasets (Publications Office of the European Union, 2020).

Fuchs-Schündeln, N., Krueger, D., Ludwig, A. & Popova, I. The Long-Term Distributional and Welfare Effects of COVID-19 School Closures (National Bureau of Economic Research, 2020).

Kaffenberger, M. Modelling the long-run learning impact of the COVID-19 learning shock: actions to (more than) mitigate loss. Int. J. Educ. Dev. 81 , 102326 (2021).

Attewell, P. & Newman, K. S. Growing Gaps: Educational Inequality around the World (Oxford Univ. Press, 2010).

Betthäuser, B. A., Kaiser, C. & Trinh, N. A. Regional variation in inequality of educational opportunity across europe. Socius https://doi.org/10.1177/23780231211019890 (2021).

Angrist, N. et al. Building back better to avert a learning catastrophe: estimating learning loss from covid-19 school shutdowns in africa and facilitating short-term and long-term learning recovery. Int. J. Educ. Dev. 84 , 102397 (2021).

Conley, D. & Johnson, T. Opinion: Past is future for the era of COVID-19 research in the social sciences. Proc. Natl Acad. Sci. USA https://doi.org/10.1073/pnas.2104155118 (2021).

Angrist, N., Bergman, P. & Matsheng, M. Experimental evidence on learning using low-tech when school is out. Nat. Hum. Behav. 6 , 941–950 (2022).

Lichand, G., Christen, J. & van Egeraat, E. Do Behavioral Nudges Work under Remote Learning? Evidence from Brazil during the Pandemic (Univ. Zurich, 2022).

Ouzzani, M., Hammady, H., Fedorowicz, Z. & Elmagarmid, A. Rayyan—a web and mobile app for systematic reviews. Syst. Rev. 5 , 1–10 (2016).

Tomasik, M. J., Helbling, L. A. & Moser, U. Educational gains of in-person vs. distance learning in primary and secondary schools: a natural experiment during the COVID-19 pandemic school closures in Switzerland. Int. J. Psychol. 56 , 566–576 (2021).

Eurybase: The Information Database on Education Systems in Europe (Eurydice, 2021).

Borenstein, M., Hedges, L. V., Higgins, J. P. & Rothstein, H. R. A basic introduction to fixed-effect and random-effects models for meta-analysis. Res. Synth. Methods 1 , 97–111 (2010).

Ogilvie, D. et al. The harvest plot: a method for synthesising evidence about the differential effects of interventions. BMC Med. Res. Methodol. 8 , 1–7 (2008).

Gore, J., Fray, L., Miller, A., Harris, J. & Taggart, W. The impact of COVID-19 on student learning in New South Wales primary schools: an empirical study. Aust. Educ. Res. 48 , 605–637 (2021).

Gambi, L. & De Witte, K. The Resiliency of School Outcomes after the COVID-19 Pandemic: Standardised Test Scores and Inequality One Year after Long Term School Closures (FEB Research Report Department of Economics, 2021).

Maldonado, J. E. & De Witte, K. The effect of school closures on standardised student test outcomes. Br. Educ. Res. J. 48 , 49–94 (2021).

Vegas, E. COVID-19’s Impact on Learning Losses and Learning Inequality in Colombia (Center for Universal Education at Brookings, 2022).

Depping, D., Lücken, M., Musekamp, F. & Thonke, F. in Schule während der Corona-Pandemie. Neue Ergebnisse und Überblick über ein dynamisches Forschungsfeld (eds Fickermann, D. & Edelstein, B.) 51–79 (Münster & New York: Waxmann, 2021).

Ludewig, U. et al. Die COVID-19 Pandemie und Lesekompetenz von Viertklässler*innen: Ergebnisse der IFS-Schulpanelstudie 2016–2021 (Institut für Schulentwicklungsforschung, Univ. Dortmund, 2022).

Schult, J., Mahler, N., Fauth, B. & Lindner, M. A. Did students learn less during the COVID-19 pandemic? Reading and mathematics competencies before and after the first pandemic wave. Sch. Eff. Sch. Improv. https://doi.org/10.1080/09243453.2022.2061014 (2022).

Schult, J., Mahler, N., Fauth, B. & Lindner, M. A. Long-term consequences of repeated school closures during the COVID-19 pandemic for reading and mathematics competencies. Front. Educ. https://doi.org/10.3389/feduc.2022.867316 (2022).

Bazoli, N., Marzadro, S., Schizzerotto, A. & Vergolini, L. Learning Loss and Students’ Social Origins during the COVID-19 Pandemic in Italy (FBK-IRVAPP Working Papers 3, 2022).

Borgonovi, F. & Ferrara, A. The effects of COVID-19 on inequalities in educational achievement in Italy. Preprint at SSRN https://doi.org/10.2139/ssrn.4171968 (2022).

Contini, D., Di Tommaso, M. L., Muratori, C., Piazzalunga, D. & Schiavon, L. Who lost the most? Mathematics achievement during the COVID-19 pandemic. BE J. Econ. Anal. Policy 22 , 399–408 (2022).

Engzell, P., Frey, A. & Verhagen, M. D. Learning loss due to school closures during the COVID-19 pandemic. Proc. Natl Acad. Sci. USA https://doi.org/10.1073/pnas.2022376118 (2021).

Haelermans, C. Learning Growth and Inequality in Primary Education: Policy Lessons from the COVID-19 Crisis (The European Liberal Forum (ELF)-FORES, 2021).

Haelermans, C. et al. A Full Year COVID-19 Crisis with Interrupted Learning and Two School Closures: The Effects on Learning Growth and Inequality in Primary Education (Maastricht Univ., Research Centre for Education and the Labour Market (ROA), 2021).

Haelermans, C. et al. Sharp increase in inequality in education in times of the COVID-19-pandemic. PLoS ONE 17 , e0261114 (2022).

Schuurman, T. M., Henrichs, L. F., Schuurman, N. K., Polderdijk, S. & Hornstra, L. Learning loss in vulnerable student populations after the first COVID-19 school closure in the Netherlands. Scand. J. Educ. Res. https://doi.org/10.1080/00313831.2021.2006307 (2021).

Arenas, A. & Gortazar, L. Learning Loss One Year after School Closures (Esade Working Paper, 2022).

Hallin, A. E., Danielsson, H., Nordström, T. & Fälth, L. No learning loss in Sweden during the pandemic evidence from primary school reading assessments. Int. J. Educ. Res. 114 , 102011 (2022).

Blainey, K. & Hannay, T. The Impact of School Closures on Autumn 2020 Attainment (RS Assessment from Hodder Education and SchoolDash, 2021).

Blainey, K. & Hannay, T. The Impact of School Closures on Spring 2021 Attainment (RS Assessment from Hodder Education and SchoolDash, 2021).

Blainey, K. & Hannay, T. The Effects of Educational Disruption on Primary School Attainment in Summer 2021 (RS Assessment from Hodder Education and SchoolDash, 2021).

Understanding Progress in the 2020/21 Academic Year: Complete Findings from the Autumn Term (London: Department for Education, 2021).

Understanding Progress in the 2020/21 Academic Year: Initial Findings from the Spring Term (London: Department for Education, 2021).

Impact of COVID-19 on Attainment: Initial Analysis (Brentford: GL Assessment, 2021).

Rose, S. et al. Impact of School Closures and Subsequent Support Strategies on Attainment and Socio-emotional Wellbeing in Key Stage 1: Interim Paper 1 (National Foundation for Educational Research (NFER) and Education Endowment Foundation (EEF) , 2021).

Rose, S. et al. Impact of School Closures and Subsequent Support Strategies on Attainment and Socio-emotional Wellbeing in Key Stage 1: Interim Paper 2 (National Foundation for Educational Research (NFER) and Education Endowment Foundation (EEF), 2021).

Weidmann, B. et al. COVID-19 Disruptions: Attainment Gaps and Primary School Responses (Education Endowment Foundation, 2021).

Bielinski, J., Brown, R. & Wagner, K. No Longer a Prediction: What New Data Tell Us About the Effects of 2020 Learning Disruptions (Illuminate Education, 2021).

Domingue, B. W., Hough, H. J., Lang, D. & Yeatman, J. Changing Patterns of Growth in Oral Reading Fluency During the COVID-19 Pandemic. PACE Working Paper (Policy Analysis for California Education, 2021).

Domingue, B. et al. The effect of COVID on oral reading fluency during the 2020–2021 academic year. AERA Open https://doi.org/10.1177/23328584221120254 (2022).

Kogan, V. & Lavertu, S. The COVID-19 Pandemic and Student Achievement on Ohio’s Third-Grade English Language Arts Assessment (Ohio State Univ., 2021).

Kogan, V. & Lavertu, S. How the COVID-19 Pandemic Affected Student Learning in Ohio: Analysis of Spring 2021 Ohio State Tests (Ohio State Univ., 2021).

Kozakowski, W., Gill, B., Lavallee, P., Burnett, A. & Ladinsky, J. Changes in Academic Achievement in Pittsburgh Public Schools during Remote Instruction in the COVID-19 Pandemic (Institute of Education Sciences (IES), US Department of Education, 2020).

Kuhfeld, M. & Lewis, K. Student Achievement in 2021–2022: Cause for Hope and Continued Urgency (NWEA, 2022).

Lewis, K., Kuhfeld, M., Ruzek, E. & McEachin, A. Learning during COVID-19: Reading and Math Achievement in the 2020–21 School Year (NWEA, 2021).

Locke, V. N., Patarapichayatham, C. & Lewis, S. Learning Loss in Reading and Math in US Schools Due to the COVID-19 Pandemic (Istation, 2021).

Pier, L., Christian, M., Tymeson, H. & Meyer, R. H. COVID-19 Impacts on Student Learning: Evidence from Interim Assessments in California. PACE Working Paper (Policy Analysis for California Education, 2021).

Download references

Acknowledgements

Carlsberg Foundation grant CF19-0102 (A.M.B.-M.); Leverhulme Trust Large Centre Grant (P.E.), the Swedish Research Council for Health, Working Life and Welfare (FORTE) grant 2016-07099 (P.E.); the French National Research Agency (ANR) as part of the ‘Investissements d’Avenir’ programme LIEPP (ANR-11-LABX-0091 and ANR-11-IDEX-0005-02) and the Université Paris Cité IdEx (ANR-18-IDEX-0001) (P.E.). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

Author information

Authors and affiliations.

Centre for Research on Social Inequalities (CRIS), Sciences Po, Paris, France

Bastian A. Betthäuser

Department of Social Policy and Intervention, University of Oxford, Oxford, UK

Bastian A. Betthäuser & Anders M. Bach-Mortensen

Nuffield College, University of Oxford, Oxford, UK

Bastian A. Betthäuser & Per Engzell

Social Research Institute, University College London, London, UK

Per Engzell

Swedish Institute for Social Research, Stockholm University, Stockholm, Sweden

You can also search for this author in PubMed   Google Scholar

Contributions

B.A.B., A.M.B.-M. and P.E. designed the study; B.A.B., A.M.B.-M. and P.E. planned and implemented the search and screened studies; B.A.B., A.M.B.-M. and P.E. extracted relevant data from studies; B.A.B., A.M.B.-M. and P.E. conducted the quality appraisal; B.A.B., A.M.B.-M. and P.E. conducted the data analysis and visualization; B.A.B., A.M.B.-M. and P.E. wrote the manuscript.

Corresponding author

Correspondence to Bastian A. Betthäuser .

Ethics declarations

Competing interests.

The authors declare no competing interests.

Peer review

Peer review information.

Nature Human Behaviour thanks Guilherme Lichand, Sébastien Goudeau and Christoph König for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary information.

Supplementary methods, results, figures, tables, PRISMA Checklist and references.

Reporting Summary

Peer review file, rights and permissions.

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Cite this article.

Betthäuser, B.A., Bach-Mortensen, A.M. & Engzell, P. A systematic review and meta-analysis of the evidence on learning during the COVID-19 pandemic. Nat Hum Behav 7 , 375–385 (2023). https://doi.org/10.1038/s41562-022-01506-4

Download citation

Received : 24 June 2022

Accepted : 30 November 2022

Published : 30 January 2023

Issue Date : March 2023

DOI : https://doi.org/10.1038/s41562-022-01506-4

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

This article is cited by

Investigating the effect of covid-19 disruption in education using reds data.

• Alice Bertoletti
• Zbigniew Karpiński

Large-scale Assessments in Education (2024)

School reopening concerns amid a pandemic among higher education students: a developing country perspective for policy development

• Manuel B. Garcia

Educational Research for Policy and Practice (2024)

A democratic curriculum for the challenges of post-truth

• David Nally

Curriculum Perspectives (2024)

SGS: SqueezeNet-guided Gaussian-kernel SVM for COVID-19 Diagnosis

• Fanfeng Shi
• Vishnuvarthanan Govindaraj

Mobile Networks and Applications (2024)

Electrochemical determination of budesonide: a common corticosteroid used to treat respiratory diseases such as COVID-19 and asthma

• Katarzyna Jedlińska
• Katarzyna Trojanowska
• Bogusław Baś

Journal of Applied Electrochemistry (2024)

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Jump to navigation

Cochrane Training

Chapter 10: analysing data and undertaking meta-analyses.

Jonathan J Deeks, Julian PT Higgins, Douglas G Altman; on behalf of the Cochrane Statistical Methods Group

Key Points:

• Meta-analysis is the statistical combination of results from two or more separate studies.
• Potential advantages of meta-analyses include an improvement in precision, the ability to answer questions not posed by individual studies, and the opportunity to settle controversies arising from conflicting claims. However, they also have the potential to mislead seriously, particularly if specific study designs, within-study biases, variation across studies, and reporting biases are not carefully considered.
• It is important to be familiar with the type of data (e.g. dichotomous, continuous) that result from measurement of an outcome in an individual study, and to choose suitable effect measures for comparing intervention groups.
• Most meta-analysis methods are variations on a weighted average of the effect estimates from the different studies.
• Studies with no events contribute no information about the risk ratio or odds ratio. For rare events, the Peto method has been observed to be less biased and more powerful than other methods.
• Variation across studies (heterogeneity) must be considered, although most Cochrane Reviews do not have enough studies to allow for the reliable investigation of its causes. Random-effects meta-analyses allow for heterogeneity by assuming that underlying effects follow a normal distribution, but they must be interpreted carefully. Prediction intervals from random-effects meta-analyses are a useful device for presenting the extent of between-study variation.
• Many judgements are required in the process of preparing a meta-analysis. Sensitivity analyses should be used to examine whether overall findings are robust to potentially influential decisions.

Cite this chapter as: Deeks JJ, Higgins JPT, Altman DG (editors). Chapter 10: Analysing data and undertaking meta-analyses. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.4 (updated August  2023). Cochrane, 2023. Available from www.training.cochrane.org/handbook .

10.1 Do not start here!

It can be tempting to jump prematurely into a statistical analysis when undertaking a systematic review. The production of a diamond at the bottom of a plot is an exciting moment for many authors, but results of meta-analyses can be very misleading if suitable attention has not been given to formulating the review question; specifying eligibility criteria; identifying and selecting studies; collecting appropriate data; considering risk of bias; planning intervention comparisons; and deciding what data would be meaningful to analyse. Review authors should consult the chapters that precede this one before a meta-analysis is undertaken.

10.2 Introduction to meta-analysis

An important step in a systematic review is the thoughtful consideration of whether it is appropriate to combine the numerical results of all, or perhaps some, of the studies. Such a meta-analysis yields an overall statistic (together with its confidence interval) that summarizes the effectiveness of an experimental intervention compared with a comparator intervention. Potential advantages of meta-analyses include the following:

• T o improve precision . Many studies are too small to provide convincing evidence about intervention effects in isolation. Estimation is usually improved when it is based on more information.
• To answer questions not posed by the individual studies . Primary studies often involve a specific type of participant and explicitly defined interventions. A selection of studies in which these characteristics differ can allow investigation of the consistency of effect across a wider range of populations and interventions. It may also, if relevant, allow reasons for differences in effect estimates to be investigated.
• To settle controversies arising from apparently conflicting studies or to generate new hypotheses . Statistical synthesis of findings allows the degree of conflict to be formally assessed, and reasons for different results to be explored and quantified.

Of course, the use of statistical synthesis methods does not guarantee that the results of a review are valid, any more than it does for a primary study. Moreover, like any tool, statistical methods can be misused.

This chapter describes the principles and methods used to carry out a meta-analysis for a comparison of two interventions for the main types of data encountered. The use of network meta-analysis to compare more than two interventions is addressed in Chapter 11 . Formulae for most of the methods described are provided in the RevMan Web Knowledge Base under Statistical Algorithms and calculations used in Review Manager (documentation.cochrane.org/revman-kb/statistical-methods-210600101.html), and a longer discussion of many of the issues is available ( Deeks et al 2001 ).

10.2.1 Principles of meta-analysis

The commonly used methods for meta-analysis follow the following basic principles:

• Meta-analysis is typically a two-stage process. In the first stage, a summary statistic is calculated for each study, to describe the observed intervention effect in the same way for every study. For example, the summary statistic may be a risk ratio if the data are dichotomous, or a difference between means if the data are continuous (see Chapter 6 ).

• The combination of intervention effect estimates across studies may optionally incorporate an assumption that the studies are not all estimating the same intervention effect, but estimate intervention effects that follow a distribution across studies. This is the basis of a random-effects meta-analysis (see Section 10.10.4 ). Alternatively, if it is assumed that each study is estimating exactly the same quantity, then a fixed-effect meta-analysis is performed.
• The standard error of the summary intervention effect can be used to derive a confidence interval, which communicates the precision (or uncertainty) of the summary estimate; and to derive a P value, which communicates the strength of the evidence against the null hypothesis of no intervention effect.
• As well as yielding a summary quantification of the intervention effect, all methods of meta-analysis can incorporate an assessment of whether the variation among the results of the separate studies is compatible with random variation, or whether it is large enough to indicate inconsistency of intervention effects across studies (see Section 10.10 ).
• The problem of missing data is one of the numerous practical considerations that must be thought through when undertaking a meta-analysis. In particular, review authors should consider the implications of missing outcome data from individual participants (due to losses to follow-up or exclusions from analysis) (see Section 10.12 ).

Meta-analyses are usually illustrated using a forest plot . An example appears in Figure 10.2.a . A forest plot displays effect estimates and confidence intervals for both individual studies and meta-analyses (Lewis and Clarke 2001). Each study is represented by a block at the point estimate of intervention effect with a horizontal line extending either side of the block. The area of the block indicates the weight assigned to that study in the meta-analysis while the horizontal line depicts the confidence interval (usually with a 95% level of confidence). The area of the block and the confidence interval convey similar information, but both make different contributions to the graphic. The confidence interval depicts the range of intervention effects compatible with the study’s result. The size of the block draws the eye towards the studies with larger weight (usually those with narrower confidence intervals), which dominate the calculation of the summary result, presented as a diamond at the bottom.

Figure 10.2.a Example of a forest plot from a review of interventions to promote ownership of smoke alarms (DiGuiseppi and Higgins 2001). Reproduced with permission of John Wiley & Sons

10.3 A generic inverse-variance approach to meta-analysis

A very common and simple version of the meta-analysis procedure is commonly referred to as the inverse-variance method . This approach is implemented in its most basic form in RevMan, and is used behind the scenes in many meta-analyses of both dichotomous and continuous data.

The inverse-variance method is so named because the weight given to each study is chosen to be the inverse of the variance of the effect estimate (i.e. 1 over the square of its standard error). Thus, larger studies, which have smaller standard errors, are given more weight than smaller studies, which have larger standard errors. This choice of weights minimizes the imprecision (uncertainty) of the pooled effect estimate.

10.3.1 Fixed-effect method for meta-analysis

A fixed-effect meta-analysis using the inverse-variance method calculates a weighted average as:

where Y i is the intervention effect estimated in the i th study, SE i is the standard error of that estimate, and the summation is across all studies. The basic data required for the analysis are therefore an estimate of the intervention effect and its standard error from each study. A fixed-effect meta-analysis is valid under an assumption that all effect estimates are estimating the same underlying intervention effect, which is referred to variously as a ‘fixed-effect’ assumption, a ‘common-effect’ assumption or an ‘equal-effects’ assumption. However, the result of the meta-analysis can be interpreted without making such an assumption (Rice et al 2018).

10.3.2 Random-effects methods for meta-analysis

A variation on the inverse-variance method is to incorporate an assumption that the different studies are estimating different, yet related, intervention effects (Higgins et al 2009). This produces a random-effects meta-analysis, and the simplest version is known as the DerSimonian and Laird method (DerSimonian and Laird 1986). Random-effects meta-analysis is discussed in detail in Section 10.10.4 .

10.3.3 Performing inverse-variance meta-analyses

Most meta-analysis programs perform inverse-variance meta-analyses. Usually the user provides summary data from each intervention arm of each study, such as a 2×2 table when the outcome is dichotomous (see Chapter 6, Section 6.4 ), or means, standard deviations and sample sizes for each group when the outcome is continuous (see Chapter 6, Section 6.5 ). This avoids the need for the author to calculate effect estimates, and allows the use of methods targeted specifically at different types of data (see Sections 10.4 and 10.5 ).

When the data are conveniently available as summary statistics from each intervention group, the inverse-variance method can be implemented directly. For example, estimates and their standard errors may be entered directly into RevMan under the ‘Generic inverse variance’ outcome type. For ratio measures of intervention effect, the data must be entered into RevMan as natural logarithms (for example, as a log odds ratio and the standard error of the log odds ratio). However, it is straightforward to instruct the software to display results on the original (e.g. odds ratio) scale. It is possible to supplement or replace this with a column providing the sample sizes in the two groups. Note that the ability to enter estimates and standard errors creates a high degree of flexibility in meta-analysis. It facilitates the analysis of properly analysed crossover trials, cluster-randomized trials and non-randomized trials (see Chapter 23 ), as well as outcome data that are ordinal, time-to-event or rates (see Chapter 6 ).

10.4 Meta-analysis of dichotomous outcomes

There are four widely used methods of meta-analysis for dichotomous outcomes, three fixed-effect methods (Mantel-Haenszel, Peto and inverse variance) and one random-effects method (DerSimonian and Laird inverse variance). All of these methods are available as analysis options in RevMan. The Peto method can only combine odds ratios, whilst the other three methods can combine odds ratios, risk ratios or risk differences. Formulae for all of the meta-analysis methods are available elsewhere (Deeks et al 2001).

Note that having no events in one group (sometimes referred to as ‘zero cells’) causes problems with computation of estimates and standard errors with some methods: see Section 10.4.4 .

10.4.1 Mantel-Haenszel methods

When data are sparse, either in terms of event risks being low or study size being small, the estimates of the standard errors of the effect estimates that are used in the inverse-variance methods may be poor. Mantel-Haenszel methods are fixed-effect meta-analysis methods using a different weighting scheme that depends on which effect measure (e.g. risk ratio, odds ratio, risk difference) is being used (Mantel and Haenszel 1959, Greenland and Robins 1985). They have been shown to have better statistical properties when there are few events. As this is a common situation in Cochrane Reviews, the Mantel-Haenszel method is generally preferable to the inverse variance method in fixed-effect meta-analyses. In other situations the two methods give similar estimates.

10.4.2 Peto odds ratio method

Peto’s method can only be used to combine odds ratios (Yusuf et al 1985). It uses an inverse-variance approach, but uses an approximate method of estimating the log odds ratio, and uses different weights. An alternative way of viewing the Peto method is as a sum of ‘O – E’ statistics. Here, O is the observed number of events and E is an expected number of events in the experimental intervention group of each study under the null hypothesis of no intervention effect.

The approximation used in the computation of the log odds ratio works well when intervention effects are small (odds ratios are close to 1), events are not particularly common and the studies have similar numbers in experimental and comparator groups. In other situations it has been shown to give biased answers. As these criteria are not always fulfilled, Peto’s method is not recommended as a default approach for meta-analysis.

Corrections for zero cell counts are not necessary when using Peto’s method. Perhaps for this reason, this method performs well when events are very rare (Bradburn et al 2007); see Section 10.4.4.1 . Also, Peto’s method can be used to combine studies with dichotomous outcome data with studies using time-to-event analyses where log-rank tests have been used (see Section 10.9 ).

10.4.3 Which effect measure for dichotomous outcomes?

Effect measures for dichotomous data are described in Chapter 6, Section 6.4.1 . The effect of an intervention can be expressed as either a relative or an absolute effect. The risk ratio (relative risk) and odds ratio are relative measures, while the risk difference and number needed to treat for an additional beneficial outcome are absolute measures. A further complication is that there are, in fact, two risk ratios. We can calculate the risk ratio of an event occurring or the risk ratio of no event occurring. These give different summary results in a meta-analysis, sometimes dramatically so.

The selection of a summary statistic for use in meta-analysis depends on balancing three criteria (Deeks 2002). First, we desire a summary statistic that gives values that are similar for all the studies in the meta-analysis and subdivisions of the population to which the interventions will be applied. The more consistent the summary statistic, the greater is the justification for expressing the intervention effect as a single summary number. Second, the summary statistic must have the mathematical properties required to perform a valid meta-analysis. Third, the summary statistic would ideally be easily understood and applied by those using the review. The summary intervention effect should be presented in a way that helps readers to interpret and apply the results appropriately. Among effect measures for dichotomous data, no single measure is uniformly best, so the choice inevitably involves a compromise.

Consistency Empirical evidence suggests that relative effect measures are, on average, more consistent than absolute measures (Engels et al 2000, Deeks 2002, Rücker et al 2009). For this reason, it is wise to avoid performing meta-analyses of risk differences, unless there is a clear reason to suspect that risk differences will be consistent in a particular clinical situation. On average there is little difference between the odds ratio and risk ratio in terms of consistency (Deeks 2002). When the study aims to reduce the incidence of an adverse event, there is empirical evidence that risk ratios of the adverse event are more consistent than risk ratios of the non-event (Deeks 2002). Selecting an effect measure based on what is the most consistent in a particular situation is not a generally recommended strategy, since it may lead to a selection that spuriously maximizes the precision of a meta-analysis estimate.

Mathematical properties The most important mathematical criterion is the availability of a reliable variance estimate. The number needed to treat for an additional beneficial outcome does not have a simple variance estimator and cannot easily be used directly in meta-analysis, although it can be computed from the meta-analysis result afterwards (see Chapter 15, Section 15.4.2 ). There is no consensus regarding the importance of two other often-cited mathematical properties: the fact that the behaviour of the odds ratio and the risk difference do not rely on which of the two outcome states is coded as the event, and the odds ratio being the only statistic which is unbounded (see Chapter 6, Section 6.4.1 ).

Ease of interpretation The odds ratio is the hardest summary statistic to understand and to apply in practice, and many practising clinicians report difficulties in using them. There are many published examples where authors have misinterpreted odds ratios from meta-analyses as risk ratios. Although odds ratios can be re-expressed for interpretation (as discussed here), there must be some concern that routine presentation of the results of systematic reviews as odds ratios will lead to frequent over-estimation of the benefits and harms of interventions when the results are applied in clinical practice. Absolute measures of effect are thought to be more easily interpreted by clinicians than relative effects (Sinclair and Bracken 1994), and allow trade-offs to be made between likely benefits and likely harms of interventions. However, they are less likely to be generalizable.

It is generally recommended that meta-analyses are undertaken using risk ratios (taking care to make a sensible choice over which category of outcome is classified as the event) or odds ratios. This is because it seems important to avoid using summary statistics for which there is empirical evidence that they are unlikely to give consistent estimates of intervention effects (the risk difference), and it is impossible to use statistics for which meta-analysis cannot be performed (the number needed to treat for an additional beneficial outcome). It may be wise to plan to undertake a sensitivity analysis to investigate whether choice of summary statistic (and selection of the event category) is critical to the conclusions of the meta-analysis (see Section 10.14 ).

It is often sensible to use one statistic for meta-analysis and to re-express the results using a second, more easily interpretable statistic. For example, often meta-analysis may be best performed using relative effect measures (risk ratios or odds ratios) and the results re-expressed using absolute effect measures (risk differences or numbers needed to treat for an additional beneficial outcome – see Chapter 15, Section 15.4 . This is one of the key motivations for ‘Summary of findings’ tables in Cochrane Reviews: see Chapter 14 ). If odds ratios are used for meta-analysis they can also be re-expressed as risk ratios (see Chapter 15, Section 15.4 ). In all cases the same formulae can be used to convert upper and lower confidence limits. However, all of these transformations require specification of a value of baseline risk that indicates the likely risk of the outcome in the ‘control’ population to which the experimental intervention will be applied. Where the chosen value for this assumed comparator group risk is close to the typical observed comparator group risks across the studies, similar estimates of absolute effect will be obtained regardless of whether odds ratios or risk ratios are used for meta-analysis. Where the assumed comparator risk differs from the typical observed comparator group risk, the predictions of absolute benefit will differ according to which summary statistic was used for meta-analysis.

10.4.4 Meta-analysis of rare events

For rare outcomes, meta-analysis may be the only way to obtain reliable evidence of the effects of healthcare interventions. Individual studies are usually under-powered to detect differences in rare outcomes, but a meta-analysis of many studies may have adequate power to investigate whether interventions do have an impact on the incidence of the rare event. However, many methods of meta-analysis are based on large sample approximations, and are unsuitable when events are rare. Thus authors must take care when selecting a method of meta-analysis (Efthimiou 2018).

There is no single risk at which events are classified as ‘rare’. Certainly risks of 1 in 1000 constitute rare events, and many would classify risks of 1 in 100 the same way. However, the performance of methods when risks are as high as 1 in 10 may also be affected by the issues discussed in this section. What is typical is that a high proportion of the studies in the meta-analysis observe no events in one or more study arms.

10.4.4.1 Studies with no events in one or more arms

Computational problems can occur when no events are observed in one or both groups in an individual study. Inverse variance meta-analytical methods involve computing an intervention effect estimate and its standard error for each study. For studies where no events were observed in one or both arms, these computations often involve dividing by a zero count, which yields a computational error. Most meta-analytical software routines (including those in RevMan) automatically check for problematic zero counts, and add a fixed value (typically 0.5) to all cells of a 2×2 table where the problems occur. The Mantel-Haenszel methods require zero-cell corrections only if the same cell is zero in all the included studies, and hence need to use the correction less often. However, in many software applications the same correction rules are applied for Mantel-Haenszel methods as for the inverse-variance methods. Odds ratio and risk ratio methods require zero cell corrections more often than difference methods, except for the Peto odds ratio method, which encounters computation problems only in the extreme situation of no events occurring in all arms of all studies.

Whilst the fixed correction meets the objective of avoiding computational errors, it usually has the undesirable effect of biasing study estimates towards no difference and over-estimating variances of study estimates (consequently down-weighting inappropriately their contribution to the meta-analysis). Where the sizes of the study arms are unequal (which occurs more commonly in non-randomized studies than randomized trials), they will introduce a directional bias in the treatment effect. Alternative non-fixed zero-cell corrections have been explored by Sweeting and colleagues, including a correction proportional to the reciprocal of the size of the contrasting study arm, which they found preferable to the fixed 0.5 correction when arm sizes were not balanced (Sweeting et al 2004).

10.4.4.2 Studies with no events in either arm

The standard practice in meta-analysis of odds ratios and risk ratios is to exclude studies from the meta-analysis where there are no events in both arms. This is because such studies do not provide any indication of either the direction or magnitude of the relative treatment effect. Whilst it may be clear that events are very rare on both the experimental intervention and the comparator intervention, no information is provided as to which group is likely to have the higher risk, or on whether the risks are of the same or different orders of magnitude (when risks are very low, they are compatible with very large or very small ratios). Whilst one might be tempted to infer that the risk would be lowest in the group with the larger sample size (as the upper limit of the confidence interval would be lower), this is not justified as the sample size allocation was determined by the study investigators and is not a measure of the incidence of the event.

Risk difference methods superficially appear to have an advantage over odds ratio methods in that the risk difference is defined (as zero) when no events occur in either arm. Such studies are therefore included in the estimation process. Bradburn and colleagues undertook simulation studies which revealed that all risk difference methods yield confidence intervals that are too wide when events are rare, and have associated poor statistical power, which make them unsuitable for meta-analysis of rare events (Bradburn et al 2007). This is especially relevant when outcomes that focus on treatment safety are being studied, as the ability to identify correctly (or attempt to refute) serious adverse events is a key issue in drug development.

It is likely that outcomes for which no events occur in either arm may not be mentioned in reports of many randomized trials, precluding their inclusion in a meta-analysis. It is unclear, though, when working with published results, whether failure to mention a particular adverse event means there were no such events, or simply that such events were not included as a measured endpoint. Whilst the results of risk difference meta-analyses will be affected by non-reporting of outcomes with no events, odds and risk ratio based methods naturally exclude these data whether or not they are published, and are therefore unaffected.

10.4.4.3 Validity of methods of meta-analysis for rare events

Simulation studies have revealed that many meta-analytical methods can give misleading results for rare events, which is unsurprising given their reliance on asymptotic statistical theory. Their performance has been judged suboptimal either through results being biased, confidence intervals being inappropriately wide, or statistical power being too low to detect substantial differences.

In the following we consider the choice of statistical method for meta-analyses of odds ratios. Appropriate choices appear to depend on the comparator group risk, the likely size of the treatment effect and consideration of balance in the numbers of experimental and comparator participants in the constituent studies. We are not aware of research that has evaluated risk ratio measures directly, but their performance is likely to be very similar to corresponding odds ratio measurements. When events are rare, estimates of odds and risks are near identical, and results of both can be interpreted as ratios of probabilities.

Bradburn and colleagues found that many of the most commonly used meta-analytical methods were biased when events were rare (Bradburn et al 2007). The bias was greatest in inverse variance and DerSimonian and Laird odds ratio and risk difference methods, and the Mantel-Haenszel odds ratio method using a 0.5 zero-cell correction. As already noted, risk difference meta-analytical methods tended to show conservative confidence interval coverage and low statistical power when risks of events were low.

At event rates below 1% the Peto one-step odds ratio method was found to be the least biased and most powerful method, and provided the best confidence interval coverage, provided there was no substantial imbalance between treatment and comparator group sizes within studies, and treatment effects were not exceptionally large. This finding was consistently observed across three different meta-analytical scenarios, and was also observed by Sweeting and colleagues (Sweeting et al 2004).

This finding was noted despite the method producing only an approximation to the odds ratio. For very large effects (e.g. risk ratio=0.2) when the approximation is known to be poor, treatment effects were under-estimated, but the Peto method still had the best performance of all the methods considered for event risks of 1 in 1000, and the bias was never more than 6% of the comparator group risk.

In other circumstances (i.e. event risks above 1%, very large effects at event risks around 1%, and meta-analyses where many studies were substantially imbalanced) the best performing methods were the Mantel-Haenszel odds ratio without zero-cell corrections, logistic regression and an exact method. None of these methods is available in RevMan.

Methods that should be avoided with rare events are the inverse-variance methods (including the DerSimonian and Laird random-effects method) (Efthimiou 2018). These directly incorporate the study’s variance in the estimation of its contribution to the meta-analysis, but these are usually based on a large-sample variance approximation, which was not intended for use with rare events. We would suggest that incorporation of heterogeneity into an estimate of a treatment effect should be a secondary consideration when attempting to produce estimates of effects from sparse data – the primary concern is to discern whether there is any signal of an effect in the data.

10.5 Meta-analysis of continuous outcomes

An important assumption underlying standard methods for meta-analysis of continuous data is that the outcomes have a normal distribution in each intervention arm in each study. This assumption may not always be met, although it is unimportant in very large studies. It is useful to consider the possibility of skewed data (see Section 10.5.3 ).

10.5.1 Which effect measure for continuous outcomes?

The two summary statistics commonly used for meta-analysis of continuous data are the mean difference (MD) and the standardized mean difference (SMD). Other options are available, such as the ratio of means (see Chapter 6, Section 6.5.1 ). Selection of summary statistics for continuous data is principally determined by whether studies all report the outcome using the same scale (when the mean difference can be used) or using different scales (when the standardized mean difference is usually used). The ratio of means can be used in either situation, but is appropriate only when outcome measurements are strictly greater than zero. Further considerations in deciding on an effect measure that will facilitate interpretation of the findings appears in Chapter 15, Section 15.5 .

The different roles played in MD and SMD approaches by the standard deviations (SDs) of outcomes observed in the two groups should be understood.

For the mean difference approach, the SDs are used together with the sample sizes to compute the weight given to each study. Studies with small SDs are given relatively higher weight whilst studies with larger SDs are given relatively smaller weights. This is appropriate if variation in SDs between studies reflects differences in the reliability of outcome measurements, but is probably not appropriate if the differences in SD reflect real differences in the variability of outcomes in the study populations.

For the standardized mean difference approach, the SDs are used to standardize the mean differences to a single scale, as well as in the computation of study weights. Thus, studies with small SDs lead to relatively higher estimates of SMD, whilst studies with larger SDs lead to relatively smaller estimates of SMD. For this to be appropriate, it must be assumed that between-study variation in SDs reflects only differences in measurement scales and not differences in the reliability of outcome measures or variability among study populations, as discussed in Chapter 6, Section 6.5.1.2 .

These assumptions of the methods should be borne in mind when unexpected variation of SDs is observed across studies.

10.5.2 Meta-analysis of change scores

In some circumstances an analysis based on changes from baseline will be more efficient and powerful than comparison of post-intervention values, as it removes a component of between-person variability from the analysis. However, calculation of a change score requires measurement of the outcome twice and in practice may be less efficient for outcomes that are unstable or difficult to measure precisely, where the measurement error may be larger than true between-person baseline variability. Change-from-baseline outcomes may also be preferred if they have a less skewed distribution than post-intervention measurement outcomes. Although sometimes used as a device to ‘correct’ for unlucky randomization, this practice is not recommended.

The preferred statistical approach to accounting for baseline measurements of the outcome variable is to include the baseline outcome measurements as a covariate in a regression model or analysis of covariance (ANCOVA). These analyses produce an ‘adjusted’ estimate of the intervention effect together with its standard error. These analyses are the least frequently encountered, but as they give the most precise and least biased estimates of intervention effects they should be included in the analysis when they are available. However, they can only be included in a meta-analysis using the generic inverse-variance method, since means and SDs are not available for each intervention group separately.

In practice an author is likely to discover that the studies included in a review include a mixture of change-from-baseline and post-intervention value scores. However, mixing of outcomes is not a problem when it comes to meta-analysis of MDs. There is no statistical reason why studies with change-from-baseline outcomes should not be combined in a meta-analysis with studies with post-intervention measurement outcomes when using the (unstandardized) MD method. In a randomized study, MD based on changes from baseline can usually be assumed to be addressing exactly the same underlying intervention effects as analyses based on post-intervention measurements. That is to say, the difference in mean post-intervention values will on average be the same as the difference in mean change scores. If the use of change scores does increase precision, appropriately, the studies presenting change scores will be given higher weights in the analysis than they would have received if post-intervention values had been used, as they will have smaller SDs.

When combining the data on the MD scale, authors must be careful to use the appropriate means and SDs (either of post-intervention measurements or of changes from baseline) for each study. Since the mean values and SDs for the two types of outcome may differ substantially, it may be advisable to place them in separate subgroups to avoid confusion for the reader, but the results of the subgroups can legitimately be pooled together.

In contrast, post-intervention value and change scores should not in principle be combined using standard meta-analysis approaches when the effect measure is an SMD. This is because the SDs used in the standardization reflect different things. The SD when standardizing post-intervention values reflects between-person variability at a single point in time. The SD when standardizing change scores reflects variation in between-person changes over time, so will depend on both within-person and between-person variability; within-person variability in turn is likely to depend on the length of time between measurements. Nevertheless, an empirical study of 21 meta-analyses in osteoarthritis did not find a difference between combined SMDs based on post-intervention values and combined SMDs based on change scores (da Costa et al 2013). One option is to standardize SMDs using post-intervention SDs rather than change score SDs. This would lead to valid synthesis of the two approaches, but we are not aware that an appropriate standard error for this has been derived.

A common practical problem associated with including change-from-baseline measures is that the SD of changes is not reported. Imputation of SDs is discussed in Chapter 6, Section 6.5.2.8 .

10.5.3 Meta-analysis of skewed data

Analyses based on means are appropriate for data that are at least approximately normally distributed, and for data from very large trials. If the true distribution of outcomes is asymmetrical, then the data are said to be skewed. Review authors should consider the possibility and implications of skewed data when analysing continuous outcomes (see MECIR Box 10.5.a ). Skew can sometimes be diagnosed from the means and SDs of the outcomes. A rough check is available, but it is only valid if a lowest or highest possible value for an outcome is known to exist. Thus, the check may be used for outcomes such as weight, volume and blood concentrations, which have lowest possible values of 0, or for scale outcomes with minimum or maximum scores, but it may not be appropriate for change-from-baseline measures. The check involves calculating the observed mean minus the lowest possible value (or the highest possible value minus the observed mean), and dividing this by the SD. A ratio less than 2 suggests skew (Altman and Bland 1996). If the ratio is less than 1, there is strong evidence of a skewed distribution.

Transformation of the original outcome data may reduce skew substantially. Reports of trials may present results on a transformed scale, usually a log scale. Collection of appropriate data summaries from the trialists, or acquisition of individual patient data, is currently the approach of choice. Appropriate data summaries and analysis strategies for the individual patient data will depend on the situation. Consultation with a knowledgeable statistician is advised.

Where data have been analysed on a log scale, results are commonly presented as geometric means and ratios of geometric means. A meta-analysis may be then performed on the scale of the log-transformed data; an example of the calculation of the required means and SD is given in Chapter 6, Section 6.5.2.4 . This approach depends on being able to obtain transformed data for all studies; methods for transforming from one scale to the other are available (Higgins et al 2008b). Log-transformed and untransformed data should not be mixed in a meta-analysis.

MECIR Box 10.5.a Relevant expectations for conduct of intervention reviews

10.6 Combining dichotomous and continuous outcomes

Occasionally authors encounter a situation where data for the same outcome are presented in some studies as dichotomous data and in other studies as continuous data. For example, scores on depression scales can be reported as means, or as the percentage of patients who were depressed at some point after an intervention (i.e. with a score above a specified cut-point). This type of information is often easier to understand, and more helpful, when it is dichotomized. However, deciding on a cut-point may be arbitrary, and information is lost when continuous data are transformed to dichotomous data.

There are several options for handling combinations of dichotomous and continuous data. Generally, it is useful to summarize results from all the relevant, valid studies in a similar way, but this is not always possible. It may be possible to collect missing data from investigators so that this can be done. If not, it may be useful to summarize the data in three ways: by entering the means and SDs as continuous outcomes, by entering the counts as dichotomous outcomes and by entering all of the data in text form as ‘Other data’ outcomes.

There are statistical approaches available that will re-express odds ratios as SMDs (and vice versa), allowing dichotomous and continuous data to be combined (Anzures-Cabrera et al 2011). A simple approach is as follows. Based on an assumption that the underlying continuous measurements in each intervention group follow a logistic distribution (which is a symmetrical distribution similar in shape to the normal distribution, but with more data in the distributional tails), and that the variability of the outcomes is the same in both experimental and comparator participants, the odds ratios can be re-expressed as a SMD according to the following simple formula (Chinn 2000):

The standard error of the log odds ratio can be converted to the standard error of a SMD by multiplying by the same constant (√3/π=0.5513). Alternatively SMDs can be re-expressed as log odds ratios by multiplying by π/√3=1.814. Once SMDs (or log odds ratios) and their standard errors have been computed for all studies in the meta-analysis, they can be combined using the generic inverse-variance method. Standard errors can be computed for all studies by entering the data as dichotomous and continuous outcome type data, as appropriate, and converting the confidence intervals for the resulting log odds ratios and SMDs into standard errors (see Chapter 6, Section 6.3 ).

10.7 Meta-analysis of ordinal outcomes and measurement scale s

Ordinal and measurement scale outcomes are most commonly meta-analysed as dichotomous data (if so, see Section 10.4 ) or continuous data (if so, see Section 10.5 ) depending on the way that the study authors performed the original analyses.

Occasionally it is possible to analyse the data using proportional odds models. This is the case when ordinal scales have a small number of categories, the numbers falling into each category for each intervention group can be obtained, and the same ordinal scale has been used in all studies. This approach may make more efficient use of all available data than dichotomization, but requires access to statistical software and results in a summary statistic for which it is challenging to find a clinical meaning.

The proportional odds model uses the proportional odds ratio as the measure of intervention effect (Agresti 1996) (see Chapter 6, Section 6.6 ), and can be used for conducting a meta-analysis in advanced statistical software packages (Whitehead and Jones 1994). Estimates of log odds ratios and their standard errors from a proportional odds model may be meta-analysed using the generic inverse-variance method (see Section 10.3.3 ). If the same ordinal scale has been used in all studies, but in some reports has been presented as a dichotomous outcome, it may still be possible to include all studies in the meta-analysis. In the context of the three-category model, this might mean that for some studies category 1 constitutes a success, while for others both categories 1 and 2 constitute a success. Methods are available for dealing with this, and for combining data from scales that are related but have different definitions for their categories (Whitehead and Jones 1994).

10.8 Meta-analysis of counts and rates

Results may be expressed as count data when each participant may experience an event, and may experience it more than once (see Chapter 6, Section 6.7 ). For example, ‘number of strokes’, or ‘number of hospital visits’ are counts. These events may not happen at all, but if they do happen there is no theoretical maximum number of occurrences for an individual. Count data may be analysed using methods for dichotomous data if the counts are dichotomized for each individual (see Section 10.4 ), continuous data (see Section 10.5 ) and time-to-event data (see Section 10.9 ), as well as being analysed as rate data.

Rate data occur if counts are measured for each participant along with the time over which they are observed. This is particularly appropriate when the events being counted are rare. For example, a woman may experience two strokes during a follow-up period of two years. Her rate of strokes is one per year of follow-up (or, equivalently 0.083 per month of follow-up). Rates are conventionally summarized at the group level. For example, participants in the comparator group of a clinical trial may experience 85 strokes during a total of 2836 person-years of follow-up. An underlying assumption associated with the use of rates is that the risk of an event is constant across participants and over time. This assumption should be carefully considered for each situation. For example, in contraception studies, rates have been used (known as Pearl indices) to describe the number of pregnancies per 100 women-years of follow-up. This is now considered inappropriate since couples have different risks of conception, and the risk for each woman changes over time. Pregnancies are now analysed more often using life tables or time-to-event methods that investigate the time elapsing before the first pregnancy.

Analysing count data as rates is not always the most appropriate approach and is uncommon in practice. This is because:

• the assumption of a constant underlying risk may not be suitable; and
• the statistical methods are not as well developed as they are for other types of data.

The results of a study may be expressed as a rate ratio , that is the ratio of the rate in the experimental intervention group to the rate in the comparator group. The (natural) logarithms of the rate ratios may be combined across studies using the generic inverse-variance method (see Section 10.3.3 ). Alternatively, Poisson regression approaches can be used (Spittal et al 2015).

In a randomized trial, rate ratios may often be very similar to risk ratios obtained after dichotomizing the participants, since the average period of follow-up should be similar in all intervention groups. Rate ratios and risk ratios will differ, however, if an intervention affects the likelihood of some participants experiencing multiple events.

It is possible also to focus attention on the rate difference (see Chapter 6, Section 6.7.1 ). The analysis again can be performed using the generic inverse-variance method (Hasselblad and McCrory 1995, Guevara et al 2004).

10.9 Meta-analysis of time-to-event outcomes

Two approaches to meta-analysis of time-to-event outcomes are readily available to Cochrane Review authors. The choice of which to use will depend on the type of data that have been extracted from the primary studies, or obtained from re-analysis of individual participant data.

If ‘O – E’ and ‘V’ statistics have been obtained (see Chapter 6, Section 6.8.2 ), either through re-analysis of individual participant data or from aggregate statistics presented in the study reports, then these statistics may be entered directly into RevMan using the ‘O – E and Variance’ outcome type. There are several ways to calculate these ‘O – E’ and ‘V’ statistics. Peto’s method applied to dichotomous data (Section 10.4.2 ) gives rise to an odds ratio; a log-rank approach gives rise to a hazard ratio; and a variation of the Peto method for analysing time-to-event data gives rise to something in between (Simmonds et al 2011). The appropriate effect measure should be specified. Only fixed-effect meta-analysis methods are available in RevMan for ‘O – E and Variance’ outcomes.

Alternatively, if estimates of log hazard ratios and standard errors have been obtained from results of Cox proportional hazards regression models, study results can be combined using generic inverse-variance methods (see Section 10.3.3 ).

If a mixture of log-rank and Cox model estimates are obtained from the studies, all results can be combined using the generic inverse-variance method, as the log-rank estimates can be converted into log hazard ratios and standard errors using the approaches discussed in Chapter 6, Section 6.8 .

10.10 Heterogeneity

10.10.1 what is heterogeneity.

Inevitably, studies brought together in a systematic review will differ. Any kind of variability among studies in a systematic review may be termed heterogeneity. It can be helpful to distinguish between different types of heterogeneity. Variability in the participants, interventions and outcomes studied may be described as clinical diversity (sometimes called clinical heterogeneity), and variability in study design, outcome measurement tools and risk of bias may be described as methodological diversity (sometimes called methodological heterogeneity). Variability in the intervention effects being evaluated in the different studies is known as statistical heterogeneity , and is a consequence of clinical or methodological diversity, or both, among the studies. Statistical heterogeneity manifests itself in the observed intervention effects being more different from each other than one would expect due to random error (chance) alone. We will follow convention and refer to statistical heterogeneity simply as heterogeneity .

Clinical variation will lead to heterogeneity if the intervention effect is affected by the factors that vary across studies; most obviously, the specific interventions or patient characteristics. In other words, the true intervention effect will be different in different studies.

Differences between studies in terms of methodological factors, such as use of blinding and concealment of allocation sequence, or if there are differences between studies in the way the outcomes are defined and measured, may be expected to lead to differences in the observed intervention effects. Significant statistical heterogeneity arising from methodological diversity or differences in outcome assessments suggests that the studies are not all estimating the same quantity, but does not necessarily suggest that the true intervention effect varies. In particular, heterogeneity associated solely with methodological diversity would indicate that the studies suffer from different degrees of bias. Empirical evidence suggests that some aspects of design can affect the result of clinical trials, although this is not always the case. Further discussion appears in Chapter 7 and Chapter 8 .

The scope of a review will largely determine the extent to which studies included in a review are diverse. Sometimes a review will include studies addressing a variety of questions, for example when several different interventions for the same condition are of interest (see also Chapter 11 ) or when the differential effects of an intervention in different populations are of interest. Meta-analysis should only be considered when a group of studies is sufficiently homogeneous in terms of participants, interventions and outcomes to provide a meaningful summary (see MECIR Box 10.10.a. ). It is often appropriate to take a broader perspective in a meta-analysis than in a single clinical trial. A common analogy is that systematic reviews bring together apples and oranges, and that combining these can yield a meaningless result. This is true if apples and oranges are of intrinsic interest on their own, but may not be if they are used to contribute to a wider question about fruit. For example, a meta-analysis may reasonably evaluate the average effect of a class of drugs by combining results from trials where each evaluates the effect of a different drug from the class.

MECIR Box 10.10.a Relevant expectations for conduct of intervention reviews

There may be specific interest in a review in investigating how clinical and methodological aspects of studies relate to their results. Where possible these investigations should be specified a priori (i.e. in the protocol for the systematic review). It is legitimate for a systematic review to focus on examining the relationship between some clinical characteristic(s) of the studies and the size of intervention effect, rather than on obtaining a summary effect estimate across a series of studies (see Section 10.11 ). Meta-regression may best be used for this purpose, although it is not implemented in RevMan (see Section 10.11.4 ).

10.10.2 Identifying and measuring heterogeneity

It is essential to consider the extent to which the results of studies are consistent with each other (see MECIR Box 10.10.b ). If confidence intervals for the results of individual studies (generally depicted graphically using horizontal lines) have poor overlap, this generally indicates the presence of statistical heterogeneity. More formally, a statistical test for heterogeneity is available. This Chi 2 (χ 2 , or chi-squared) test is included in the forest plots in Cochrane Reviews. It assesses whether observed differences in results are compatible with chance alone. A low P value (or a large Chi 2 statistic relative to its degree of freedom) provides evidence of heterogeneity of intervention effects (variation in effect estimates beyond chance).

MECIR Box 10.10.b Relevant expectations for conduct of intervention reviews

Care must be taken in the interpretation of the Chi 2 test, since it has low power in the (common) situation of a meta-analysis when studies have small sample size or are few in number. This means that while a statistically significant result may indicate a problem with heterogeneity, a non-significant result must not be taken as evidence of no heterogeneity. This is also why a P value of 0.10, rather than the conventional level of 0.05, is sometimes used to determine statistical significance. A further problem with the test, which seldom occurs in Cochrane Reviews, is that when there are many studies in a meta-analysis, the test has high power to detect a small amount of heterogeneity that may be clinically unimportant.

Some argue that, since clinical and methodological diversity always occur in a meta-analysis, statistical heterogeneity is inevitable (Higgins et al 2003). Thus, the test for heterogeneity is irrelevant to the choice of analysis; heterogeneity will always exist whether or not we happen to be able to detect it using a statistical test. Methods have been developed for quantifying inconsistency across studies that move the focus away from testing whether heterogeneity is present to assessing its impact on the meta-analysis. A useful statistic for quantifying inconsistency is:

In this equation, Q is the Chi 2 statistic and df is its degrees of freedom (Higgins and Thompson 2002, Higgins et al 2003). I 2 describes the percentage of the variability in effect estimates that is due to heterogeneity rather than sampling error (chance).

Thresholds for the interpretation of the I 2 statistic can be misleading, since the importance of inconsistency depends on several factors. A rough guide to interpretation in the context of meta-analyses of randomized trials is as follows:

• 0% to 40%: might not be important;
• 30% to 60%: may represent moderate heterogeneity*;
• 50% to 90%: may represent substantial heterogeneity*;
• 75% to 100%: considerable heterogeneity*.

*The importance of the observed value of I 2 depends on (1) magnitude and direction of effects, and (2) strength of evidence for heterogeneity (e.g. P value from the Chi 2 test, or a confidence interval for I 2 : uncertainty in the value of I 2 is substantial when the number of studies is small).

10.10.3 Strategies for addressing heterogeneity

Review authors must take into account any statistical heterogeneity when interpreting results, particularly when there is variation in the direction of effect (see MECIR Box 10.10.c ). A number of options are available if heterogeneity is identified among a group of studies that would otherwise be considered suitable for a meta-analysis.

MECIR Box 10.10.c  Relevant expectations for conduct of intervention reviews

• Check again that the data are correct. Severe apparent heterogeneity can indicate that data have been incorrectly extracted or entered into meta-analysis software. For example, if standard errors have mistakenly been entered as SDs for continuous outcomes, this could manifest itself in overly narrow confidence intervals with poor overlap and hence substantial heterogeneity. Unit-of-analysis errors may also be causes of heterogeneity (see Chapter 6, Section 6.2 ).  
• Do not do a meta -analysis. A systematic review need not contain any meta-analyses. If there is considerable variation in results, and particularly if there is inconsistency in the direction of effect, it may be misleading to quote an average value for the intervention effect.  
• Explore heterogeneity. It is clearly of interest to determine the causes of heterogeneity among results of studies. This process is problematic since there are often many characteristics that vary across studies from which one may choose. Heterogeneity may be explored by conducting subgroup analyses (see Section 10.11.3 ) or meta-regression (see Section 10.11.4 ). Reliable conclusions can only be drawn from analyses that are truly pre-specified before inspecting the studies’ results, and even these conclusions should be interpreted with caution. Explorations of heterogeneity that are devised after heterogeneity is identified can at best lead to the generation of hypotheses. They should be interpreted with even more caution and should generally not be listed among the conclusions of a review. Also, investigations of heterogeneity when there are very few studies are of questionable value.  
• Ignore heterogeneity. Fixed-effect meta-analyses ignore heterogeneity. The summary effect estimate from a fixed-effect meta-analysis is normally interpreted as being the best estimate of the intervention effect. However, the existence of heterogeneity suggests that there may not be a single intervention effect but a variety of intervention effects. Thus, the summary fixed-effect estimate may be an intervention effect that does not actually exist in any population, and therefore have a confidence interval that is meaningless as well as being too narrow (see Section 10.10.4 ).  
• Perform a random-effects meta-analysis. A random-effects meta-analysis may be used to incorporate heterogeneity among studies. This is not a substitute for a thorough investigation of heterogeneity. It is intended primarily for heterogeneity that cannot be explained. An extended discussion of this option appears in Section 10.10.4 .  
• Reconsider the effect measure. Heterogeneity may be an artificial consequence of an inappropriate choice of effect measure. For example, when studies collect continuous outcome data using different scales or different units, extreme heterogeneity may be apparent when using the mean difference but not when the more appropriate standardized mean difference is used. Furthermore, choice of effect measure for dichotomous outcomes (odds ratio, risk ratio, or risk difference) may affect the degree of heterogeneity among results. In particular, when comparator group risks vary, homogeneous odds ratios or risk ratios will necessarily lead to heterogeneous risk differences, and vice versa. However, it remains unclear whether homogeneity of intervention effect in a particular meta-analysis is a suitable criterion for choosing between these measures (see also Section 10.4.3 ).  
• Exclude studies. Heterogeneity may be due to the presence of one or two outlying studies with results that conflict with the rest of the studies. In general it is unwise to exclude studies from a meta-analysis on the basis of their results as this may introduce bias. However, if an obvious reason for the outlying result is apparent, the study might be removed with more confidence. Since usually at least one characteristic can be found for any study in any meta-analysis which makes it different from the others, this criterion is unreliable because it is all too easy to fulfil. It is advisable to perform analyses both with and without outlying studies as part of a sensitivity analysis (see Section 10.14 ). Whenever possible, potential sources of clinical diversity that might lead to such situations should be specified in the protocol.

10.10.4 Incorporating heterogeneity into random-effects models

The random-effects meta-analysis approach incorporates an assumption that the different studies are estimating different, yet related, intervention effects (DerSimonian and Laird 1986, Borenstein et al 2010). The approach allows us to address heterogeneity that cannot readily be explained by other factors. A random-effects meta-analysis model involves an assumption that the effects being estimated in the different studies follow some distribution. The model represents our lack of knowledge about why real, or apparent, intervention effects differ, by considering the differences as if they were random. The centre of the assumed distribution describes the average of the effects, while its width describes the degree of heterogeneity. The conventional choice of distribution is a normal distribution. It is difficult to establish the validity of any particular distributional assumption, and this is a common criticism of random-effects meta-analyses. The importance of the assumed shape for this distribution has not been widely studied.

To undertake a random-effects meta-analysis, the standard errors of the study-specific estimates (SE i in Section 10.3.1 ) are adjusted to incorporate a measure of the extent of variation, or heterogeneity, among the intervention effects observed in different studies (this variation is often referred to as Tau-squared, τ 2 , or Tau 2 ). The amount of variation, and hence the adjustment, can be estimated from the intervention effects and standard errors of the studies included in the meta-analysis.

In a heterogeneous set of studies, a random-effects meta-analysis will award relatively more weight to smaller studies than such studies would receive in a fixed-effect meta-analysis. This is because small studies are more informative for learning about the distribution of effects across studies than for learning about an assumed common intervention effect.

Note that a random-effects model does not ‘take account’ of the heterogeneity, in the sense that it is no longer an issue. It is always preferable to explore possible causes of heterogeneity, although there may be too few studies to do this adequately (see Section 10.11 ).

10.10.4.1 Fixed or random effects?

A fixed-effect meta-analysis provides a result that may be viewed as a ‘typical intervention effect’ from the studies included in the analysis. In order to calculate a confidence interval for a fixed-effect meta-analysis the assumption is usually made that the true effect of intervention (in both magnitude and direction) is the same value in every study (i.e. fixed across studies). This assumption implies that the observed differences among study results are due solely to the play of chance (i.e. that there is no statistical heterogeneity).

A random-effects model provides a result that may be viewed as an ‘average intervention effect’, where this average is explicitly defined according to an assumed distribution of effects across studies. Instead of assuming that the intervention effects are the same, we assume that they follow (usually) a normal distribution. The assumption implies that the observed differences among study results are due to a combination of the play of chance and some genuine variation in the intervention effects.

The random-effects method and the fixed-effect method will give identical results when there is no heterogeneity among the studies.

When heterogeneity is present, a confidence interval around the random-effects summary estimate is wider than a confidence interval around a fixed-effect summary estimate. This will happen whenever the I 2 statistic is greater than zero, even if the heterogeneity is not detected by the Chi 2 test for heterogeneity (see Section 10.10.2 ).

Sometimes the central estimate of the intervention effect is different between fixed-effect and random-effects analyses. In particular, if results of smaller studies are systematically different from results of larger ones, which can happen as a result of publication bias or within-study bias in smaller studies (Egger et al 1997, Poole and Greenland 1999, Kjaergard et al 2001), then a random-effects meta-analysis will exacerbate the effects of the bias (see also Chapter 13, Section 13.3.5.6 ). A fixed-effect analysis will be affected less, although strictly it will also be inappropriate.

The decision between fixed- and random-effects meta-analyses has been the subject of much debate, and we do not provide a universal recommendation. Some considerations in making this choice are as follows:

• Many have argued that the decision should be based on an expectation of whether the intervention effects are truly identical, preferring the fixed-effect model if this is likely and a random-effects model if this is unlikely (Borenstein et al 2010). Since it is generally considered to be implausible that intervention effects across studies are identical (unless the intervention has no effect at all), this leads many to advocate use of the random-effects model.
• Others have argued that a fixed-effect analysis can be interpreted in the presence of heterogeneity, and that it makes fewer assumptions than a random-effects meta-analysis. They then refer to it as a ‘fixed-effects’ meta-analysis (Peto et al 1995, Rice et al 2018).
• Under any interpretation, a fixed-effect meta-analysis ignores heterogeneity. If the method is used, it is therefore important to supplement it with a statistical investigation of the extent of heterogeneity (see Section 10.10.2 ).
• In the presence of heterogeneity, a random-effects analysis gives relatively more weight to smaller studies and relatively less weight to larger studies. If there is additionally some funnel plot asymmetry (i.e. a relationship between intervention effect magnitude and study size), then this will push the results of the random-effects analysis towards the findings in the smaller studies. In the context of randomized trials, this is generally regarded as an unfortunate consequence of the model.
• A pragmatic approach is to plan to undertake both a fixed-effect and a random-effects meta-analysis, with an intention to present the random-effects result if there is no indication of funnel plot asymmetry. If there is an indication of funnel plot asymmetry, then both methods are problematic. It may be reasonable to present both analyses or neither, or to perform a sensitivity analysis in which small studies are excluded or addressed directly using meta-regression (see Chapter 13, Section 13.3.5.6 ).
• The choice between a fixed-effect and a random-effects meta-analysis should never be made on the basis of a statistical test for heterogeneity.

10.10.4.2 Interpretation of random-effects meta-analyses

The summary estimate and confidence interval from a random-effects meta-analysis refer to the centre of the distribution of intervention effects, but do not describe the width of the distribution. Often the summary estimate and its confidence interval are quoted in isolation and portrayed as a sufficient summary of the meta-analysis. This is inappropriate. The confidence interval from a random-effects meta-analysis describes uncertainty in the location of the mean of systematically different effects in the different studies. It does not describe the degree of heterogeneity among studies, as may be commonly believed. For example, when there are many studies in a meta-analysis, we may obtain a very tight confidence interval around the random-effects estimate of the mean effect even when there is a large amount of heterogeneity. A solution to this problem is to consider a prediction interval (see Section 10.10.4.3 ).

Methodological diversity creates heterogeneity through biases variably affecting the results of different studies. The random-effects summary estimate will only correctly estimate the average intervention effect if the biases are symmetrically distributed, leading to a mixture of over-estimates and under-estimates of effect, which is unlikely to be the case. In practice it can be very difficult to distinguish whether heterogeneity results from clinical or methodological diversity, and in most cases it is likely to be due to both, so these distinctions are hard to draw in the interpretation.

When there is little information, either because there are few studies or if the studies are small with few events, a random-effects analysis will provide poor estimates of the amount of heterogeneity (i.e. of the width of the distribution of intervention effects). Fixed-effect methods such as the Mantel-Haenszel method will provide more robust estimates of the average intervention effect, but at the cost of ignoring any heterogeneity.

10.10.4.3 Prediction intervals from a random-effects meta-analysis

An estimate of the between-study variance in a random-effects meta-analysis is typically presented as part of its results. The square root of this number (i.e. Tau) is the estimated standard deviation of underlying effects across studies. Prediction intervals are a way of expressing this value in an interpretable way.

To motivate the idea of a prediction interval, note that for absolute measures of effect (e.g. risk difference, mean difference, standardized mean difference), an approximate 95% range of normally distributed underlying effects can be obtained by creating an interval from 1.96´Tau below the random-effects mean, to 1.96✕Tau above it. (For relative measures such as the odds ratio and risk ratio, an equivalent interval needs to be based on the natural logarithm of the summary estimate.) In reality, both the summary estimate and the value of Tau are associated with uncertainty. A prediction interval seeks to present the range of effects in a way that acknowledges this uncertainty (Higgins et al 2009). A simple 95% prediction interval can be calculated as:

where M is the summary mean from the random-effects meta-analysis, t k −2 is the 95% percentile of a t -distribution with k –2 degrees of freedom, k is the number of studies, Tau 2 is the estimated amount of heterogeneity and SE( M ) is the standard error of the summary mean.

The term ‘prediction interval’ relates to the use of this interval to predict the possible underlying effect in a new study that is similar to the studies in the meta-analysis. A more useful interpretation of the interval is as a summary of the spread of underlying effects in the studies included in the random-effects meta-analysis.

Prediction intervals have proved a popular way of expressing the amount of heterogeneity in a meta-analysis (Riley et al 2011). They are, however, strongly based on the assumption of a normal distribution for the effects across studies, and can be very problematic when the number of studies is small, in which case they can appear spuriously wide or spuriously narrow. Nevertheless, we encourage their use when the number of studies is reasonable (e.g. more than ten) and there is no clear funnel plot asymmetry.

10.10.4.4 Implementing random-effects meta-analyses

As introduced in Section 10.3.2 , the random-effects model can be implemented using an inverse-variance approach, incorporating a measure of the extent of heterogeneity into the study weights. RevMan implements a version of random-effects meta-analysis that is described by DerSimonian and Laird, making use of a ‘moment-based’ estimate of the between-study variance (DerSimonian and Laird 1986). The attraction of this method is that the calculations are straightforward, but it has a theoretical disadvantage in that the confidence intervals are slightly too narrow to encompass full uncertainty resulting from having estimated the degree of heterogeneity.

For many years, RevMan has implemented two random-effects methods for dichotomous data: a Mantel-Haenszel method and an inverse-variance method. Both use the moment-based approach to estimating the amount of between-studies variation. The difference between the two is subtle: the former estimates the between-study variation by comparing each study’s result with a Mantel-Haenszel fixed-effect meta-analysis result, whereas the latter estimates it by comparing each study’s result with an inverse-variance fixed-effect meta-analysis result. In practice, the difference is likely to be trivial.

There are alternative methods for performing random-effects meta-analyses that have better technical properties than the DerSimonian and Laird approach with a moment-based estimate (Veroniki et al 2016). Most notable among these is an adjustment to the confidence interval proposed by Hartung and Knapp and by Sidik and Jonkman (Hartung and Knapp 2001, Sidik and Jonkman 2002). This adjustment widens the confidence interval to reflect uncertainty in the estimation of between-study heterogeneity, and it should be used if available to review authors. An alternative option to encompass full uncertainty in the degree of heterogeneity is to take a Bayesian approach (see Section 10.13 ).

An empirical comparison of different ways to estimate between-study variation in Cochrane meta-analyses has shown that they can lead to substantial differences in estimates of heterogeneity, but seldom have major implications for estimating summary effects (Langan et al 2015). Several simulation studies have concluded that an approach proposed by Paule and Mandel should be recommended (Langan et al 2017); whereas a comprehensive recent simulation study recommended a restricted maximum likelihood approach, although noted that no single approach is universally preferable (Langan et al 2019). Review authors are encouraged to select one of these options if it is available to them.

10.11 Investigating heterogeneity

10.11.1 interaction and effect modification.

Does the intervention effect vary with different populations or intervention characteristics (such as dose or duration)? Such variation is known as interaction by statisticians and as effect modification by epidemiologists. Methods to search for such interactions include subgroup analyses and meta-regression. All methods have considerable pitfalls.

10.11.2 What are subgroup analyses?

Subgroup analyses involve splitting all the participant data into subgroups, often in order to make comparisons between them. Subgroup analyses may be done for subsets of participants (such as males and females), or for subsets of studies (such as different geographical locations). Subgroup analyses may be done as a means of investigating heterogeneous results, or to answer specific questions about particular patient groups, types of intervention or types of study.

Subgroup analyses of subsets of participants within studies are uncommon in systematic reviews based on published literature because sufficient details to extract data about separate participant types are seldom published in reports. By contrast, such subsets of participants are easily analysed when individual participant data have been collected (see Chapter 26 ). The methods we describe in the remainder of this chapter are for subgroups of studies.

Findings from multiple subgroup analyses may be misleading. Subgroup analyses are observational by nature and are not based on randomized comparisons. False negative and false positive significance tests increase in likelihood rapidly as more subgroup analyses are performed. If their findings are presented as definitive conclusions there is clearly a risk of people being denied an effective intervention or treated with an ineffective (or even harmful) intervention. Subgroup analyses can also generate misleading recommendations about directions for future research that, if followed, would waste scarce resources.

It is useful to distinguish between the notions of ‘qualitative interaction’ and ‘quantitative interaction’ (Yusuf et al 1991). Qualitative interaction exists if the direction of effect is reversed, that is if an intervention is beneficial in one subgroup but is harmful in another. Qualitative interaction is rare. This may be used as an argument that the most appropriate result of a meta-analysis is the overall effect across all subgroups. Quantitative interaction exists when the size of the effect varies but not the direction, that is if an intervention is beneficial to different degrees in different subgroups.

10.11.3 Undertaking subgroup analyses

Meta-analyses can be undertaken in RevMan both within subgroups of studies as well as across all studies irrespective of their subgroup membership. It is tempting to compare effect estimates in different subgroups by considering the meta-analysis results from each subgroup separately. This should only be done informally by comparing the magnitudes of effect. Noting that either the effect or the test for heterogeneity in one subgroup is statistically significant whilst that in the other subgroup is not statistically significant does not indicate that the subgroup factor explains heterogeneity. Since different subgroups are likely to contain different amounts of information and thus have different abilities to detect effects, it is extremely misleading simply to compare the statistical significance of the results.

10.11.3.1 Is the effect different in different subgroups?

Valid investigations of whether an intervention works differently in different subgroups involve comparing the subgroups with each other. It is a mistake to compare within-subgroup inferences such as P values. If one subgroup analysis is statistically significant and another is not, then the latter may simply reflect a lack of information rather than a smaller (or absent) effect. When there are only two subgroups, non-overlap of the confidence intervals indicates statistical significance, but note that the confidence intervals can overlap to a small degree and the difference still be statistically significant.

A formal statistical approach should be used to examine differences among subgroups (see MECIR Box 10.11.a ). A simple significance test to investigate differences between two or more subgroups can be performed (Borenstein and Higgins 2013). This procedure consists of undertaking a standard test for heterogeneity across subgroup results rather than across individual study results. When the meta-analysis uses a fixed-effect inverse-variance weighted average approach, the method is exactly equivalent to the test described by Deeks and colleagues (Deeks et al 2001). An I 2 statistic is also computed for subgroup differences. This describes the percentage of the variability in effect estimates from the different subgroups that is due to genuine subgroup differences rather than sampling error (chance). Note that these methods for examining subgroup differences should be used only when the data in the subgroups are independent (i.e. they should not be used if the same study participants contribute to more than one of the subgroups in the forest plot).

If fixed-effect models are used for the analysis within each subgroup, then these statistics relate to differences in typical effects across different subgroups. If random-effects models are used for the analysis within each subgroup, then the statistics relate to variation in the mean effects in the different subgroups.

An alternative method for testing for differences between subgroups is to use meta-regression techniques, in which case a random-effects model is generally preferred (see Section 10.11.4 ). Tests for subgroup differences based on random-effects models may be regarded as preferable to those based on fixed-effect models, due to the high risk of false-positive results when a fixed-effect model is used to compare subgroups (Higgins and Thompson 2004).

MECIR Box 10.11.a Relevant expectations for conduct of intervention reviews

10.11.4 Meta-regression

If studies are divided into subgroups (see Section 10.11.2 ), this may be viewed as an investigation of how a categorical study characteristic is associated with the intervention effects in the meta-analysis. For example, studies in which allocation sequence concealment was adequate may yield different results from those in which it was inadequate. Here, allocation sequence concealment, being either adequate or inadequate, is a categorical characteristic at the study level. Meta-regression is an extension to subgroup analyses that allows the effect of continuous, as well as categorical, characteristics to be investigated, and in principle allows the effects of multiple factors to be investigated simultaneously (although this is rarely possible due to inadequate numbers of studies) (Thompson and Higgins 2002). Meta-regression should generally not be considered when there are fewer than ten studies in a meta-analysis.

Meta-regressions are similar in essence to simple regressions, in which an outcome variable is predicted according to the values of one or more explanatory variables . In meta-regression, the outcome variable is the effect estimate (for example, a mean difference, a risk difference, a log odds ratio or a log risk ratio). The explanatory variables are characteristics of studies that might influence the size of intervention effect. These are often called ‘potential effect modifiers’ or covariates. Meta-regressions usually differ from simple regressions in two ways. First, larger studies have more influence on the relationship than smaller studies, since studies are weighted by the precision of their respective effect estimate. Second, it is wise to allow for the residual heterogeneity among intervention effects not modelled by the explanatory variables. This gives rise to the term ‘random-effects meta-regression’, since the extra variability is incorporated in the same way as in a random-effects meta-analysis (Thompson and Sharp 1999).

The regression coefficient obtained from a meta-regression analysis will describe how the outcome variable (the intervention effect) changes with a unit increase in the explanatory variable (the potential effect modifier). The statistical significance of the regression coefficient is a test of whether there is a linear relationship between intervention effect and the explanatory variable. If the intervention effect is a ratio measure, the log-transformed value of the intervention effect should always be used in the regression model (see Chapter 6, Section 6.1.2.1 ), and the exponential of the regression coefficient will give an estimate of the relative change in intervention effect with a unit increase in the explanatory variable.

Meta-regression can also be used to investigate differences for categorical explanatory variables as done in subgroup analyses. If there are J subgroups, membership of particular subgroups is indicated by using J minus 1 dummy variables (which can only take values of zero or one) in the meta-regression model (as in standard linear regression modelling). The regression coefficients will estimate how the intervention effect in each subgroup differs from a nominated reference subgroup. The P value of each regression coefficient will indicate the strength of evidence against the null hypothesis that the characteristic is not associated with the intervention effect.

Meta-regression may be performed using the ‘metareg’ macro available for the Stata statistical package, or using the ‘metafor’ package for R, as well as other packages.

10.11.5 Selection of study characteristics for subgroup analyses and meta-regression

Authors need to be cautious about undertaking subgroup analyses, and interpreting any that they do. Some considerations are outlined here for selecting characteristics (also called explanatory variables, potential effect modifiers or covariates) that will be investigated for their possible influence on the size of the intervention effect. These considerations apply similarly to subgroup analyses and to meta-regressions. Further details may be obtained elsewhere (Oxman and Guyatt 1992, Berlin and Antman 1994).

10.11.5.1 Ensure that there are adequate studies to justify subgroup analyses and meta-regressions

It is very unlikely that an investigation of heterogeneity will produce useful findings unless there is a substantial number of studies. Typical advice for undertaking simple regression analyses: that at least ten observations (i.e. ten studies in a meta-analysis) should be available for each characteristic modelled. However, even this will be too few when the covariates are unevenly distributed across studies.

10.11.5.2 Specify characteristics in advance

Authors should, whenever possible, pre-specify characteristics in the protocol that later will be subject to subgroup analyses or meta-regression. The plan specified in the protocol should then be followed (data permitting), without undue emphasis on any particular findings (see MECIR Box 10.11.b ). Pre-specifying characteristics reduces the likelihood of spurious findings, first by limiting the number of subgroups investigated, and second by preventing knowledge of the studies’ results influencing which subgroups are analysed. True pre-specification is difficult in systematic reviews, because the results of some of the relevant studies are often known when the protocol is drafted. If a characteristic was overlooked in the protocol, but is clearly of major importance and justified by external evidence, then authors should not be reluctant to explore it. However, such post-hoc analyses should be identified as such.

MECIR Box 10.11.b Relevant expectations for conduct of intervention reviews

10.11.5.3 Select a small number of characteristics

The likelihood of a false-positive result among subgroup analyses and meta-regression increases with the number of characteristics investigated. It is difficult to suggest a maximum number of characteristics to look at, especially since the number of available studies is unknown in advance. If more than one or two characteristics are investigated it may be sensible to adjust the level of significance to account for making multiple comparisons.

10.11.5.4 Ensure there is scientific rationale for investigating each characteristic

Selection of characteristics should be motivated by biological and clinical hypotheses, ideally supported by evidence from sources other than the included studies. Subgroup analyses using characteristics that are implausible or clinically irrelevant are not likely to be useful and should be avoided. For example, a relationship between intervention effect and year of publication is seldom in itself clinically informative, and if identified runs the risk of initiating a post-hoc data dredge of factors that may have changed over time.

Prognostic factors are those that predict the outcome of a disease or condition, whereas effect modifiers are factors that influence how well an intervention works in affecting the outcome. Confusion between prognostic factors and effect modifiers is common in planning subgroup analyses, especially at the protocol stage. Prognostic factors are not good candidates for subgroup analyses unless they are also believed to modify the effect of intervention. For example, being a smoker may be a strong predictor of mortality within the next ten years, but there may not be reason for it to influence the effect of a drug therapy on mortality (Deeks 1998). Potential effect modifiers may include participant characteristics (age, setting), the precise interventions (dose of active intervention, choice of comparison intervention), how the study was done (length of follow-up) or methodology (design and quality).

10.11.5.5 Be aware that the effect of a characteristic may not always be identified

Many characteristics that might have important effects on how well an intervention works cannot be investigated using subgroup analysis or meta-regression. These are characteristics of participants that might vary substantially within studies, but that can only be summarized at the level of the study. An example is age. Consider a collection of clinical trials involving adults ranging from 18 to 60 years old. There may be a strong relationship between age and intervention effect that is apparent within each study. However, if the mean ages for the trials are similar, then no relationship will be apparent by looking at trial mean ages and trial-level effect estimates. The problem is one of aggregating individuals’ results and is variously known as aggregation bias, ecological bias or the ecological fallacy (Morgenstern 1982, Greenland 1987, Berlin et al 2002). It is even possible for the direction of the relationship across studies be the opposite of the direction of the relationship observed within each study.

10.11.5.6 Think about whether the characteristic is closely related to another characteristic (confounded)

The problem of ‘confounding’ complicates interpretation of subgroup analyses and meta-regressions and can lead to incorrect conclusions. Two characteristics are confounded if their influences on the intervention effect cannot be disentangled. For example, if those studies implementing an intensive version of a therapy happened to be the studies that involved patients with more severe disease, then one cannot tell which aspect is the cause of any difference in effect estimates between these studies and others. In meta-regression, co-linearity between potential effect modifiers leads to similar difficulties (Berlin and Antman 1994). Computing correlations between study characteristics will give some information about which study characteristics may be confounded with each other.

10.11.6 Interpretation of subgroup analyses and meta-regressions

Appropriate interpretation of subgroup analyses and meta-regressions requires caution (Oxman and Guyatt 1992).

• Subgroup comparisons are observational. It must be remembered that subgroup analyses and meta-regressions are entirely observational in their nature. These analyses investigate differences between studies. Even if individuals are randomized to one group or other within a clinical trial, they are not randomized to go in one trial or another. Hence, subgroup analyses suffer the limitations of any observational investigation, including possible bias through confounding by other study-level characteristics. Furthermore, even a genuine difference between subgroups is not necessarily due to the classification of the subgroups. As an example, a subgroup analysis of bone marrow transplantation for treating leukaemia might show a strong association between the age of a sibling donor and the success of the transplant. However, this probably does not mean that the age of donor is important. In fact, the age of the recipient is probably a key factor and the subgroup finding would simply be due to the strong association between the age of the recipient and the age of their sibling.  
• Was the analysis pre-specified or post hoc? Authors should state whether subgroup analyses were pre-specified or undertaken after the results of the studies had been compiled (post hoc). More reliance may be placed on a subgroup analysis if it was one of a small number of pre-specified analyses. Performing numerous post-hoc subgroup analyses to explain heterogeneity is a form of data dredging. Data dredging is condemned because it is usually possible to find an apparent, but false, explanation for heterogeneity by considering lots of different characteristics.  
• Is there indirect evidence in support of the findings? Differences between subgroups should be clinically plausible and supported by other external or indirect evidence, if they are to be convincing.  
• Is the magnitude of the difference practically important? If the magnitude of a difference between subgroups will not result in different recommendations for different subgroups, then it may be better to present only the overall analysis results.  
• Is there a statistically significant difference between subgroups? To establish whether there is a different effect of an intervention in different situations, the magnitudes of effects in different subgroups should be compared directly with each other. In particular, statistical significance of the results within separate subgroup analyses should not be compared (see Section 10.11.3.1 ).  
• Are analyses looking at within-study or between-study relationships? For patient and intervention characteristics, differences in subgroups that are observed within studies are more reliable than analyses of subsets of studies. If such within-study relationships are replicated across studies then this adds confidence to the findings.

10.11.7 Investigating the effect of underlying risk

One potentially important source of heterogeneity among a series of studies is when the underlying average risk of the outcome event varies between the studies. The underlying risk of a particular event may be viewed as an aggregate measure of case-mix factors such as age or disease severity. It is generally measured as the observed risk of the event in the comparator group of each study (the comparator group risk, or CGR). The notion is controversial in its relevance to clinical practice since underlying risk represents a summary of both known and unknown risk factors. Problems also arise because comparator group risk will depend on the length of follow-up, which often varies across studies. However, underlying risk has received particular attention in meta-analysis because the information is readily available once dichotomous data have been prepared for use in meta-analyses. Sharp provides a full discussion of the topic (Sharp 2001).

Intuition would suggest that participants are more or less likely to benefit from an effective intervention according to their risk status. However, the relationship between underlying risk and intervention effect is a complicated issue. For example, suppose an intervention is equally beneficial in the sense that for all patients it reduces the risk of an event, say a stroke, to 80% of the underlying risk. Then it is not equally beneficial in terms of absolute differences in risk in the sense that it reduces a 50% stroke rate by 10 percentage points to 40% (number needed to treat=10), but a 20% stroke rate by 4 percentage points to 16% (number needed to treat=25).

Use of different summary statistics (risk ratio, odds ratio and risk difference) will demonstrate different relationships with underlying risk. Summary statistics that show close to no relationship with underlying risk are generally preferred for use in meta-analysis (see Section 10.4.3 ).

Investigating any relationship between effect estimates and the comparator group risk is also complicated by a technical phenomenon known as regression to the mean. This arises because the comparator group risk forms an integral part of the effect estimate. A high risk in a comparator group, observed entirely by chance, will on average give rise to a higher than expected effect estimate, and vice versa. This phenomenon results in a false correlation between effect estimates and comparator group risks. There are methods, which require sophisticated software, that correct for regression to the mean (McIntosh 1996, Thompson et al 1997). These should be used for such analyses, and statistical expertise is recommended.

10.11.8 Dose-response analyses

The principles of meta-regression can be applied to the relationships between intervention effect and dose (commonly termed dose-response), treatment intensity or treatment duration (Greenland and Longnecker 1992, Berlin et al 1993). Conclusions about differences in effect due to differences in dose (or similar factors) are on stronger ground if participants are randomized to one dose or another within a study and a consistent relationship is found across similar studies. While authors should consider these effects, particularly as a possible explanation for heterogeneity, they should be cautious about drawing conclusions based on between-study differences. Authors should be particularly cautious about claiming that a dose-response relationship does not exist, given the low power of many meta-regression analyses to detect genuine relationships.

10.12 Missing data

10.12.1 types of missing data.

There are many potential sources of missing data in a systematic review or meta-analysis (see Table 10.12.a ). For example, a whole study may be missing from the review, an outcome may be missing from a study, summary data may be missing for an outcome, and individual participants may be missing from the summary data. Here we discuss a variety of potential sources of missing data, highlighting where more detailed discussions are available elsewhere in the Handbook .

Whole studies may be missing from a review because they are never published, are published in obscure places, are rarely cited, or are inappropriately indexed in databases. Thus, review authors should always be aware of the possibility that they have failed to identify relevant studies. There is a strong possibility that such studies are missing because of their ‘uninteresting’ or ‘unwelcome’ findings (that is, in the presence of publication bias). This problem is discussed at length in Chapter 13 . Details of comprehensive search methods are provided in Chapter 4 .

Some studies might not report any information on outcomes of interest to the review. For example, there may be no information on quality of life, or on serious adverse effects. It is often difficult to determine whether this is because the outcome was not measured or because the outcome was not reported. Furthermore, failure to report that outcomes were measured may be dependent on the unreported results (selective outcome reporting bias; see Chapter 7, Section 7.2.3.3 ). Similarly, summary data for an outcome, in a form that can be included in a meta-analysis, may be missing. A common example is missing standard deviations (SDs) for continuous outcomes. This is often a problem when change-from-baseline outcomes are sought. We discuss imputation of missing SDs in Chapter 6, Section 6.5.2.8 . Other examples of missing summary data are missing sample sizes (particularly those for each intervention group separately), numbers of events, standard errors, follow-up times for calculating rates, and sufficient details of time-to-event outcomes. Inappropriate analyses of studies, for example of cluster-randomized and crossover trials, can lead to missing summary data. It is sometimes possible to approximate the correct analyses of such studies, for example by imputing correlation coefficients or SDs, as discussed in Chapter 23, Section 23.1 , for cluster-randomized studies and Chapter 23,Section 23.2 , for crossover trials. As a general rule, most methodologists believe that missing summary data (e.g. ‘no usable data’) should not be used as a reason to exclude a study from a systematic review. It is more appropriate to include the study in the review, and to discuss the potential implications of its absence from a meta-analysis.

It is likely that in some, if not all, included studies, there will be individuals missing from the reported results. Review authors are encouraged to consider this problem carefully (see MECIR Box 10.12.a ). We provide further discussion of this problem in Section 10.12.3 ; see also Chapter 8, Section 8.5 .

Missing data can also affect subgroup analyses. If subgroup analyses or meta-regressions are planned (see Section 10.11 ), they require details of the study-level characteristics that distinguish studies from one another. If these are not available for all studies, review authors should consider asking the study authors for more information.

Table 10.12.a Types of missing data in a meta-analysis

MECIR Box 10.12.a Relevant expectations for conduct of intervention reviews

10.12.2 General principles for dealing with missing data

There is a large literature of statistical methods for dealing with missing data. Here we briefly review some key concepts and make some general recommendations for Cochrane Review authors. It is important to think why data may be missing. Statisticians often use the terms ‘missing at random’ and ‘not missing at random’ to represent different scenarios.

Data are said to be ‘missing at random’ if the fact that they are missing is unrelated to actual values of the missing data. For instance, if some quality-of-life questionnaires were lost in the postal system, this would be unlikely to be related to the quality of life of the trial participants who completed the forms. In some circumstances, statisticians distinguish between data ‘missing at random’ and data ‘missing completely at random’, although in the context of a systematic review the distinction is unlikely to be important. Data that are missing at random may not be important. Analyses based on the available data will often be unbiased, although based on a smaller sample size than the original data set.

Data are said to be ‘not missing at random’ if the fact that they are missing is related to the actual missing data. For instance, in a depression trial, participants who had a relapse of depression might be less likely to attend the final follow-up interview, and more likely to have missing outcome data. Such data are ‘non-ignorable’ in the sense that an analysis of the available data alone will typically be biased. Publication bias and selective reporting bias lead by definition to data that are ‘not missing at random’, and attrition and exclusions of individuals within studies often do as well.

The principal options for dealing with missing data are:

• analysing only the available data (i.e. ignoring the missing data);
• imputing the missing data with replacement values, and treating these as if they were observed (e.g. last observation carried forward, imputing an assumed outcome such as assuming all were poor outcomes, imputing the mean, imputing based on predicted values from a regression analysis);
• imputing the missing data and accounting for the fact that these were imputed with uncertainty (e.g. multiple imputation, simple imputation methods (as point 2) with adjustment to the standard error); and
• using statistical models to allow for missing data, making assumptions about their relationships with the available data.

Option 2 is practical in most circumstances and very commonly used in systematic reviews. However, it fails to acknowledge uncertainty in the imputed values and results, typically, in confidence intervals that are too narrow. Options 3 and 4 would require involvement of a knowledgeable statistician.

Five general recommendations for dealing with missing data in Cochrane Reviews are as follows:

• Whenever possible, contact the original investigators to request missing data.
• Make explicit the assumptions of any methods used to address missing data: for example, that the data are assumed missing at random, or that missing values were assumed to have a particular value such as a poor outcome.
• Follow the guidance in Chapter 8 to assess risk of bias due to missing outcome data in randomized trials.
• Perform sensitivity analyses to assess how sensitive results are to reasonable changes in the assumptions that are made (see Section 10.14 ).
• Address the potential impact of missing data on the findings of the review in the Discussion section.

10.12.3 Dealing with missing outcome data from individual participants

Review authors may undertake sensitivity analyses to assess the potential impact of missing outcome data, based on assumptions about the relationship between missingness in the outcome and its true value. Several methods are available (Akl et al 2015). For dichotomous outcomes, Higgins and colleagues propose a strategy involving different assumptions about how the risk of the event among the missing participants differs from the risk of the event among the observed participants, taking account of uncertainty introduced by the assumptions (Higgins et al 2008a). Akl and colleagues propose a suite of simple imputation methods, including a similar approach to that of Higgins and colleagues based on relative risks of the event in missing versus observed participants. Similar ideas can be applied to continuous outcome data (Ebrahim et al 2013, Ebrahim et al 2014). Particular care is required to avoid double counting events, since it can be unclear whether reported numbers of events in trial reports apply to the full randomized sample or only to those who did not drop out (Akl et al 2016).

Although there is a tradition of implementing ‘worst case’ and ‘best case’ analyses clarifying the extreme boundaries of what is theoretically possible, such analyses may not be informative for the most plausible scenarios (Higgins et al 2008a).

10.13 Bayesian approaches to meta-analysis

Bayesian statistics is an approach to statistics based on a different philosophy from that which underlies significance tests and confidence intervals. It is essentially about updating of evidence. In a Bayesian analysis, initial uncertainty is expressed through a prior distribution about the quantities of interest. Current data and assumptions concerning how they were generated are summarized in the likelihood . The posterior distribution for the quantities of interest can then be obtained by combining the prior distribution and the likelihood. The likelihood summarizes both the data from studies included in the meta-analysis (for example, 2×2 tables from randomized trials) and the meta-analysis model (for example, assuming a fixed effect or random effects). The result of the analysis is usually presented as a point estimate and 95% credible interval from the posterior distribution for each quantity of interest, which look much like classical estimates and confidence intervals. Potential advantages of Bayesian analyses are summarized in Box 10.13.a . Bayesian analysis may be performed using WinBUGS software (Smith et al 1995, Lunn et al 2000), within R (Röver 2017), or – for some applications – using standard meta-regression software with a simple trick (Rhodes et al 2016).

A difference between Bayesian analysis and classical meta-analysis is that the interpretation is directly in terms of belief: a 95% credible interval for an odds ratio is that region in which we believe the odds ratio to lie with probability 95%. This is how many practitioners actually interpret a classical confidence interval, but strictly in the classical framework the 95% refers to the long-term frequency with which 95% intervals contain the true value. The Bayesian framework also allows a review author to calculate the probability that the odds ratio has a particular range of values, which cannot be done in the classical framework. For example, we can determine the probability that the odds ratio is less than 1 (which might indicate a beneficial effect of an experimental intervention), or that it is no larger than 0.8 (which might indicate a clinically important effect). It should be noted that these probabilities are specific to the choice of the prior distribution. Different meta-analysts may analyse the same data using different prior distributions and obtain different results. It is therefore important to carry out sensitivity analyses to investigate how the results depend on any assumptions made.

In the context of a meta-analysis, prior distributions are needed for the particular intervention effect being analysed (such as the odds ratio or the mean difference) and – in the context of a random-effects meta-analysis – on the amount of heterogeneity among intervention effects across studies. Prior distributions may represent subjective belief about the size of the effect, or may be derived from sources of evidence not included in the meta-analysis, such as information from non-randomized studies of the same intervention or from randomized trials of other interventions. The width of the prior distribution reflects the degree of uncertainty about the quantity. When there is little or no information, a ‘non-informative’ prior can be used, in which all values across the possible range are equally likely.

Most Bayesian meta-analyses use non-informative (or very weakly informative) prior distributions to represent beliefs about intervention effects, since many regard it as controversial to combine objective trial data with subjective opinion. However, prior distributions are increasingly used for the extent of among-study variation in a random-effects analysis. This is particularly advantageous when the number of studies in the meta-analysis is small, say fewer than five or ten. Libraries of data-based prior distributions are available that have been derived from re-analyses of many thousands of meta-analyses in the Cochrane Database of Systematic Reviews (Turner et al 2012).

Box 10.13.a Some potential advantages of Bayesian meta-analysis

Statistical expertise is strongly recommended for review authors who wish to carry out Bayesian analyses. There are several good texts (Sutton et al 2000, Sutton and Abrams 2001, Spiegelhalter et al 2004).

10.14 Sensitivity analyses

The process of undertaking a systematic review involves a sequence of decisions. Whilst many of these decisions are clearly objective and non-contentious, some will be somewhat arbitrary or unclear. For instance, if eligibility criteria involve a numerical value, the choice of value is usually arbitrary: for example, defining groups of older people may reasonably have lower limits of 60, 65, 70 or 75 years, or any value in between. Other decisions may be unclear because a study report fails to include the required information. Some decisions are unclear because the included studies themselves never obtained the information required: for example, the outcomes of those who were lost to follow-up. Further decisions are unclear because there is no consensus on the best statistical method to use for a particular problem.

It is highly desirable to prove that the findings from a systematic review are not dependent on such arbitrary or unclear decisions by using sensitivity analysis (see MECIR Box 10.14.a ). A sensitivity analysis is a repeat of the primary analysis or meta-analysis in which alternative decisions or ranges of values are substituted for decisions that were arbitrary or unclear. For example, if the eligibility of some studies in the meta-analysis is dubious because they do not contain full details, sensitivity analysis may involve undertaking the meta-analysis twice: the first time including all studies and, second, including only those that are definitely known to be eligible. A sensitivity analysis asks the question, ‘Are the findings robust to the decisions made in the process of obtaining them?’

MECIR Box 10.14.a Relevant expectations for conduct of intervention reviews

There are many decision nodes within the systematic review process that can generate a need for a sensitivity analysis. Examples include:

Searching for studies:

• Should abstracts whose results cannot be confirmed in subsequent publications be included in the review?

Eligibility criteria:

• Characteristics of participants: where a majority but not all people in a study meet an age range, should the study be included?
• Characteristics of the intervention: what range of doses should be included in the meta-analysis?
• Characteristics of the comparator: what criteria are required to define usual care to be used as a comparator group?
• Characteristics of the outcome: what time point or range of time points are eligible for inclusion?
• Study design: should blinded and unblinded outcome assessment be included, or should study inclusion be restricted by other aspects of methodological criteria?

What data should be analysed?

• Time-to-event data: what assumptions of the distribution of censored data should be made?
• Continuous data: where standard deviations are missing, when and how should they be imputed? Should analyses be based on change scores or on post-intervention values?
• Ordinal scales: what cut-point should be used to dichotomize short ordinal scales into two groups?
• Cluster-randomized trials: what values of the intraclass correlation coefficient should be used when trial analyses have not been adjusted for clustering?
• Crossover trials: what values of the within-subject correlation coefficient should be used when this is not available in primary reports?
• All analyses: what assumptions should be made about missing outcomes? Should adjusted or unadjusted estimates of intervention effects be used?

Analysis methods:

• Should fixed-effect or random-effects methods be used for the analysis?
• For dichotomous outcomes, should odds ratios, risk ratios or risk differences be used?
• For continuous outcomes, where several scales have assessed the same dimension, should results be analysed as a standardized mean difference across all scales or as mean differences individually for each scale?

Some sensitivity analyses can be pre-specified in the study protocol, but many issues suitable for sensitivity analysis are only identified during the review process where the individual peculiarities of the studies under investigation are identified. When sensitivity analyses show that the overall result and conclusions are not affected by the different decisions that could be made during the review process, the results of the review can be regarded with a higher degree of certainty. Where sensitivity analyses identify particular decisions or missing information that greatly influence the findings of the review, greater resources can be deployed to try and resolve uncertainties and obtain extra information, possibly through contacting trial authors and obtaining individual participant data. If this cannot be achieved, the results must be interpreted with an appropriate degree of caution. Such findings may generate proposals for further investigations and future research.

Reporting of sensitivity analyses in a systematic review may best be done by producing a summary table. Rarely is it informative to produce individual forest plots for each sensitivity analysis undertaken.

Sensitivity analyses are sometimes confused with subgroup analysis. Although some sensitivity analyses involve restricting the analysis to a subset of the totality of studies, the two methods differ in two ways. First, sensitivity analyses do not attempt to estimate the effect of the intervention in the group of studies removed from the analysis, whereas in subgroup analyses, estimates are produced for each subgroup. Second, in sensitivity analyses, informal comparisons are made between different ways of estimating the same thing, whereas in subgroup analyses, formal statistical comparisons are made across the subgroups.

10.15 Chapter information

Editors: Jonathan J Deeks, Julian PT Higgins, Douglas G Altman; on behalf of the Cochrane Statistical Methods Group

Contributing authors: Douglas Altman, Deborah Ashby, Jacqueline Birks, Michael Borenstein, Marion Campbell, Jonathan Deeks, Matthias Egger, Julian Higgins, Joseph Lau, Keith O’Rourke, Gerta Rücker, Rob Scholten, Jonathan Sterne, Simon Thompson, Anne Whitehead

Acknowledgements: We are grateful to the following for commenting helpfully on earlier drafts: Bodil Als-Nielsen, Deborah Ashby, Jesse Berlin, Joseph Beyene, Jacqueline Birks, Michael Bracken, Marion Campbell, Chris Cates, Wendong Chen, Mike Clarke, Albert Cobos, Esther Coren, Francois Curtin, Roberto D’Amico, Keith Dear, Heather Dickinson, Diana Elbourne, Simon Gates, Paul Glasziou, Christian Gluud, Peter Herbison, Sally Hollis, David Jones, Steff Lewis, Tianjing Li, Joanne McKenzie, Philippa Middleton, Nathan Pace, Craig Ramsey, Keith O’Rourke, Rob Scholten, Guido Schwarzer, Jack Sinclair, Jonathan Sterne, Simon Thompson, Andy Vail, Clarine van Oel, Paula Williamson and Fred Wolf.

Funding: JJD received support from the National Institute for Health Research (NIHR) Birmingham Biomedical Research Centre at the University Hospitals Birmingham NHS Foundation Trust and the University of Birmingham. JPTH is a member of the NIHR Biomedical Research Centre at University Hospitals Bristol NHS Foundation Trust and the University of Bristol. JPTH received funding from National Institute for Health Research Senior Investigator award NF-SI-0617-10145. The views expressed are those of the author(s) and not necessarily those of the NHS, the NIHR or the Department of Health.

10.16 References

Agresti A. An Introduction to Categorical Data Analysis . New York (NY): John Wiley & Sons; 1996.

Akl EA, Kahale LA, Agoritsas T, Brignardello-Petersen R, Busse JW, Carrasco-Labra A, Ebrahim S, Johnston BC, Neumann I, Sola I, Sun X, Vandvik P, Zhang Y, Alonso-Coello P, Guyatt G. Handling trial participants with missing outcome data when conducting a meta-analysis: a systematic survey of proposed approaches. Systematic Reviews 2015; 4 : 98.

Akl EA, Kahale LA, Ebrahim S, Alonso-Coello P, Schünemann HJ, Guyatt GH. Three challenges described for identifying participants with missing data in trials reports, and potential solutions suggested to systematic reviewers. Journal of Clinical Epidemiology 2016; 76 : 147-154.

Altman DG, Bland JM. Detecting skewness from summary information. BMJ 1996; 313 : 1200.

Anzures-Cabrera J, Sarpatwari A, Higgins JPT. Expressing findings from meta-analyses of continuous outcomes in terms of risks. Statistics in Medicine 2011; 30 : 2967-2985.

Berlin JA, Longnecker MP, Greenland S. Meta-analysis of epidemiologic dose-response data. Epidemiology 1993; 4 : 218-228.

Berlin JA, Antman EM. Advantages and limitations of metaanalytic regressions of clinical trials data. Online Journal of Current Clinical Trials 1994; Doc No 134 .

Berlin JA, Santanna J, Schmid CH, Szczech LA, Feldman KA, Group A-LAITS. Individual patient- versus group-level data meta-regressions for the investigation of treatment effect modifiers: ecological bias rears its ugly head. Statistics in Medicine 2002; 21 : 371-387.

Borenstein M, Hedges LV, Higgins JPT, Rothstein HR. A basic introduction to fixed-effect and random-effects models for meta-analysis. Research Synthesis Methods 2010; 1 : 97-111.

Borenstein M, Higgins JPT. Meta-analysis and subgroups. Prev Sci 2013; 14 : 134-143.

Bradburn MJ, Deeks JJ, Berlin JA, Russell Localio A. Much ado about nothing: a comparison of the performance of meta-analytical methods with rare events. Statistics in Medicine 2007; 26 : 53-77.

Chinn S. A simple method for converting an odds ratio to effect size for use in meta-analysis. Statistics in Medicine 2000; 19 : 3127-3131.

da Costa BR, Nuesch E, Rutjes AW, Johnston BC, Reichenbach S, Trelle S, Guyatt GH, Jüni P. Combining follow-up and change data is valid in meta-analyses of continuous outcomes: a meta-epidemiological study. Journal of Clinical Epidemiology 2013; 66 : 847-855.

Deeks JJ. Systematic reviews of published evidence: Miracles or minefields? Annals of Oncology 1998; 9 : 703-709.

Deeks JJ, Altman DG, Bradburn MJ. Statistical methods for examining heterogeneity and combining results from several studies in meta-analysis. In: Egger M, Davey Smith G, Altman DG, editors. Systematic Reviews in Health Care: Meta-analysis in Context . 2nd edition ed. London (UK): BMJ Publication Group; 2001. p. 285-312.

Deeks JJ. Issues in the selection of a summary statistic for meta-analysis of clinical trials with binary outcomes. Statistics in Medicine 2002; 21 : 1575-1600.

DerSimonian R, Laird N. Meta-analysis in clinical trials. Controlled Clinical Trials 1986; 7 : 177-188.

DiGuiseppi C, Higgins JPT. Interventions for promoting smoke alarm ownership and function. Cochrane Database of Systematic Reviews 2001; 2 : CD002246.

Ebrahim S, Akl EA, Mustafa RA, Sun X, Walter SD, Heels-Ansdell D, Alonso-Coello P, Johnston BC, Guyatt GH. Addressing continuous data for participants excluded from trial analysis: a guide for systematic reviewers. Journal of Clinical Epidemiology 2013; 66 : 1014-1021 e1011.

Ebrahim S, Johnston BC, Akl EA, Mustafa RA, Sun X, Walter SD, Heels-Ansdell D, Alonso-Coello P, Guyatt GH. Addressing continuous data measured with different instruments for participants excluded from trial analysis: a guide for systematic reviewers. Journal of Clinical Epidemiology 2014; 67 : 560-570.

Efthimiou O. Practical guide to the meta-analysis of rare events. Evidence-Based Mental Health 2018; 21 : 72-76.

Egger M, Davey Smith G, Schneider M, Minder C. Bias in meta-analysis detected by a simple, graphical test. BMJ 1997; 315 : 629-634.

Engels EA, Schmid CH, Terrin N, Olkin I, Lau J. Heterogeneity and statistical significance in meta-analysis: an empirical study of 125 meta-analyses. Statistics in Medicine 2000; 19 : 1707-1728.

Greenland S, Robins JM. Estimation of a common effect parameter from sparse follow-up data. Biometrics 1985; 41 : 55-68.

Greenland S. Quantitative methods in the review of epidemiologic literature. Epidemiologic Reviews 1987; 9 : 1-30.

Greenland S, Longnecker MP. Methods for trend estimation from summarized dose-response data, with applications to meta-analysis. American Journal of Epidemiology 1992; 135 : 1301-1309.

Guevara JP, Berlin JA, Wolf FM. Meta-analytic methods for pooling rates when follow-up duration varies: a case study. BMC Medical Research Methodology 2004; 4 : 17.

Hartung J, Knapp G. A refined method for the meta-analysis of controlled clinical trials with binary outcome. Statistics in Medicine 2001; 20 : 3875-3889.

Hasselblad V, McCrory DC. Meta-analytic tools for medical decision making: A practical guide. Medical Decision Making 1995; 15 : 81-96.

Higgins JPT, Thompson SG. Quantifying heterogeneity in a meta-analysis. Statistics in Medicine 2002; 21 : 1539-1558.

Higgins JPT, Thompson SG, Deeks JJ, Altman DG. Measuring inconsistency in meta-analyses. BMJ 2003; 327 : 557-560.

Higgins JPT, Thompson SG. Controlling the risk of spurious findings from meta-regression. Statistics in Medicine 2004; 23 : 1663-1682.

Higgins JPT, White IR, Wood AM. Imputation methods for missing outcome data in meta-analysis of clinical trials. Clinical Trials 2008a; 5 : 225-239.

Higgins JPT, White IR, Anzures-Cabrera J. Meta-analysis of skewed data: combining results reported on log-transformed or raw scales. Statistics in Medicine 2008b; 27 : 6072-6092.

Higgins JPT, Thompson SG, Spiegelhalter DJ. A re-evaluation of random-effects meta-analysis. Journal of the Royal Statistical Society: Series A (Statistics in Society) 2009; 172 : 137-159.

Kjaergard LL, Villumsen J, Gluud C. Reported methodologic quality and discrepancies between large and small randomized trials in meta-analyses. Annals of Internal Medicine 2001; 135 : 982-989.

Langan D, Higgins JPT, Simmonds M. An empirical comparison of heterogeneity variance estimators in 12 894 meta-analyses. Research Synthesis Methods 2015; 6 : 195-205.

Langan D, Higgins JPT, Simmonds M. Comparative performance of heterogeneity variance estimators in meta-analysis: a review of simulation studies. Research Synthesis Methods 2017; 8 : 181-198.

Langan D, Higgins JPT, Jackson D, Bowden J, Veroniki AA, Kontopantelis E, Viechtbauer W, Simmonds M. A comparison of heterogeneity variance estimators in simulated random-effects meta-analyses. Research Synthesis Methods 2019; 10 : 83-98.

Lewis S, Clarke M. Forest plots: trying to see the wood and the trees. BMJ 2001; 322 : 1479-1480.

Lunn DJ, Thomas A, Best N, Spiegelhalter D. WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility. Statistics and Computing 2000; 10 : 325-337.

Mantel N, Haenszel W. Statistical aspects of the analysis of data from retrospective studies of disease. Journal of the National Cancer Institute 1959; 22 : 719-748.

McIntosh MW. The population risk as an explanatory variable in research synthesis of clinical trials. Statistics in Medicine 1996; 15 : 1713-1728.

Morgenstern H. Uses of ecologic analysis in epidemiologic research. American Journal of Public Health 1982; 72 : 1336-1344.

Oxman AD, Guyatt GH. A consumers guide to subgroup analyses. Annals of Internal Medicine 1992; 116 : 78-84.

Peto R, Collins R, Gray R. Large-scale randomized evidence: large, simple trials and overviews of trials. Journal of Clinical Epidemiology 1995; 48 : 23-40.

Poole C, Greenland S. Random-effects meta-analyses are not always conservative. American Journal of Epidemiology 1999; 150 : 469-475.

Rhodes KM, Turner RM, White IR, Jackson D, Spiegelhalter DJ, Higgins JPT. Implementing informative priors for heterogeneity in meta-analysis using meta-regression and pseudo data. Statistics in Medicine 2016; 35 : 5495-5511.

Rice K, Higgins JPT, Lumley T. A re-evaluation of fixed effect(s) meta-analysis. Journal of the Royal Statistical Society Series A (Statistics in Society) 2018; 181 : 205-227.

Riley RD, Higgins JPT, Deeks JJ. Interpretation of random effects meta-analyses. BMJ 2011; 342 : d549.

Röver C. Bayesian random-effects meta-analysis using the bayesmeta R package 2017. https://arxiv.org/abs/1711.08683 .

Rücker G, Schwarzer G, Carpenter J, Olkin I. Why add anything to nothing? The arcsine difference as a measure of treatment effect in meta-analysis with zero cells. Statistics in Medicine 2009; 28 : 721-738.

Sharp SJ. Analysing the relationship between treatment benefit and underlying risk: precautions and practical recommendations. In: Egger M, Davey Smith G, Altman DG, editors. Systematic Reviews in Health Care: Meta-analysis in Context . 2nd edition ed. London (UK): BMJ Publication Group; 2001. p. 176-188.

Sidik K, Jonkman JN. A simple confidence interval for meta-analysis. Statistics in Medicine 2002; 21 : 3153-3159.

Simmonds MC, Tierney J, Bowden J, Higgins JPT. Meta-analysis of time-to-event data: a comparison of two-stage methods. Research Synthesis Methods 2011; 2 : 139-149.

Sinclair JC, Bracken MB. Clinically useful measures of effect in binary analyses of randomized trials. Journal of Clinical Epidemiology 1994; 47 : 881-889.

Smith TC, Spiegelhalter DJ, Thomas A. Bayesian approaches to random-effects meta-analysis: a comparative study. Statistics in Medicine 1995; 14 : 2685-2699.

Spiegelhalter DJ, Abrams KR, Myles JP. Bayesian Approaches to Clinical Trials and Health-Care Evaluation . Chichester (UK): John Wiley & Sons; 2004.

Spittal MJ, Pirkis J, Gurrin LC. Meta-analysis of incidence rate data in the presence of zero events. BMC Medical Research Methodology 2015; 15 : 42.

Sutton AJ, Abrams KR, Jones DR, Sheldon TA, Song F. Methods for Meta-analysis in Medical Research . Chichester (UK): John Wiley & Sons; 2000.

Sutton AJ, Abrams KR. Bayesian methods in meta-analysis and evidence synthesis. Statistical Methods in Medical Research 2001; 10 : 277-303.

Sweeting MJ, Sutton AJ, Lambert PC. What to add to nothing? Use and avoidance of continuity corrections in meta-analysis of sparse data. Statistics in Medicine 2004; 23 : 1351-1375.

Thompson SG, Smith TC, Sharp SJ. Investigating underlying risk as a source of heterogeneity in meta-analysis. Statistics in Medicine 1997; 16 : 2741-2758.

Thompson SG, Sharp SJ. Explaining heterogeneity in meta-analysis: a comparison of methods. Statistics in Medicine 1999; 18 : 2693-2708.

Thompson SG, Higgins JPT. How should meta-regression analyses be undertaken and interpreted? Statistics in Medicine 2002; 21 : 1559-1574.

Turner RM, Davey J, Clarke MJ, Thompson SG, Higgins JPT. Predicting the extent of heterogeneity in meta-analysis, using empirical data from the Cochrane Database of Systematic Reviews. International Journal of Epidemiology 2012; 41 : 818-827.

Veroniki AA, Jackson D, Viechtbauer W, Bender R, Bowden J, Knapp G, Kuss O, Higgins JPT, Langan D, Salanti G. Methods to estimate the between-study variance and its uncertainty in meta-analysis. Research Synthesis Methods 2016; 7 : 55-79.

Whitehead A, Jones NMB. A meta-analysis of clinical trials involving different classifications of response into ordered categories. Statistics in Medicine 1994; 13 : 2503-2515.

Yusuf S, Peto R, Lewis J, Collins R, Sleight P. Beta blockade during and after myocardial infarction: an overview of the randomized trials. Progress in Cardiovascular Diseases 1985; 27 : 335-371.

Yusuf S, Wittes J, Probstfield J, Tyroler HA. Analysis and interpretation of treatment effects in subgroups of patients in randomized clinical trials. JAMA 1991; 266 : 93-98.

For permission to re-use material from the Handbook (either academic or commercial), please see here for full details.

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

• Advanced Search
• Journal List
• Hippokratia
• v.14(Suppl 1); 2010 Dec

Meta-analysis in medical research

The objectives of this paper are to provide an introduction to meta-analysis and to discuss the rationale for this type of research and other general considerations. Methods used to produce a rigorous meta-analysis are highlighted and some aspects of presentation and interpretation of meta-analysis are discussed.

Meta-analysis is a quantitative, formal, epidemiological study design used to systematically assess previous research studies to derive conclusions about that body of research. Outcomes from a meta-analysis may include a more precise estimate of the effect of treatment or risk factor for disease, or other outcomes, than any individual study contributing to the pooled analysis. The examination of variability or heterogeneity in study results is also a critical outcome. The benefits of meta-analysis include a consolidated and quantitative review of a large, and often complex, sometimes apparently conflicting, body of literature. The specification of the outcome and hypotheses that are tested is critical to the conduct of meta-analyses, as is a sensitive literature search. A failure to identify the majority of existing studies can lead to erroneous conclusions; however, there are methods of examining data to identify the potential for studies to be missing; for example, by the use of funnel plots. Rigorously conducted meta-analyses are useful tools in evidence-based medicine. The need to integrate findings from many studies ensures that meta-analytic research is desirable and the large body of research now generated makes the conduct of this research feasible.

Important medical questions are typically studied more than once, often by different research teams in different locations. In many instances, the results of these multiple small studies of an issue are diverse and conflicting, which makes the clinical decision-making difficult. The need to arrive at decisions affecting clinical practise fostered the momentum toward "evidence-based medicine" 1 – 2 . Evidence-based medicine may be defined as the systematic, quantitative, preferentially experimental approach to obtaining and using medical information. Therefore, meta-analysis, a statistical procedure that integrates the results of several independent studies, plays a central role in evidence-based medicine. In fact, in the hierarchy of evidence ( Figure 1 ), where clinical evidence is ranked according to the strength of the freedom from various biases that beset medical research, meta-analyses are in the top. In contrast, animal research, laboratory studies, case series and case reports have little clinical value as proof, hence being in the bottom.

Meta-analysis did not begin to appear regularly in the medical literature until the late 1970s but since then a plethora of meta-analyses have emerged and the growth is exponential over time ( Figure 2 ) 3 . Moreover, it has been shown that meta-analyses are the most frequently cited form of clinical research 4 . The merits and perils of the somewhat mysterious procedure of meta-analysis, however, continue to be debated in the medical community 5 – 8 . The objectives of this paper are to introduce meta-analysis and to discuss the rationale for this type of research and other general considerations.

Meta-Analysis and Systematic Review

Glass first defined meta-analysis in the social science literature as "The statistical analysis of a large collection of analysis results from individual studies for the purpose of integrating the findings" 9 . Meta-analysis is a quantitative, formal, epidemiological study design used to systematically assess the results of previous research to derive conclusions about that body of research. Typically, but not necessarily, the study is based on randomized, controlled clinical trials. Outcomes from a meta-analysis may include a more precise estimate of the effect of treatment or risk factor for disease, or other outcomes, than any individual study contributing to the pooled analysis. Identifying sources of variation in responses; that is, examining heterogeneity of a group of studies, and generalizability of responses can lead to more effective treatments or modifications of management. Examination of heterogeneity is perhaps the most important task in meta-analysis. The Cochrane collaboration has been a long-standing, rigorous, and innovative leader in developing methods in the field 10 . Major contributions include the development of protocols that provide structure for literature search methods, and new and extended analytic and diagnostic methods for evaluating the output of meta-analyses. Use of the methods outlined in the handbook should provide a consistent approach to the conduct of meta-analysis. Moreover, a useful guide to improve reporting of systematic reviews and meta-analyses is the PRISMA (Preferred Reporting Items for Systematic reviews and Meta-analyses) statement that replaced the QUOROM (QUality Of Reporting of Meta-analyses) statement 11 – 13 .

Meta-analyses are a subset of systematic review. A systematic review attempts to collate empirical evidence that fits prespecified eligibility criteria to answer a specific research question. The key characteristics of a systematic review are a clearly stated set of objectives with predefined eligibility criteria for studies; an explicit, reproducible methodology; a systematic search that attempts to identify all studies that meet the eligibility criteria; an assessment of the validity of the findings of the included studies (e.g., through the assessment of risk of bias); and a systematic presentation and synthesis of the attributes and findings from the studies used. Systematic methods are used to minimize bias, thus providing more reliable findings from which conclusions can be drawn and decisions made than traditional review methods 14 , 15 . Systematic reviews need not contain a meta-analysisthere are times when it is not appropriate or possible; however, many systematic reviews contain meta-analyses 16 .

The inclusion of observational medical studies in meta-analyses led to considerable debate over the validity of meta-analytical approaches, as there was necessarily a concern that the observational studies were likely to be subject to unidentified sources of confounding and risk modification 17 . Pooling such findings may not lead to more certain outcomes. Moreover, an empirical study showed that in meta-analyses were both randomized and non-randomized was included, nonrandomized studies tended to show larger treatment effects 18 .

Meta-analyses are conducted to assess the strength of evidence present on a disease and treatment. One aim is to determine whether an effect exists; another aim is to determine whether the effect is positive or negative and, ideally, to obtain a single summary estimate of the effect. The results of a meta-analysis can improve precision of estimates of effect, answer questions not posed by the individual studies, settle controversies arising from apparently conflicting studies, and generate new hypotheses. In particular, the examination of heterogeneity is vital to the development of new hypotheses.

Individual or Aggregated Data

The majority of meta-analyses are based on a series of studies to produce a point estimate of an effect and measures of the precision of that estimate. However, methods have been developed for the meta-analyses to be conducted on data obtained from original trials 19 , 20 . This approach may be considered the "gold standard" in metaanalysis because it offers advantages over analyses using aggregated data, including a greater ability to validate the quality of data and to conduct appropriate statistical analysis. Further, it is easier to explore differences in effect across subgroups within the study population than with aggregated data. The use of standardized individual-level information may help to avoid the problems encountered in meta-analyses of prognostic factors 21 , 22 . It is the best way to obtain a more global picture of the natural history and predictors of risk for major outcomes, such as in scleroderma 23 – 26 .This approach relies on cooperation between researchers who conducted the relevant studies. Researchers who are aware of the potential to contribute or conduct these studies will provide and obtain additional benefits by careful maintenance of original databases and making these available for future studies.

Literature Search

A sound meta-analysis is characterized by a thorough and disciplined literature search. A clear definition of hypotheses to be investigated provides the framework for such an investigation. According to the PRISMA statement, an explicit statement of questions being addressed with reference to participants, interventions, comparisons, outcomes and study design (PICOS) should be provided 11 , 12 . It is important to obtain all relevant studies, because loss of studies can lead to bias in the study. Typically, published papers and abstracts are identified by a computerized literature search of electronic databases that can include PubMed ( www.ncbi.nlm.nih.gov./entrez/query.fcgi ), ScienceDirect ( www.sciencedirect.com ), Scirus ( www.scirus.com/srsapp ), ISI Web of Knowledge ( http://www.isiwebofknowledge.com ), Google Scholar ( http://scholar.google.com ) and CENTRAL (Cochrane Central Register of Controlled Trials, http://www.mrw.interscience.wiley.com/cochrane/cochrane_clcentral_articles_fs.htm ). PRISMA statement recommends that a full electronic search strategy for at least one major database to be presented 12 . Database searches should be augmented with hand searches of library resources for relevant papers, books, abstracts, and conference proceedings. Crosschecking of references, citations in review papers, and communication with scientists who have been working in the relevant field are important methods used to provide a comprehensive search. Communication with pharmaceutical companies manufacturing and distributing test products can be appropriate for studies examining the use of pharmaceutical interventions.

It is not feasible to find absolutely every relevant study on a subject. Some or even many studies may not be published, and those that are might not be indexed in computer-searchable databases. Useful sources for unpublished trials are the clinical trials registers, such as the National Library of Medicine's ClinicalTrials.gov Website. The reviews should attempt to be sensitive; that is, find as many studies as possible, to minimize bias and be efficient. It may be appropriate to frame a hypothesis that considers the time over which a study is conducted or to target a particular subpopulation. The decision whether to include unpublished studies is difficult. Although language of publication can provide a difficulty, it is important to overcome this difficulty, provided that the populations studied are relevant to the hypothesis being tested.

Inclusion or Exclusion Criteria and Potential for Bias

Studies are chosen for meta-analysis based on inclusion criteria. If there is more than one hypothesis to be tested, separate selection criteria should be defined for each hypothesis. Inclusion criteria are ideally defined at the stage of initial development of the study protocol. The rationale for the criteria for study selection used should be clearly stated.

One important potential source of bias in meta-analysis is the loss of trials and subjects. Ideally, all randomized subjects in all studies satisfy all of the trial selection criteria, comply with all the trial procedures, and provide complete data. Under these conditions, an "intention-totreat" analysis is straightforward to implement; that is, statistical analysis is conducted on all subjects that are enrolled in a study rather than those that complete all stages of study considered desirable. Some empirical studies had shown that certain methodological characteristics, such as poor concealment of treatment allocation or no blinding in studies exaggerate treatment effects 27 . Therefore, it is important to critically appraise the quality of studies in order to assess the risk of bias.

The study design, including details of the method of randomization of subjects to treatment groups, criteria for eligibility in the study, blinding, method of assessing the outcome, and handling of protocol deviations are important features defining study quality. When studies are excluded from a meta-analysis, reasons for exclusion should be provided for each excluded study. Usually, more than one assessor decides independently which studies to include or exclude, together with a well-defined checklist and a procedure that is followed when the assessors disagree. Two people familiar with the study topic perform the quality assessment for each study, independently. This is followed by a consensus meeting to discuss the studies excluded or included. Practically, the blinding of reviewers from details of a study such as authorship and journal source is difficult.

Before assessing study quality, a quality assessment protocol and data forms should be developed. The goal of this process is to reduce the risk of bias in the estimate of effect. Quality scores that summarize multiple components into a single number exist but are misleading and unhelpful 28 . Rather, investigators should use individual components of quality assessment and describe trials that do not meet the specified quality standards and probably assess the effect on the overall results by excluding them, as part of the sensitivity analyses.

Further, not all studies are completed, because of protocol failure, treatment failure, or other factors. Nonetheless, missing subjects and studies can provide important evidence. It is desirable to obtain data from all relevant randomized trials, so that the most appropriate analysis can be undertaken. Previous studies have discussed the significance of missing trials to the interpretation of intervention studies in medicine 29 , 30 . Journal editors and reviewers need to be aware of the existing bias toward publishing positive findings and ensure that papers that publish negative or even failed trials be published, as long as these meet the quality guidelines for publication.

There are occasions when authors of the selected papers have chosen different outcome criteria for their main analysis. In practice, it may be necessary to revise the inclusion criteria for a meta-analysis after reviewing all of the studies found through the search strategy. Variation in studies reflects the type of study design used, type and application of experimental and control therapies, whether or not the study was published, and, if published, subjected to peer review, and the definition used for the outcome of interest. There are no standardized criteria for inclusion of studies in meta-analysis. Universal criteria are not appropriate, however, because meta-analysis can be applied to a broad spectrum of topics. Published data in journal papers should also be cross-checked with conference papers to avoid repetition in presented data.

Clearly, unpublished studies are not found by searching the literature. It is possible that published studies are systemically different from unpublished studies; for example, positive trial findings may be more likely to be published. Therefore, a meta-analysis based on literature search results alone may lead to publication bias.

Efforts to minimize this potential bias include working from the references in published studies, searching computerized databases of unpublished material, and investigating other sources of information including conference proceedings, graduate dissertations and clinical trial registers.

Statistical analysis

The most common measures of effect used for dichotomous data are the risk ratio (also called relative risk) and the odds ratio. The dominant method used for continuous data are standardized mean difference (SMD) estimation. Methods used in meta-analysis for post hoc analysis of findings are relatively specific to meta-analysis and include heterogeneity analysis, sensitivity analysis, and evaluation of publication bias.

All methods used should allow for the weighting of studies. The concept of weighting reflects the value of the evidence of any particular study. Usually, studies are weighted according to the inverse of their variance 31 . It is important to recognize that smaller studies, therefore, usually contribute less to the estimates of overall effect. However, well-conducted studies with tight control of measurement variation and sources of confounding contribute more to estimates of overall effect than a study of identical size less well conducted.

One of the foremost decisions to be made when conducting a meta-analysis is whether to use a fixed-effects or a random-effects model. A fixed-effects model is based on the assumption that the sole source of variation in observed outcomes is that occurring within the study; that is, the effect expected from each study is the same. Consequently, it is assumed that the models are homogeneous; there are no differences in the underlying study population, no differences in subject selection criteria, and treatments are applied the same way 32 . Fixed-effect methods used for dichotomous data include most often the Mantel-Haenzel method 33 and the Peto method 34 (only for odds ratios).

Random-effects models have an underlying assumption that a distribution of effects exists, resulting in heterogeneity among study results, known as τ2. Consequently, as software has improved, random-effects models that require greater computing power have become more frequently conducted. This is desirable because the strong assumption that the effect of interest is the same in all studies is frequently untenable. Moreover, the fixed effects model is not appropriate when statistical heterogeneity (τ2) is present in the results of studies in the meta-analysis. In the random-effects model, studies are weighted with the inverse of their variance and the heterogeneity parameter. Therefore, it is usually a more conservative approach with wider confidence intervals than the fixed-effects model where the studies are weighted only with the inverse of their variance. The most commonly used random-effects method is the DerSimonian and Laird method 35 . Furthermore, it is suggested that comparing the fixed-effects and random-effect models developed as this process can yield insights to the data 36 .

Heterogeneity

Arguably, the greatest benefit of conducting metaanalysis is to examine sources of heterogeneity, if present, among studies. If heterogeneity is present, the summary measure must be interpreted with caution 37 . When heterogeneity is present, one should question whether and how to generalize the results. Understanding sources of heterogeneity will lead to more effective targeting of prevention and treatment strategies and will result in new research topics being identified. Part of the strategy in conducting a meta-analysis is to identify factors that may be significant determinants of subpopulation analysis or covariates that may be appropriate to explore in all studies.

To understand the nature of variability in studies, it is important to distinguish between different sources of heterogeneity. Variability in the participants, interventions, and outcomes studied has been described as clinical diversity, and variability in study design and risk of bias has been described as methodological diversity 10 . Variability in the intervention effects being evaluated among the different studies is known as statistical heterogeneity and is a consequence of clinical or methodological diversity, or both, among the studies. Statistical heterogeneity manifests itself in the observed intervention effects varying by more than the differences expected among studies that would be attributable to random error alone. Usually, in the literature, statistical heterogeneity is simply referred to as heterogeneity.

Clinical variation will cause heterogeneity if the intervention effect is modified by the factors that vary across studies; most obviously, the specific interventions or participant characteristics that are often reflected in different levels of risk in the control group when the outcome is dichotomous. In other words, the true intervention effect will differ for different studies. Differences between studies in terms of methods used, such as use of blinding or differences between studies in the definition or measurement of outcomes, may lead to differences in observed effects. Significant statistical heterogeneity arising from differences in methods used or differences in outcome assessments suggests that the studies are not all estimating the same effect, but does not necessarily suggest that the true intervention effect varies. In particular, heterogeneity associated solely with methodological diversity indicates that studies suffer from different degrees of bias. Empirical evidence suggests that some aspects of design can affect the result of clinical trials, although this may not always be the case.

The scope of a meta-analysis will largely determine the extent to which studies included in a review are diverse. Meta-analysis should be conducted when a group of studies is sufficiently homogeneous in terms of subjects involved, interventions, and outcomes to provide a meaningful summary. However, it is often appropriate to take a broader perspective in a meta-analysis than in a single clinical trial. Combining studies that differ substantially in design and other factors can yield a meaningless summary result, but the evaluation of reasons for the heterogeneity among studies can be very insightful. It may be argued that these studies are of intrinsic interest on their own, even though it is not appropriate to produce a single summary estimate of effect.

Variation among k trials is usually assessed using Cochran's Q statistic, a chi-squared (χ 2 ) test of heterogeneity with k-1 degrees of freedom. This test has relatively poor power to detect heterogeneity among small numbers of trials; consequently, an α-level of 0.10 is used to test hypotheses 38 , 39 .

Heterogeneity of results among trials is better quantified using the inconsistency index I 2 , which describes the percentage of total variation across studies 40 . Uncertainty intervals for I 2 (dependent on Q and k) are calculated using the method described by Higgins and Thompson 41 . Negative values of I 2 are put equal to zero, consequently I 2 lies between 0 and 100%. A value >75% may be considered substantial heterogeneity 41 . This statistic is less influenced by the number of trials compared with other methods used to estimate the heterogeneity and provides a logical and readily interpretable metric but it still can be unstable when only a few studies are combined 42 .

Given that there are several potential sources of heterogeneity in the data, several steps should be considered in the investigation of the causes. Although random-effects models are appropriate, it may be still very desirable to examine the data to identify sources of heterogeneity and to take steps to produce models that have a lower level of heterogeneity, if appropriate. Further, if the studies examined are highly heterogeneous, it may be not appropriate to present an overall summary estimate, even when random effects models are used. As Petiti notes 43 , statistical analysis alone will not make contradictory studies agree; critically, however, one should use common sense in decision-making. Despite heterogeneity in responses, if all studies had a positive point direction and the pooled confidence interval did not include zero, it would not be logical to conclude that there was not a positive effect, provided that sufficient studies and subject numbers were present. The appropriateness of the point estimate of the effect is much more in question.

Some of the ways to investigate the reasons for heterogeneity; are subgroup analysis and meta-regression. The subgroup analysis approach, a variation on those described above, groups categories of subjects (e.g., by age, sex) to compare effect sizes. The meta-regression approach uses regression analysis to determine the influence of selected variables (the independent variables) on the effect size (the dependent variable). In a meta-regresregression, studies are regarded as if they were individual patients, but their effects are properly weighted to account for their different variances 44 .

Sensitivity analyses have also been used to examine the effects of studies identified as being aberrant concerning conduct or result, or being highly influential in the analysis. Recently, another method has been proposed that reduces the weight of studies that are outliers in meta-analyses 45 . All of these methods for examining heterogeneity have merit, and the variety of methods available reflects the importance of this activity.

Presentation of results

A useful graph, presented in the PRISMA statement 11 , is the four-phase flow diagram ( Figure 3 ).

This flow-diagram depicts the flow of information through the different phases of a systematic review or meta-analysis. It maps out the number of records identified, included and excluded, and the reasons for exclusions. The results of meta-analyses are often presented in a forest plot, where each study is shown with its effect size and the corresponding 95% confidence interval ( Figure 4 ).

The pooled effect and 95% confidence interval is shown in the bottom in the same line with "Overall". In the right panel of Figure 4 , the cumulative meta-analysis is graphically displayed, where data are entered successively, typically in the order of their chronological appearance 46 , 47 . Such cumulative meta-analysis can retrospectively identify the point in time when a treatment effect first reached conventional levels of significance. Cumulative meta-analysis is a compelling way to examine trends in the evolution of the summary-effect size, and to assess the impact of a specific study on the overall conclusions 46 . The figure shows that many studies were performed long after cumulative meta-analysis would have shown a significant beneficial effect of antibiotic prophylaxis in colon surgery.

Biases in meta-analysis

Although the intent of a meta-analysis is to find and assess all studies meeting the inclusion criteria, it is not always possible to obtain these. A critical concern is the papers that may have been missed. There is good reason to be concerned about this potential loss because studies with significant, positive results (positive studies) are more likely to be published and, in the case of interventions with a commercial value, to be promoted, than studies with non-significant or "negative" results (negative studies). Studies that produce a positive result, especially large studies, are more likely to have been published and, conversely, there has been a reluctance to publish small studies that have non-significant results. Further, publication bias is not solely the responsibility of editorial policy as there is reluctance among researchers to publish results that were either uninteresting or are not randomized 48 . There are, however, problems with simply including all studies that have failed to meet peer-review standards. All methods of retrospectively dealing with bias in studies are imperfect.

It is important to examine the results of each meta-analysis for evidence of publication bias. An estimation of likely size of the publication bias in the review and an approach to dealing with the bias is inherent to the conduct of many meta-analyses. Several methods have been developed to provide an assessment of publication bias; the most commonly used is the funnel plot. The funnel plot provides a graphical evaluation of the potential for bias and was developed by Light and Pillemer 49 and discussed in detail by Egger and colleagues 50 , 51 . A funnel plot is a scatterplot of treatment effect against a measure of study size. If publication bias is not present, the plot is expected to have a symmetric inverted funnel shape, as shown in Figure 5A .

In a study in which there is no publication bias, larger studies (i.e., have lower standard error) tend to cluster closely to the point estimate. As studies become less precise, such as in smaller trials (i.e., have a higher standard error), the results of the studies can be expected to be more variable and are scattered to both sides of the more precise larger studies. Figure 5A shows that the smaller, less precise studies are, indeed, scattered to both sides of the point estimate of effect and that these seem to be symmetrical, as an inverted funnel-plot, showing no evidence of publication bias. In contrast to Figure 5A , Figure 5B shows evidence of publication bias. There is evidence of the possibility that studies using smaller numbers of subjects and showing an decrease in effect size (lower odds ratio) were not published.

Asymmetry of funnel plots is not solely attributable to publication bias, but may also result from clinical heterogeneity among studies. Sources of clinical heterogeneity include differences in control or exposure of subjects to confounders or effect modifiers, or methodological heterogeneity between studies; for example, a failure to conceal treatment allocation. There are several statistical tests for detecting funnel plot asymmetry; for example, Eggers linear regression test 50 , and Begg's rank correlation test 52 but these do not have considerable power and are rarely used. However, the funnel plot is not without problems. If high precision studies really are different than low precision studies with respect to effect size (e.g., due different populations examined) a funnel plot may give a wrong impression of publication bias 53 . The appearance of the funnel plot plot can change quite dramatically depending on the scale on the y-axis - whether it is the inverse square error or the trial size 54 .

Other types of biases in meta-analysis include the time lag bias, selective reporting bias and the language bias. The time lag bias arises from the published studies, when those with striking results are published earlier than those with non-significant findings 55 . Moreover, it has been shown that positive studies with high early accrual of patients are published sooner than negative trials with low early accrual 56 . However, missing studies, either due to publication bias or time-lag bias may increasingly be identified from trials registries.

The selective reporting bias exists when published articles have incomplete or inadequate reporting. Empirical studies have shown that this bias is widespread and of considerable importance when published studies were compared with their study protocols 29 , 30 . Furthermore, recent evidence suggests that selective reporting might be an issue in safety outcomes and the reporting of harms in clinical trials is still suboptimal 57 . Therefore, it might not be possible to use quantitative objective evidence for harms in performing meta-analyses and making therapeutic decisions.

Excluding clinical trials reported in languages other than English from meta-analyses may introduce the language bias and reduce the precision of combined estimates of treatment effects. Trials with statistically significant results have been shown to be published in English 58 . In contrast, a later more extensive investigation showed that trials published in languages other than English tend to be of lower quality and produce more favourable treatment effects than trials published in English and concluded that excluding non-English language trials has generally only modest effects on summary treatment effect estimates but the effect is difficult to predict for individual meta-analyses 59 .

Evolution of meta-analyses

The classical meta-analysis compares two treatments while network meta-analysis (or multiple treatment metaanalysis) can provide estimates of treatment efficacy of multiple treatment regimens, even when direct comparisons are unavailable by indirect comparisons 60 . An example of a network analysis would be the following. An initial trial compares drug A to drug B. A different trial studying the same patient population compares drug B to drug C. Assume that drug A is found to be superior to drug B in the first trial. Assume drug B is found to be equivalent to drug C in a second trial. Network analysis then, allows one to potentially say statistically that drug A is also superior to drug C for this particular patient population. (Since drug A is better than drug B, and drug B is equivalent to drug C, then drug A is also better to drug C even though it was not directly tested against drug C.)

Meta-analysis can also be used to summarize the performance of diagnostic and prognostic tests. However, studies that evaluate the accuracy of tests have a unique design requiring different criteria to appropriately assess the quality of studies and the potential for bias. Additionally, each study reports a pair of related summary statistics (for example, sensitivity and specificity) rather than a single statistic (such as a risk ratio) and hence requires different statistical methods to pool the results of the studies 61 . Various techniques to summarize results from diagnostic and prognostic test results have been proposed 62 – 64 . Furthermore, there are many methodologies for advanced meta-analysis that have been developed to address specific concerns, such as multivariate meta-analysis 65 – 67 , and special types of meta-analysis in genetics 68 but will not be discussed here.

Meta-analysis is no longer a novelty in medicine. Numerous meta-analyses have been conducted for the same medical topic by different researchers. Recently, there is a trend to combine the results of different meta-analyses, known as a meta-epidemiological study, to assess the risk of bias 79 , 70 .

Conclusions

The traditional basis of medical practice has been changed by the use of randomized, blinded, multicenter clinical trials and meta-analysis, leading to the widely used term "evidence-based medicine". Leaders in initiating this change have been the Cochrane Collaboration who have produced guidelines for conducting systematic reviews and meta-analyses 10 and recently the PRISMA statement, a helpful resource to improve reporting of systematic reviews and meta-analyses has been released 11 . Moreover, standards by which to conduct and report meta-analyses of observational studies have been published to improve the quality of reporting 71 .

Meta-analysis of randomized clinical trials is not an infallible tool, however, and several examples exist of meta-analyses which were later contradicted by single large randomized controlled trials, and of meta-analyses addressing the same issue which have reached opposite conclusions 72 . A recent example, was the controversy between a meta-analysis of 42 studies 73 and the subsequent publication of the large-scale trial (RECORD trial) that did not support the cardiovascular risk of rosiglitazone 74 . However, the reason for this controversy was explained by the numerous methodological flaws found both in the meta-analysis and the large clinical trial 75 .

No single study, whether meta-analytic or not, will provide the definitive understanding of responses to treatment, diagnostic tests, or risk factors influencing disease. Despite this limitation, meta-analytic approaches have demonstrable benefits in addressing the limitations of study size, can include diverse populations, provide the opportunity to evaluate new hypotheses, and are more valuable than any single study contributing to the analysis. The conduct of the studies is critical to the value of a meta-analysis and the methods used need to be as rigorous as any other study conducted.

• Open access
• Published: 01 August 2019

A step by step guide for conducting a systematic review and meta-analysis with simulation data

• Gehad Mohamed Tawfik 1 , 2 ,
• Kadek Agus Surya Dila 2 , 3 ,
• Muawia Yousif Fadlelmola Mohamed 2 , 4 ,
• Dao Ngoc Hien Tam 2 , 5 ,
• Nguyen Dang Kien 2 , 6 ,
• Ali Mahmoud Ahmed 2 , 7 &
• Nguyen Tien Huy 8 , 9 , 10  

Tropical Medicine and Health volume  47 , Article number:  46 ( 2019 ) Cite this article

792k Accesses

291 Citations

92 Altmetric

Metrics details

The massive abundance of studies relating to tropical medicine and health has increased strikingly over the last few decades. In the field of tropical medicine and health, a well-conducted systematic review and meta-analysis (SR/MA) is considered a feasible solution for keeping clinicians abreast of current evidence-based medicine. Understanding of SR/MA steps is of paramount importance for its conduction. It is not easy to be done as there are obstacles that could face the researcher. To solve those hindrances, this methodology study aimed to provide a step-by-step approach mainly for beginners and junior researchers, in the field of tropical medicine and other health care fields, on how to properly conduct a SR/MA, in which all the steps here depicts our experience and expertise combined with the already well-known and accepted international guidance.

We suggest that all steps of SR/MA should be done independently by 2–3 reviewers’ discussion, to ensure data quality and accuracy.

SR/MA steps include the development of research question, forming criteria, search strategy, searching databases, protocol registration, title, abstract, full-text screening, manual searching, extracting data, quality assessment, data checking, statistical analysis, double data checking, and manuscript writing.

Introduction

The amount of studies published in the biomedical literature, especially tropical medicine and health, has increased strikingly over the last few decades. This massive abundance of literature makes clinical medicine increasingly complex, and knowledge from various researches is often needed to inform a particular clinical decision. However, available studies are often heterogeneous with regard to their design, operational quality, and subjects under study and may handle the research question in a different way, which adds to the complexity of evidence and conclusion synthesis [ 1 ].

Systematic review and meta-analyses (SR/MAs) have a high level of evidence as represented by the evidence-based pyramid. Therefore, a well-conducted SR/MA is considered a feasible solution in keeping health clinicians ahead regarding contemporary evidence-based medicine.

Differing from a systematic review, unsystematic narrative review tends to be descriptive, in which the authors select frequently articles based on their point of view which leads to its poor quality. A systematic review, on the other hand, is defined as a review using a systematic method to summarize evidence on questions with a detailed and comprehensive plan of study. Furthermore, despite the increasing guidelines for effectively conducting a systematic review, we found that basic steps often start from framing question, then identifying relevant work which consists of criteria development and search for articles, appraise the quality of included studies, summarize the evidence, and interpret the results [ 2 , 3 ]. However, those simple steps are not easy to be reached in reality. There are many troubles that a researcher could be struggled with which has no detailed indication.

Conducting a SR/MA in tropical medicine and health may be difficult especially for young researchers; therefore, understanding of its essential steps is crucial. It is not easy to be done as there are obstacles that could face the researcher. To solve those hindrances, we recommend a flow diagram (Fig. 1 ) which illustrates a detailed and step-by-step the stages for SR/MA studies. This methodology study aimed to provide a step-by-step approach mainly for beginners and junior researchers, in the field of tropical medicine and other health care fields, on how to properly and succinctly conduct a SR/MA; all the steps here depicts our experience and expertise combined with the already well known and accepted international guidance.

Detailed flow diagram guideline for systematic review and meta-analysis steps. Note : Star icon refers to “2–3 reviewers screen independently”

Methods and results

Detailed steps for conducting any systematic review and meta-analysis.

We searched the methods reported in published SR/MA in tropical medicine and other healthcare fields besides the published guidelines like Cochrane guidelines {Higgins, 2011 #7} [ 4 ] to collect the best low-bias method for each step of SR/MA conduction steps. Furthermore, we used guidelines that we apply in studies for all SR/MA steps. We combined these methods in order to conclude and conduct a detailed flow diagram that shows the SR/MA steps how being conducted.

Any SR/MA must follow the widely accepted Preferred Reporting Items for Systematic Review and Meta-analysis statement (PRISMA checklist 2009) (Additional file 5 : Table S1) [ 5 ].

We proposed our methods according to a valid explanatory simulation example choosing the topic of “evaluating safety of Ebola vaccine,” as it is known that Ebola is a very rare tropical disease but fatal. All the explained methods feature the standards followed internationally, with our compiled experience in the conduct of SR beside it, which we think proved some validity. This is a SR under conduct by a couple of researchers teaming in a research group, moreover, as the outbreak of Ebola which took place (2013–2016) in Africa resulted in a significant mortality and morbidity. Furthermore, since there are many published and ongoing trials assessing the safety of Ebola vaccines, we thought this would provide a great opportunity to tackle this hotly debated issue. Moreover, Ebola started to fire again and new fatal outbreak appeared in the Democratic Republic of Congo since August 2018, which caused infection to more than 1000 people according to the World Health Organization, and 629 people have been killed till now. Hence, it is considered the second worst Ebola outbreak, after the first one in West Africa in 2014 , which infected more than 26,000 and killed about 11,300 people along outbreak course.

Research question and objectives

Like other study designs, the research question of SR/MA should be feasible, interesting, novel, ethical, and relevant. Therefore, a clear, logical, and well-defined research question should be formulated. Usually, two common tools are used: PICO or SPIDER. PICO (Population, Intervention, Comparison, Outcome) is used mostly in quantitative evidence synthesis. Authors demonstrated that PICO holds more sensitivity than the more specific SPIDER approach [ 6 ]. SPIDER (Sample, Phenomenon of Interest, Design, Evaluation, Research type) was proposed as a method for qualitative and mixed methods search.

We here recommend a combined approach of using either one or both the SPIDER and PICO tools to retrieve a comprehensive search depending on time and resources limitations. When we apply this to our assumed research topic, being of qualitative nature, the use of SPIDER approach is more valid.

PICO is usually used for systematic review and meta-analysis of clinical trial study. For the observational study (without intervention or comparator), in many tropical and epidemiological questions, it is usually enough to use P (Patient) and O (outcome) only to formulate a research question. We must indicate clearly the population (P), then intervention (I) or exposure. Next, it is necessary to compare (C) the indicated intervention with other interventions, i.e., placebo. Finally, we need to clarify which are our relevant outcomes.

To facilitate comprehension, we choose the Ebola virus disease (EVD) as an example. Currently, the vaccine for EVD is being developed and under phase I, II, and III clinical trials; we want to know whether this vaccine is safe and can induce sufficient immunogenicity to the subjects.

An example of a research question for SR/MA based on PICO for this issue is as follows: How is the safety and immunogenicity of Ebola vaccine in human? (P: healthy subjects (human), I: vaccination, C: placebo, O: safety or adverse effects)

Preliminary research and idea validation

We recommend a preliminary search to identify relevant articles, ensure the validity of the proposed idea, avoid duplication of previously addressed questions, and assure that we have enough articles for conducting its analysis. Moreover, themes should focus on relevant and important health-care issues, consider global needs and values, reflect the current science, and be consistent with the adopted review methods. Gaining familiarity with a deep understanding of the study field through relevant videos and discussions is of paramount importance for better retrieval of results. If we ignore this step, our study could be canceled whenever we find out a similar study published before. This means we are wasting our time to deal with a problem that has been tackled for a long time.

To do this, we can start by doing a simple search in PubMed or Google Scholar with search terms Ebola AND vaccine. While doing this step, we identify a systematic review and meta-analysis of determinant factors influencing antibody response from vaccination of Ebola vaccine in non-human primate and human [ 7 ], which is a relevant paper to read to get a deeper insight and identify gaps for better formulation of our research question or purpose. We can still conduct systematic review and meta-analysis of Ebola vaccine because we evaluate safety as a different outcome and different population (only human).

Inclusion and exclusion criteria

Eligibility criteria are based on the PICO approach, study design, and date. Exclusion criteria mostly are unrelated, duplicated, unavailable full texts, or abstract-only papers. These exclusions should be stated in advance to refrain the researcher from bias. The inclusion criteria would be articles with the target patients, investigated interventions, or the comparison between two studied interventions. Briefly, it would be articles which contain information answering our research question. But the most important is that it should be clear and sufficient information, including positive or negative, to answer the question.

For the topic we have chosen, we can make inclusion criteria: (1) any clinical trial evaluating the safety of Ebola vaccine and (2) no restriction regarding country, patient age, race, gender, publication language, and date. Exclusion criteria are as follows: (1) study of Ebola vaccine in non-human subjects or in vitro studies; (2) study with data not reliably extracted, duplicate, or overlapping data; (3) abstract-only papers as preceding papers, conference, editorial, and author response theses and books; (4) articles without available full text available; and (5) case reports, case series, and systematic review studies. The PRISMA flow diagram template that is used in SR/MA studies can be found in Fig. 2 .

PRISMA flow diagram of studies’ screening and selection

Search strategy

A standard search strategy is used in PubMed, then later it is modified according to each specific database to get the best relevant results. The basic search strategy is built based on the research question formulation (i.e., PICO or PICOS). Search strategies are constructed to include free-text terms (e.g., in the title and abstract) and any appropriate subject indexing (e.g., MeSH) expected to retrieve eligible studies, with the help of an expert in the review topic field or an information specialist. Additionally, we advise not to use terms for the Outcomes as their inclusion might hinder the database being searched to retrieve eligible studies because the used outcome is not mentioned obviously in the articles.

The improvement of the search term is made while doing a trial search and looking for another relevant term within each concept from retrieved papers. To search for a clinical trial, we can use these descriptors in PubMed: “clinical trial”[Publication Type] OR “clinical trials as topic”[MeSH terms] OR “clinical trial”[All Fields]. After some rounds of trial and refinement of search term, we formulate the final search term for PubMed as follows: (ebola OR ebola virus OR ebola virus disease OR EVD) AND (vaccine OR vaccination OR vaccinated OR immunization) AND (“clinical trial”[Publication Type] OR “clinical trials as topic”[MeSH Terms] OR “clinical trial”[All Fields]). Because the study for this topic is limited, we do not include outcome term (safety and immunogenicity) in the search term to capture more studies.

Search databases, import all results to a library, and exporting to an excel sheet

According to the AMSTAR guidelines, at least two databases have to be searched in the SR/MA [ 8 ], but as you increase the number of searched databases, you get much yield and more accurate and comprehensive results. The ordering of the databases depends mostly on the review questions; being in a study of clinical trials, you will rely mostly on Cochrane, mRCTs, or International Clinical Trials Registry Platform (ICTRP). Here, we propose 12 databases (PubMed, Scopus, Web of Science, EMBASE, GHL, VHL, Cochrane, Google Scholar, Clinical trials.gov , mRCTs, POPLINE, and SIGLE), which help to cover almost all published articles in tropical medicine and other health-related fields. Among those databases, POPLINE focuses on reproductive health. Researchers should consider to choose relevant database according to the research topic. Some databases do not support the use of Boolean or quotation; otherwise, there are some databases that have special searching way. Therefore, we need to modify the initial search terms for each database to get appreciated results; therefore, manipulation guides for each online database searches are presented in Additional file 5 : Table S2. The detailed search strategy for each database is found in Additional file 5 : Table S3. The search term that we created in PubMed needs customization based on a specific characteristic of the database. An example for Google Scholar advanced search for our topic is as follows:

With all of the words: ebola virus

With at least one of the words: vaccine vaccination vaccinated immunization

Where my words occur: in the title of the article

With all of the words: EVD

Finally, all records are collected into one Endnote library in order to delete duplicates and then to it export into an excel sheet. Using remove duplicating function with two options is mandatory. All references which have (1) the same title and author, and published in the same year, and (2) the same title and author, and published in the same journal, would be deleted. References remaining after this step should be exported to an excel file with essential information for screening. These could be the authors’ names, publication year, journal, DOI, URL link, and abstract.

Protocol writing and registration

Protocol registration at an early stage guarantees transparency in the research process and protects from duplication problems. Besides, it is considered a documented proof of team plan of action, research question, eligibility criteria, intervention/exposure, quality assessment, and pre-analysis plan. It is recommended that researchers send it to the principal investigator (PI) to revise it, then upload it to registry sites. There are many registry sites available for SR/MA like those proposed by Cochrane and Campbell collaborations; however, we recommend registering the protocol into PROSPERO as it is easier. The layout of a protocol template, according to PROSPERO, can be found in Additional file 5 : File S1.

Title and abstract screening

Decisions to select retrieved articles for further assessment are based on eligibility criteria, to minimize the chance of including non-relevant articles. According to the Cochrane guidance, two reviewers are a must to do this step, but as for beginners and junior researchers, this might be tiresome; thus, we propose based on our experience that at least three reviewers should work independently to reduce the chance of error, particularly in teams with a large number of authors to add more scrutiny and ensure proper conduct. Mostly, the quality with three reviewers would be better than two, as two only would have different opinions from each other, so they cannot decide, while the third opinion is crucial. And here are some examples of systematic reviews which we conducted following the same strategy (by a different group of researchers in our research group) and published successfully, and they feature relevant ideas to tropical medicine and disease [ 9 , 10 , 11 ].

In this step, duplications will be removed manually whenever the reviewers find them out. When there is a doubt about an article decision, the team should be inclusive rather than exclusive, until the main leader or PI makes a decision after discussion and consensus. All excluded records should be given exclusion reasons.

Full text downloading and screening

Many search engines provide links for free to access full-text articles. In case not found, we can search in some research websites as ResearchGate, which offer an option of direct full-text request from authors. Additionally, exploring archives of wanted journals, or contacting PI to purchase it if available. Similarly, 2–3 reviewers work independently to decide about included full texts according to eligibility criteria, with reporting exclusion reasons of articles. In case any disagreement has occurred, the final decision has to be made by discussion.

Manual search

One has to exhaust all possibilities to reduce bias by performing an explicit hand-searching for retrieval of reports that may have been dropped from first search [ 12 ]. We apply five methods to make manual searching: searching references from included studies/reviews, contacting authors and experts, and looking at related articles/cited articles in PubMed and Google Scholar.

We describe here three consecutive methods to increase and refine the yield of manual searching: firstly, searching reference lists of included articles; secondly, performing what is known as citation tracking in which the reviewers track all the articles that cite each one of the included articles, and this might involve electronic searching of databases; and thirdly, similar to the citation tracking, we follow all “related to” or “similar” articles. Each of the abovementioned methods can be performed by 2–3 independent reviewers, and all the possible relevant article must undergo further scrutiny against the inclusion criteria, after following the same records yielded from electronic databases, i.e., title/abstract and full-text screening.

We propose an independent reviewing by assigning each member of the teams a “tag” and a distinct method, to compile all the results at the end for comparison of differences and discussion and to maximize the retrieval and minimize the bias. Similarly, the number of included articles has to be stated before addition to the overall included records.

Data extraction and quality assessment

This step entitles data collection from included full-texts in a structured extraction excel sheet, which is previously pilot-tested for extraction using some random studies. We recommend extracting both adjusted and non-adjusted data because it gives the most allowed confounding factor to be used in the analysis by pooling them later [ 13 ]. The process of extraction should be executed by 2–3 independent reviewers. Mostly, the sheet is classified into the study and patient characteristics, outcomes, and quality assessment (QA) tool.

Data presented in graphs should be extracted by software tools such as Web plot digitizer [ 14 ]. Most of the equations that can be used in extraction prior to analysis and estimation of standard deviation (SD) from other variables is found inside Additional file 5 : File S2 with their references as Hozo et al. [ 15 ], Xiang et al. [ 16 ], and Rijkom et al. [ 17 ]. A variety of tools are available for the QA, depending on the design: ROB-2 Cochrane tool for randomized controlled trials [ 18 ] which is presented as Additional file 1 : Figure S1 and Additional file 2 : Figure S2—from a previous published article data—[ 19 ], NIH tool for observational and cross-sectional studies [ 20 ], ROBINS-I tool for non-randomize trials [ 21 ], QUADAS-2 tool for diagnostic studies, QUIPS tool for prognostic studies, CARE tool for case reports, and ToxRtool for in vivo and in vitro studies. We recommend that 2–3 reviewers independently assess the quality of the studies and add to the data extraction form before the inclusion into the analysis to reduce the risk of bias. In the NIH tool for observational studies—cohort and cross-sectional—as in this EBOLA case, to evaluate the risk of bias, reviewers should rate each of the 14 items into dichotomous variables: yes, no, or not applicable. An overall score is calculated by adding all the items scores as yes equals one, while no and NA equals zero. A score will be given for every paper to classify them as poor, fair, or good conducted studies, where a score from 0–5 was considered poor, 6–9 as fair, and 10–14 as good.

In the EBOLA case example above, authors can extract the following information: name of authors, country of patients, year of publication, study design (case report, cohort study, or clinical trial or RCT), sample size, the infected point of time after EBOLA infection, follow-up interval after vaccination time, efficacy, safety, adverse effects after vaccinations, and QA sheet (Additional file 6 : Data S1).

Data checking

Due to the expected human error and bias, we recommend a data checking step, in which every included article is compared with its counterpart in an extraction sheet by evidence photos, to detect mistakes in data. We advise assigning articles to 2–3 independent reviewers, ideally not the ones who performed the extraction of those articles. When resources are limited, each reviewer is assigned a different article than the one he extracted in the previous stage.

Statistical analysis

Investigators use different methods for combining and summarizing findings of included studies. Before analysis, there is an important step called cleaning of data in the extraction sheet, where the analyst organizes extraction sheet data in a form that can be read by analytical software. The analysis consists of 2 types namely qualitative and quantitative analysis. Qualitative analysis mostly describes data in SR studies, while quantitative analysis consists of two main types: MA and network meta-analysis (NMA). Subgroup, sensitivity, cumulative analyses, and meta-regression are appropriate for testing whether the results are consistent or not and investigating the effect of certain confounders on the outcome and finding the best predictors. Publication bias should be assessed to investigate the presence of missing studies which can affect the summary.

To illustrate basic meta-analysis, we provide an imaginary data for the research question about Ebola vaccine safety (in terms of adverse events, 14 days after injection) and immunogenicity (Ebola virus antibodies rise in geometric mean titer, 6 months after injection). Assuming that from searching and data extraction, we decided to do an analysis to evaluate Ebola vaccine “A” safety and immunogenicity. Other Ebola vaccines were not meta-analyzed because of the limited number of studies (instead, it will be included for narrative review). The imaginary data for vaccine safety meta-analysis can be accessed in Additional file 7 : Data S2. To do the meta-analysis, we can use free software, such as RevMan [ 22 ] or R package meta [ 23 ]. In this example, we will use the R package meta. The tutorial of meta package can be accessed through “General Package for Meta-Analysis” tutorial pdf [ 23 ]. The R codes and its guidance for meta-analysis done can be found in Additional file 5 : File S3.

For the analysis, we assume that the study is heterogenous in nature; therefore, we choose a random effect model. We did an analysis on the safety of Ebola vaccine A. From the data table, we can see some adverse events occurring after intramuscular injection of vaccine A to the subject of the study. Suppose that we include six studies that fulfill our inclusion criteria. We can do a meta-analysis for each of the adverse events extracted from the studies, for example, arthralgia, from the results of random effect meta-analysis using the R meta package.

From the results shown in Additional file 3 : Figure S3, we can see that the odds ratio (OR) of arthralgia is 1.06 (0.79; 1.42), p value = 0.71, which means that there is no association between the intramuscular injection of Ebola vaccine A and arthralgia, as the OR is almost one, and besides, the P value is insignificant as it is > 0.05.

In the meta-analysis, we can also visualize the results in a forest plot. It is shown in Fig. 3 an example of a forest plot from the simulated analysis.

Random effect model forest plot for comparison of vaccine A versus placebo

From the forest plot, we can see six studies (A to F) and their respective OR (95% CI). The green box represents the effect size (in this case, OR) of each study. The bigger the box means the study weighted more (i.e., bigger sample size). The blue diamond shape represents the pooled OR of the six studies. We can see the blue diamond cross the vertical line OR = 1, which indicates no significance for the association as the diamond almost equalized in both sides. We can confirm this also from the 95% confidence interval that includes one and the p value > 0.05.

For heterogeneity, we see that I 2 = 0%, which means no heterogeneity is detected; the study is relatively homogenous (it is rare in the real study). To evaluate publication bias related to the meta-analysis of adverse events of arthralgia, we can use the metabias function from the R meta package (Additional file 4 : Figure S4) and visualization using a funnel plot. The results of publication bias are demonstrated in Fig. 4 . We see that the p value associated with this test is 0.74, indicating symmetry of the funnel plot. We can confirm it by looking at the funnel plot.

Publication bias funnel plot for comparison of vaccine A versus placebo

Looking at the funnel plot, the number of studies at the left and right side of the funnel plot is the same; therefore, the plot is symmetry, indicating no publication bias detected.

Sensitivity analysis is a procedure used to discover how different values of an independent variable will influence the significance of a particular dependent variable by removing one study from MA. If all included study p values are < 0.05, hence, removing any study will not change the significant association. It is only performed when there is a significant association, so if the p value of MA done is 0.7—more than one—the sensitivity analysis is not needed for this case study example. If there are 2 studies with p value > 0.05, removing any of the two studies will result in a loss of the significance.

Double data checking

For more assurance on the quality of results, the analyzed data should be rechecked from full-text data by evidence photos, to allow an obvious check for the PI of the study.

Manuscript writing, revision, and submission to a journal

Writing based on four scientific sections: introduction, methods, results, and discussion, mostly with a conclusion. Performing a characteristic table for study and patient characteristics is a mandatory step which can be found as a template in Additional file 5 : Table S3.

After finishing the manuscript writing, characteristics table, and PRISMA flow diagram, the team should send it to the PI to revise it well and reply to his comments and, finally, choose a suitable journal for the manuscript which fits with considerable impact factor and fitting field. We need to pay attention by reading the author guidelines of journals before submitting the manuscript.

The role of evidence-based medicine in biomedical research is rapidly growing. SR/MAs are also increasing in the medical literature. This paper has sought to provide a comprehensive approach to enable reviewers to produce high-quality SR/MAs. We hope that readers could gain general knowledge about how to conduct a SR/MA and have the confidence to perform one, although this kind of study requires complex steps compared to narrative reviews.

Having the basic steps for conduction of MA, there are many advanced steps that are applied for certain specific purposes. One of these steps is meta-regression which is performed to investigate the association of any confounder and the results of the MA. Furthermore, there are other types rather than the standard MA like NMA and MA. In NMA, we investigate the difference between several comparisons when there were not enough data to enable standard meta-analysis. It uses both direct and indirect comparisons to conclude what is the best between the competitors. On the other hand, mega MA or MA of patients tend to summarize the results of independent studies by using its individual subject data. As a more detailed analysis can be done, it is useful in conducting repeated measure analysis and time-to-event analysis. Moreover, it can perform analysis of variance and multiple regression analysis; however, it requires homogenous dataset and it is time-consuming in conduct [ 24 ].

Conclusions

Systematic review/meta-analysis steps include development of research question and its validation, forming criteria, search strategy, searching databases, importing all results to a library and exporting to an excel sheet, protocol writing and registration, title and abstract screening, full-text screening, manual searching, extracting data and assessing its quality, data checking, conducting statistical analysis, double data checking, manuscript writing, revising, and submitting to a journal.

Availability of data and materials

Not applicable.

Abbreviations

Network meta-analysis

Principal investigator

Population, Intervention, Comparison, Outcome

Preferred Reporting Items for Systematic Review and Meta-analysis statement

Quality assessment

Sample, Phenomenon of Interest, Design, Evaluation, Research type

Systematic review and meta-analyses

Bello A, Wiebe N, Garg A, Tonelli M. Evidence-based decision-making 2: systematic reviews and meta-analysis. Methods Mol Biol (Clifton, NJ). 2015;1281:397–416.

Article   Google Scholar  

Khan KS, Kunz R, Kleijnen J, Antes G. Five steps to conducting a systematic review. J R Soc Med. 2003;96(3):118–21.

Rys P, Wladysiuk M, Skrzekowska-Baran I, Malecki MT. Review articles, systematic reviews and meta-analyses: which can be trusted? Polskie Archiwum Medycyny Wewnetrznej. 2009;119(3):148–56.

PubMed   Google Scholar  

Higgins JPT, Green S. Cochrane Handbook for Systematic Reviews of Interventions Version 5.1.0 [updated March 2011]. 2011.

Moher D, Liberati A, Tetzlaff J, Altman DG. Preferred reporting items for systematic reviews and meta-analyses: the PRISMA statement. BMJ. 2009;339:b2535.

Methley AM, Campbell S, Chew-Graham C, McNally R, Cheraghi-Sohi S. PICO, PICOS and SPIDER: a comparison study of specificity and sensitivity in three search tools for qualitative systematic reviews. BMC Health Serv Res. 2014;14:579.

Gross L, Lhomme E, Pasin C, Richert L, Thiebaut R. Ebola vaccine development: systematic review of pre-clinical and clinical studies, and meta-analysis of determinants of antibody response variability after vaccination. Int J Infect Dis. 2018;74:83–96.

Article   CAS   Google Scholar  

Shea BJ, Reeves BC, Wells G, Thuku M, Hamel C, Moran J, ... Henry DA. AMSTAR 2: a critical appraisal tool for systematic reviews that include randomised or non-randomised studies of healthcare interventions, or both. BMJ. 2017;358:j4008.

Giang HTN, Banno K, Minh LHN, Trinh LT, Loc LT, Eltobgy A, et al. Dengue hemophagocytic syndrome: a systematic review and meta-analysis on epidemiology, clinical signs, outcomes, and risk factors. Rev Med Virol. 2018;28(6):e2005.

Morra ME, Altibi AMA, Iqtadar S, Minh LHN, Elawady SS, Hallab A, et al. Definitions for warning signs and signs of severe dengue according to the WHO 2009 classification: systematic review of literature. Rev Med Virol. 2018;28(4):e1979.

Morra ME, Van Thanh L, Kamel MG, Ghazy AA, Altibi AMA, Dat LM, et al. Clinical outcomes of current medical approaches for Middle East respiratory syndrome: a systematic review and meta-analysis. Rev Med Virol. 2018;28(3):e1977.

Vassar M, Atakpo P, Kash MJ. Manual search approaches used by systematic reviewers in dermatology. Journal of the Medical Library Association: JMLA. 2016;104(4):302.

Naunheim MR, Remenschneider AK, Scangas GA, Bunting GW, Deschler DG. The effect of initial tracheoesophageal voice prosthesis size on postoperative complications and voice outcomes. Ann Otol Rhinol Laryngol. 2016;125(6):478–84.

Rohatgi AJaiWa. Web Plot Digitizer. ht tp. 2014;2.

Hozo SP, Djulbegovic B, Hozo I. Estimating the mean and variance from the median, range, and the size of a sample. BMC Med Res Methodol. 2005;5(1):13.

Wan X, Wang W, Liu J, Tong T. Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Med Res Methodol. 2014;14(1):135.

Van Rijkom HM, Truin GJ, Van’t Hof MA. A meta-analysis of clinical studies on the caries-inhibiting effect of fluoride gel treatment. Carries Res. 1998;32(2):83–92.

Higgins JP, Altman DG, Gotzsche PC, Juni P, Moher D, Oxman AD, et al. The Cochrane Collaboration's tool for assessing risk of bias in randomised trials. BMJ. 2011;343:d5928.

Tawfik GM, Tieu TM, Ghozy S, Makram OM, Samuel P, Abdelaal A, et al. Speech efficacy, safety and factors affecting lifetime of voice prostheses in patients with laryngeal cancer: a systematic review and network meta-analysis of randomized controlled trials. J Clin Oncol. 2018;36(15_suppl):e18031-e.

Wannemuehler TJ, Lobo BC, Johnson JD, Deig CR, Ting JY, Gregory RL. Vibratory stimulus reduces in vitro biofilm formation on tracheoesophageal voice prostheses. Laryngoscope. 2016;126(12):2752–7.

Sterne JAC, Hernán MA, Reeves BC, Savović J, Berkman ND, Viswanathan M, et al. ROBINS-I: a tool for assessing risk of bias in non-randomised studies of interventions. BMJ. 2016;355.

RevMan The Cochrane Collaboration %J Copenhagen TNCCTCC. Review Manager (RevMan). 5.0. 2008.

Schwarzer GJRn. meta: An R package for meta-analysis. 2007;7(3):40-45.

Google Scholar  

Simms LLH. Meta-analysis versus mega-analysis: is there a difference? Oral budesonide for the maintenance of remission in Crohn’s disease: Faculty of Graduate Studies, University of Western Ontario; 1998.

Download references

Acknowledgements

This study was conducted (in part) at the Joint Usage/Research Center on Tropical Disease, Institute of Tropical Medicine, Nagasaki University, Japan.

Author information

Authors and affiliations.

Faculty of Medicine, Ain Shams University, Cairo, Egypt

Gehad Mohamed Tawfik

Online research Club http://www.onlineresearchclub.org/

Gehad Mohamed Tawfik, Kadek Agus Surya Dila, Muawia Yousif Fadlelmola Mohamed, Dao Ngoc Hien Tam, Nguyen Dang Kien & Ali Mahmoud Ahmed

Pratama Giri Emas Hospital, Singaraja-Amlapura street, Giri Emas village, Sawan subdistrict, Singaraja City, Buleleng, Bali, 81171, Indonesia

Kadek Agus Surya Dila

Faculty of Medicine, University of Khartoum, Khartoum, Sudan

Muawia Yousif Fadlelmola Mohamed

Nanogen Pharmaceutical Biotechnology Joint Stock Company, Ho Chi Minh City, Vietnam

Dao Ngoc Hien Tam

Department of Obstetrics and Gynecology, Thai Binh University of Medicine and Pharmacy, Thai Binh, Vietnam

Nguyen Dang Kien

Faculty of Medicine, Al-Azhar University, Cairo, Egypt

Ali Mahmoud Ahmed

Evidence Based Medicine Research Group & Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, 70000, Vietnam

Nguyen Tien Huy

Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, 70000, Vietnam

Department of Clinical Product Development, Institute of Tropical Medicine (NEKKEN), Leading Graduate School Program, and Graduate School of Biomedical Sciences, Nagasaki University, 1-12-4 Sakamoto, Nagasaki, 852-8523, Japan

You can also search for this author in PubMed   Google Scholar

Contributions

NTH and GMT were responsible for the idea and its design. The figure was done by GMT. All authors contributed to the manuscript writing and approval of the final version.

Corresponding author

Correspondence to Nguyen Tien Huy .

Ethics declarations

Ethics approval and consent to participate, consent for publication, competing interests.

The authors declare that they have no competing interests.

Additional information

Publisher’s note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Additional files

Additional file 1:.

Figure S1. Risk of bias assessment graph of included randomized controlled trials. (TIF 20 kb)

Additional file 2:

Figure S2. Risk of bias assessment summary. (TIF 69 kb)

Additional file 3:

Figure S3. Arthralgia results of random effect meta-analysis using R meta package. (TIF 20 kb)

Additional file 4:

Figure S4. Arthralgia linear regression test of funnel plot asymmetry using R meta package. (TIF 13 kb)

Additional file 5:

Table S1. PRISMA 2009 Checklist. Table S2. Manipulation guides for online database searches. Table S3. Detailed search strategy for twelve database searches. Table S4. Baseline characteristics of the patients in the included studies. File S1. PROSPERO protocol template file. File S2. Extraction equations that can be used prior to analysis to get missed variables. File S3. R codes and its guidance for meta-analysis done for comparison between EBOLA vaccine A and placebo. (DOCX 49 kb)

Additional file 6:

Data S1. Extraction and quality assessment data sheets for EBOLA case example. (XLSX 1368 kb)

Additional file 7:

Data S2. Imaginary data for EBOLA case example. (XLSX 10 kb)

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver ( http://creativecommons.org/publicdomain/zero/1.0/ ) applies to the data made available in this article, unless otherwise stated.

Reprints and permissions

About this article

Cite this article.

Tawfik, G.M., Dila, K.A.S., Mohamed, M.Y.F. et al. A step by step guide for conducting a systematic review and meta-analysis with simulation data. Trop Med Health 47 , 46 (2019). https://doi.org/10.1186/s41182-019-0165-6

Download citation

Received : 30 January 2019

Accepted : 24 May 2019

Published : 01 August 2019

DOI : https://doi.org/10.1186/s41182-019-0165-6

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Tropical Medicine and Health

ISSN: 1349-4147

• Submission enquiries: Access here and click Contact Us
• General enquiries: [email protected]

• How it works

Meta-Analysis – Guide with Definition, Steps & Examples

Published by Owen Ingram at April 26th, 2023 , Revised On April 26, 2023

“A meta-analysis is a formal, epidemiological, quantitative study design that uses statistical methods to generalise the findings of the selected independent studies. “

Meta-analysis and systematic review are the two most authentic strategies in research. When researchers start looking for the best available evidence concerning their research work, they are advised to begin from the top of the evidence pyramid. The evidence available in the form of meta-analysis or systematic reviews addressing important questions is significant in academics because it informs decision-making.

What is Meta-Analysis  

Meta-analysis estimates the absolute effect of individual independent research studies by systematically synthesising or merging the results. Meta-analysis isn’t only about achieving a wider population by combining several smaller studies. It involves systematic methods to evaluate the inconsistencies in participants, variability (also known as heterogeneity), and findings to check how sensitive their findings are to the selected systematic review protocol.   

When Should you Conduct a Meta-Analysis?

Meta-analysis has become a widely-used research method in medical sciences and other fields of work for several reasons. The technique involves summarising the results of independent systematic review studies. 

The Cochrane Handbook explains that “an important step in a systematic review is the thoughtful consideration of whether it is appropriate to combine the numerical results of all, or perhaps some, of the studies. Such a meta-analysis yields an overall statistic (together with its confidence interval) that summarizes the effectiveness of an experimental intervention compared with a comparator intervention” (section 10.2).

A researcher or a practitioner should choose meta-analysis when the following outcomes are desirable. 

For generating new hypotheses or ending controversies resulting from different research studies. Quantifying and evaluating the variable results and identifying the extent of conflict in literature through meta-analysis is possible. 

To find research gaps left unfilled and address questions not posed by individual studies. Primary research studies involve specific types of participants and interventions. A review of these studies with variable characteristics and methodologies can allow the researcher to gauge the consistency of findings across a wider range of participants and interventions. With the help of meta-analysis, the reasons for differences in the effect can also be explored. 

To provide convincing evidence. Estimating the effects with a larger sample size and interventions can provide convincing evidence. Many academic studies are based on a very small dataset, so the estimated intervention effects in isolation are not fully reliable.

Elements of a Meta-Analysis

Deeks et al. (2019), Haidilch (2010), and Grant & Booth (2009) explored the characteristics, strengths, and weaknesses of conducting the meta-analysis. They are briefly explained below. 

Characteristics: 

• A systematic review must be completed before conducting the meta-analysis because it provides a summary of the findings of the individual studies synthesised. 
• You can only conduct a meta-analysis by synthesising studies in a systematic review. 
• The studies selected for statistical analysis for the purpose of meta-analysis should be similar in terms of comparison, intervention, and population. 

Strengths: 

• A meta-analysis takes place after the systematic review. The end product is a comprehensive quantitative analysis that is complicated but reliable. 
• It gives more value and weightage to existing studies that do not hold practical value on their own. 
• Policy-makers and academicians cannot base their decisions on individual research studies. Meta-analysis provides them with a complex and solid analysis of evidence to make informed decisions. 

Criticisms: 

• The meta-analysis uses studies exploring similar topics. Finding similar studies for the meta-analysis can be challenging.
• When and if biases in the individual studies or those related to reporting and specific research methodologies are involved, the meta-analysis results could be misleading.

Steps of Conducting the Meta-Analysis 

The process of conducting the meta-analysis has remained a topic of debate among researchers and scientists. However, the following 5-step process is widely accepted. 

Step 1: Research Question

The first step in conducting clinical research involves identifying a research question and proposing a hypothesis . The potential clinical significance of the research question is then explained, and the study design and analytical plan are justified.

Step 2: Systematic Review 

The purpose of a systematic review (SR) is to address a research question by identifying all relevant studies that meet the required quality standards for inclusion. While established journals typically serve as the primary source for identified studies, it is important to also consider unpublished data to avoid publication bias or the exclusion of studies with negative results.

While some meta-analyses may limit their focus to randomized controlled trials (RCTs) for the sake of obtaining the highest quality evidence, other experimental and quasi-experimental studies may be included if they meet the specific inclusion/exclusion criteria established for the review.

Step 3: Data Extraction

After selecting studies for the meta-analysis, researchers extract summary data or outcomes, as well as sample sizes and measures of data variability for both intervention and control groups. The choice of outcome measures depends on the research question and the type of study, and may include numerical or categorical measures.

For instance, numerical means may be used to report differences in scores on a questionnaire or changes in a measurement, such as blood pressure. In contrast, risk measures like odds ratios (OR) or relative risks (RR) are typically used to report differences in the probability of belonging to one category or another, such as vaginal birth versus cesarean birth.

Step 4: Standardisation and Weighting Studies

After gathering all the required data, the fourth step involves computing suitable summary measures from each study for further examination. These measures are typically referred to as Effect Sizes and indicate the difference in average scores between the control and intervention groups. For instance, it could be the variation in blood pressure changes between study participants who used drug X and those who used a placebo.

Since the units of measurement often differ across the included studies, standardization is necessary to create comparable effect size estimates. Standardization is accomplished by determining, for each study, the average score for the intervention group, subtracting the average score for the control group, and dividing the result by the relevant measure of variability in that dataset.

In some cases, the results of certain studies must carry more significance than others. Larger studies, as measured by their sample sizes, are deemed to produce more precise estimates of effect size than smaller studies. Additionally, studies with less variability in data, such as smaller standard deviation or narrower confidence intervals, are typically regarded as higher quality in study design. A weighting statistic that aims to incorporate both of these factors, known as inverse variance, is commonly employed.

Step 5: Absolute Effect Estimation

The ultimate step in conducting a meta-analysis is to choose and utilize an appropriate model for comparing Effect Sizes among diverse studies. Two popular models for this purpose are the Fixed Effects and Random Effects models. The Fixed Effects model relies on the premise that each study is evaluating a common treatment effect, implying that all studies would have estimated the same Effect Size if sample variability were equal across all studies.

Conversely, the Random Effects model posits that the true treatment effects in individual studies may vary from each other, and endeavors to consider this additional source of interstudy variation in Effect Sizes. The existence and magnitude of this latter variability is usually evaluated within the meta-analysis through a test for ‘heterogeneity.’

Forest Plot

The results of a meta-analysis are often visually presented using a “Forest Plot”. This type of plot displays, for each study, included in the analysis, a horizontal line that indicates the standardized Effect Size estimate and 95% confidence interval for the risk ratio used. Figure A provides an example of a hypothetical Forest Plot in which drug X reduces the risk of death in all three studies.

However, the first study was larger than the other two, and as a result, the estimates for the smaller studies were not statistically significant. This is indicated by the lines emanating from their boxes, including the value of 1. The size of the boxes represents the relative weights assigned to each study by the meta-analysis. The combined estimate of the drug’s effect, represented by the diamond, provides a more precise estimate of the drug’s effect, with the diamond indicating both the combined risk ratio estimate and the 95% confidence interval limits.

Figure-A: Hypothetical Forest Plot

Relevance to Practice and Research 

  Evidence Based Nursing commentaries often include recently published systematic reviews and meta-analyses, as they can provide new insights and strengthen recommendations for effective healthcare practices. Additionally, they can identify gaps or limitations in current evidence and guide future research directions.

The quality of the data available for synthesis is a critical factor in the strength of conclusions drawn from meta-analyses, and this is influenced by the quality of individual studies and the systematic review itself. However, meta-analysis cannot overcome issues related to underpowered or poorly designed studies.

Therefore, clinicians may still encounter situations where the evidence is weak or uncertain, and where higher-quality research is required to improve clinical decision-making. While such findings can be frustrating, they remain important for informing practice and highlighting the need for further research to fill gaps in the evidence base.

Methods and Assumptions in Meta-Analysis 

Ensuring the credibility of findings is imperative in all types of research, including meta-analyses. To validate the outcomes of a meta-analysis, the researcher must confirm that the research techniques used were accurate in measuring the intended variables. Typically, researchers establish the validity of a meta-analysis by testing the outcomes for homogeneity or the degree of similarity between the results of the combined studies.

Homogeneity is preferred in meta-analyses as it allows the data to be combined without needing adjustments to suit the study’s requirements. To determine homogeneity, researchers assess heterogeneity, the opposite of homogeneity. Two widely used statistical methods for evaluating heterogeneity in research results are Cochran’s-Q and I-Square, also known as I-2 Index.

Difference Between Meta-Analysis and Systematic Reviews

Meta-analysis and systematic reviews are both research methods used to synthesise evidence from multiple studies on a particular topic. However, there are some key differences between the two.

Systematic reviews involve a comprehensive and structured approach to identifying, selecting, and critically appraising all available evidence relevant to a specific research question. This process involves searching multiple databases, screening the identified studies for relevance and quality, and summarizing the findings in a narrative report.

Meta-analysis, on the other hand, involves using statistical methods to combine and analyze the data from multiple studies, with the aim of producing a quantitative summary of the overall effect size. Meta-analysis requires the studies to be similar enough in terms of their design, methodology, and outcome measures to allow for meaningful comparison and analysis.

Therefore, systematic reviews are broader in scope and summarize the findings of all studies on a topic, while meta-analyses are more focused on producing a quantitative estimate of the effect size of an intervention across multiple studies that meet certain criteria. In some cases, a systematic review may be conducted without a meta-analysis if the studies are too diverse or the quality of the data is not sufficient to allow for statistical pooling.

Software Packages For Meta-Analysis

Meta-analysis can be done through software packages, including free and paid options. One of the most commonly used software packages for meta-analysis is RevMan by the Cochrane Collaboration.

Assessing the Quality of Meta-Analysis 

Assessing the quality of a meta-analysis involves evaluating the methods used to conduct the analysis and the quality of the studies included. Here are some key factors to consider:

• Study selection: The studies included in the meta-analysis should be relevant to the research question and meet predetermined criteria for quality.
• Search strategy: The search strategy should be comprehensive and transparent, including databases and search terms used to identify relevant studies.
• Study quality assessment: The quality of included studies should be assessed using appropriate tools, and this assessment should be reported in the meta-analysis.
• Data extraction: The data extraction process should be systematic and clearly reported, including any discrepancies that arose.
• Analysis methods: The meta-analysis should use appropriate statistical methods to combine the results of the included studies, and these methods should be transparently reported.
• Publication bias: The potential for publication bias should be assessed and reported in the meta-analysis, including any efforts to identify and include unpublished studies.
• Interpretation of results: The results should be interpreted in the context of the study limitations and the overall quality of the evidence.
• Sensitivity analysis: Sensitivity analysis should be conducted to evaluate the impact of study quality, inclusion criteria, and other factors on the overall results.

Overall, a high-quality meta-analysis should be transparent in its methods and clearly report the included studies’ limitations and the evidence’s overall quality.

Hire an Expert Writer

Orders completed by our expert writers are

• Formally drafted in an academic style
• Free Amendments and 100% Plagiarism Free – or your money back!
• 100% Confidential and Timely Delivery!
• Free anti-plagiarism report
• Appreciated by thousands of clients. Check client reviews

Examples of Meta-Analysis

• STANLEY T.D. et JARRELL S.B. (1989), « Meta-regression analysis : a quantitative method of literature surveys », Journal of Economics Surveys, vol. 3, n°2, pp. 161-170.
• DATTA D.K., PINCHES G.E. et NARAYANAN V.K. (1992), « Factors influencing wealth creation from mergers and acquisitions : a meta-analysis », Strategic Management Journal, Vol. 13, pp. 67-84.
• GLASS G. (1983), « Synthesising empirical research : Meta-analysis » in S.A. Ward and L.J. Reed (Eds), Knowledge structure and use : Implications for synthesis and interpretation, Philadelphia : Temple University Press.
• WOLF F.M. (1986), Meta-analysis : Quantitative methods for research synthesis, Sage University Paper n°59.
• HUNTER J.E., SCHMIDT F.L. et JACKSON G.B. (1982), « Meta-analysis : cumulating research findings across studies », Beverly Hills, CA : Sage.

Frequently Asked Questions

What is a meta-analysis in research.

Meta-analysis is a statistical method used to combine results from multiple studies on a specific topic. By pooling data from various sources, meta-analysis can provide a more precise estimate of the effect size of a treatment or intervention and identify areas for future research.

Why is meta-analysis important?

Meta-analysis is important because it combines and summarizes results from multiple studies to provide a more precise and reliable estimate of the effect of a treatment or intervention. This helps clinicians and policymakers make evidence-based decisions and identify areas for further research.

What is an example of a meta-analysis?

A meta-analysis of studies evaluating physical exercise’s effect on depression in adults is an example. Researchers gathered data from 49 studies involving a total of 2669 participants. The studies used different types of exercise and measures of depression, which made it difficult to compare the results.

Through meta-analysis, the researchers calculated an overall effect size and determined that exercise was associated with a statistically significant reduction in depression symptoms. The study also identified that moderate-intensity aerobic exercise, performed three to five times per week, was the most effective. The meta-analysis provided a more comprehensive understanding of the impact of exercise on depression than any single study could provide.

What is the definition of meta-analysis in clinical research?

Meta-analysis in clinical research is a statistical technique that combines data from multiple independent studies on a particular topic to generate a summary or “meta” estimate of the effect of a particular intervention or exposure.

This type of analysis allows researchers to synthesise the results of multiple studies, potentially increasing the statistical power and providing more precise estimates of treatment effects. Meta-analyses are commonly used in clinical research to evaluate the effectiveness and safety of medical interventions and to inform clinical practice guidelines.

Is meta-analysis qualitative or quantitative?

Meta-analysis is a quantitative method used to combine and analyze data from multiple studies. It involves the statistical synthesis of results from individual studies to obtain a pooled estimate of the effect size of a particular intervention or treatment. Therefore, meta-analysis is considered a quantitative approach to research synthesis.

You May Also Like

What are the different research strategies you can use in your dissertation? Here are some guidelines to help you choose a research strategy that would make your research more credible.

Ethnography is a type of research where a researcher observes the people in their natural environment. Here is all you need to know about ethnography.

This article provides the key advantages of primary research over secondary research so you can make an informed decision.

USEFUL LINKS

LEARNING RESOURCES

COMPANY DETAILS

• How It Works

Meta-analysis in medical research

Affiliation.

• 1 Department of Hygiene and Epidemiology, Aristotle University of Thessaloniki School of Medicine, Thessaloniki, Greece.
• PMID: 21487488
• PMCID: PMC3049418

The objectives of this paper are to provide an introduction to meta-analysis and to discuss the rationale for this type of research and other general considerations. Methods used to produce a rigorous meta-analysis are highlighted and some aspects of presentation and interpretation of meta-analysis are discussed.Meta-analysis is a quantitative, formal, epidemiological study design used to systematically assess previous research studies to derive conclusions about that body of research. Outcomes from a meta-analysis may include a more precise estimate of the effect of treatment or risk factor for disease, or other outcomes, than any individual study contributing to the pooled analysis. The examination of variability or heterogeneity in study results is also a critical outcome. The benefits of meta-analysis include a consolidated and quantitative review of a large, and often complex, sometimes apparently conflicting, body of literature. The specification of the outcome and hypotheses that are tested is critical to the conduct of meta-analyses, as is a sensitive literature search. A failure to identify the majority of existing studies can lead to erroneous conclusions; however, there are methods of examining data to identify the potential for studies to be missing; for example, by the use of funnel plots. Rigorously conducted meta-analyses are useful tools in evidence-based medicine. The need to integrate findings from many studies ensures that meta-analytic research is desirable and the large body of research now generated makes the conduct of this research feasible.

Keywords: bias; evidence-based medicine; meta-analysis; quality; randomized clinical trial; systematic review.

This paper is in the following e-collection/theme issue:

Published on 23.4.2024 in Vol 26 (2024)

Electronic Media Use and Sleep Quality: Updated Systematic Review and Meta-Analysis

Authors of this article:

• Xiaoning Han * , PhD   ; 
• Enze Zhou * , MA   ; 
• Dong Liu * , PhD  

School of Journalism and Communication, Renmin University of China, Beijing, China

*all authors contributed equally

Corresponding Author:

Dong Liu, PhD

School of Journalism and Communication

Renmin University of China

No. 59 Zhongguancun Street, Haidian District

Beijing, 100872

Phone: 86 13693388506

Email: [email protected]

Background: This paper explores the widely discussed relationship between electronic media use and sleep quality, indicating negative effects due to various factors. However, existing meta-analyses on the topic have some limitations.

Objective: The study aims to analyze and compare the impacts of different digital media types, such as smartphones, online games, and social media, on sleep quality.

Methods: Adhering to Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines, the study performed a systematic meta-analysis of literature across multiple databases, including Web of Science, MEDLINE, PsycINFO, PubMed, Science Direct, Scopus, and Google Scholar, from January 2018 to October 2023. Two trained coders coded the study characteristics independently. The effect sizes were calculated using the correlation coefficient as a standardized measure of the relationship between electronic media use and sleep quality across studies. The Comprehensive Meta-Analysis software (version 3.0) was used to perform the meta-analysis. Statistical methods such as funnel plots were used to assess the presence of asymmetry and a p -curve test to test the p -hacking problem, which can indicate publication bias.

Results: Following a thorough screening process, the study involved 55 papers (56 items) with 41,716 participants from over 20 countries, classifying electronic media use into “general use” and “problematic use.” The meta-analysis revealed that electronic media use was significantly linked with decreased sleep quality and increased sleep problems with varying effect sizes across subgroups. A significant cultural difference was also observed in these effects. General use was associated with a significant decrease in sleep quality ( P <.001). The pooled effect size was 0.28 (95% CI 0.21-0.35; k =20). Problematic use was associated with a significant increase in sleep problems ( P ≤.001). The pooled effect size was 0.33 (95% CI 0.28-0.38; k =36). The subgroup analysis indicated that the effect of general smartphone use and sleep problems was r =0.33 (95% CI 0.27-0.40), which was the highest among the general group. The effect of problematic internet use and sleep problems was r =0.51 (95% CI 0.43-0.59), which was the highest among the problematic groups. There were significant differences among these subgroups (general: Q between =14.46, P =.001; problematic: Q between =27.37, P <.001). The results of the meta-regression analysis using age, gender, and culture as moderators indicated that only cultural difference in the relationship between Eastern and Western culture was significant ( Q between =6.69; P =.01). All funnel plots and p -curve analyses showed no evidence of publication and selection bias.

Conclusions: Despite some variability, the study overall confirms the correlation between increased electronic media use and poorer sleep outcomes, which is notably more significant in Eastern cultures.

Introduction

Sleep is vital to our health. Research has shown that high sleep quality can lead to improvements in a series of health outcomes, such as an improved immune system, better mood and mental health, enhanced physical performance, lower risk of chronic diseases, and a longer life span [ 1 - 5 ].

Electronic media refers to forms of media or communication that use electronic devices or technology to create, distribute, and display content. This can include various forms of digital media such as smartphones, tablets, instant messaging, phone calls, social media, online games, short video platforms, etc. Electronic media has permeated every aspect of our lives [ 6 ]. Many prefer to use smartphones or tablets before sleep, which can negatively affect sleep in many aspects, including delayed sleep onset, disrupted sleep patterns, shortened sleep duration, and poor sleep quality [ 7 - 10 ]. Furthermore, problematic use occurs when the behavior surpasses a certain limit. In this study, problematic use of electronic media is not solely determined by the amount of time spent on these platforms, but rather by behavioral indicators that suggest an unhealthy or harmful relationship with them.

Smartphones or tablet use can affect sleep quality in many ways. At first, the use of these devices may directly displace, delay, or interrupt sleep time, resulting in inadequate sleep quantity [ 11 ]. The sound of notifications and vibrations of these devices may interrupt sleep. Second, the screens of smartphones and tablets emit blue light, which can suppress the production of melatonin, the hormone responsible for regulating sleep-wake cycles [ 12 ]. Third, consuming emotionally charged content, such as news, suspenseful movies, or engaging in online arguments, can increase emotional arousal, making it harder to relax and fall asleep. This emotional arousal can also lead to disrupted sleep and nightmares [ 13 ]. Finally, the use of electronic devices before bedtime can lead to a delay in bedtime and a shortened sleep duration, as individuals may lose track of time while engaging with their devices. This can result in a disrupted sleep routine and decreased sleep quality [ 14 ].

Some studies have conducted meta-analyses on screen media use and sleep outcomes in 2016, 2019, and 2021 [ 15 - 17 ]. However, these studies had their own limitations. First, the sample size included in their meta-analyses was small (around 10). Second, these studies only focused on 1 aspect of the effect of digital media on sleep quality. For example, Carter et al [ 16 ] focused only on adolescents, and both Alimoradi et al [ 15 ] and Kristensen et al [ 17 ] only reviewed the relationship between problematic use of digital media or devices and sleep quality. Despite of the high heterogeneity found in the meta-analyses, none have compared the effects of different digital media or devices. This study aims to clarify and compare the effects of these different channels.

Literature Search

The research adhered to Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines ( Multimedia Appendix 1 ) and followed a predetermined protocol [ 18 , 19 ]. As the idea and scope of this study evolved over time, the meta-analysis was not preregistered. However, the methodology was defined a priori and strictly followed to reduce biases, and the possible influence of post hoc decisions was minimized. All relevant studies in English, published from January 1, 2018, to October 9, 2023, were searched. We searched the following databases: Web of Science, MEDLINE, PsycINFO, PubMed, Science Direct, Scopus, and Google Scholar. The abstracts were examined manually. The keywords used to search were the combination of the following words: “sleep” OR “sleep duration” OR “sleep quality” OR “sleep problems” AND “electronic media” OR “smartphone” OR “tablet” OR “social media” OR “Facebook” OR “Twitter” OR “online gaming” OR “internet” OR “addiction” OR “problematic” ( Multimedia Appendix 2 ). Additionally, the reference lists of relevant studies were examined.

Two trained coders independently screened the titles and abstracts of the identified papers for eligibility, followed by a full-text review of the selected studies. Discrepancies between the coders were resolved through discussion until a consensus was reached. The reference lists of the included studies were also manually screened to identify any additional relevant studies. Through this rigorous process, we ensured a comprehensive and replicable literature search that could contribute to the robustness of our meta-analysis findings.

Inclusion or Exclusion Criteria

Titles and abstracts from search results were scrutinized for relevance, with duplicates removed. Full texts of pertinent papers were obtained, and their eligibility for inclusion was evaluated. We mainly included correlational studies that used both continuous measures of time spent using electronic media use and sleep quality. Studies must have been available in English. Four criteria were used to screen studies: (1) only peer-reviewed empirical studies, published in English, were considered for inclusion in the meta-analysis; (2) the studies should report quantitative statistics on electronic media use and sleep quality, including sample size and essential information to calculate the effect size, and review papers, qualitative studies, case studies, and conference abstracts were excluded; (3) studies on both general use and problematic use of electronic media or devices should be included; and (4) only studies that used correlation, regression, or odds ratio were included to ensure consistency.

Study Coding

Two trained coders were used to code the characteristics of the studies independently. Discrepancies were discussed with the first author of the paper to resolve. Sample size and characteristics of participants were coded: country, female ratio, average age, publication year, and electronic types. Effect sizes were either extracted directly from the original publications or manually calculated. If a study reported multiple dependent effects, the effects were merged into one. If a study reported multiple independent effects from different samples, the effects were included separately. Additionally, to evaluate the study quality, the papers were classified into 3 tiers (high, middle, and low) according to Journal Citation Reports 2022 , a ranking of journals based on their impact factor as reported in the Web of Science. The few unindexed papers were rated based on their citation counts as reported in Google Scholar.

Meta-Analysis and Moderator Analyses

The effect sizes were calculated using the correlation coefficient ( r ) as a standardized measure of the relationship between electronic media or device use and sleep quality across studies. When studies reported multiple effect sizes, we selected the one that best represented the overall association between electronic media use and sleep quality. If studies did not provide correlation coefficients, we converted other reported statistics (eg, standardized regression coefficients) into correlation coefficients using established formulas. Once calculated, the correlation coefficients were transformed into Fisher z scores to stabilize the variance and normalize the distribution.

Previous meta-studies have shown high levels of heterogeneity. Hence, the random effects model was adopted for all analyses. To explore potential factors contributing to the heterogeneity and to further understand the relationship between electronic media use and sleep quality, we conducted moderator analyses. The following categorical and continuous moderators were examined: media types (online gaming, social media, smartphone, or intent), participants’ average age, culture, female ratio, and sleep quality assessment method. For categorical moderators, subgroup analyses were performed, while for continuous moderators, meta-regression analyses were conducted. All analyses were completed in the Comprehensive Meta-Analysis software (version 3.0; Biostat, Inc).

Publication Bias

We used statistical methods such as funnel plots to assess the presence of asymmetry and a p -curve test to test the p -hacking problem, which may indicate publication bias. In case of detected asymmetry, we applied techniques such as the trim-and-fill method to adjust the effect size estimates.

By addressing publication bias, we aimed to provide a more accurate and reliable synthesis of the available evidence, enhancing the validity and generalizability of our meta-analytic findings. Nevertheless, it is essential for readers to interpret the results cautiously, considering the potential limitations imposed by publication bias and other methodological concerns.

Search Findings

A total of 98,806 studies were identified from databases, especially Scopus (n=49,643), Google Scholar (n=18,600), Science Direct (n=15,084), and Web of Science (n=11,689). Upon removing duplicate records and excluding studies that did not meet the inclusion criteria, 754 studies remained for the screening phase. After screening titles, abstracts, and full texts, 703 studies were excluded. A total of 4 additional studies were identified from the references of relevant reviews. Finally, 55 studies [ 20 - 74 ] were included in the meta-analysis. The flow diagram of the selection is shown in Figure 1 .

Characteristics of Included Studies

In 20 studies, 21,594 participants were included in the analysis of the general use of electronic media and sleep quality. The average age of the sample ranged from 9.9 to 44 years. The category of general online gaming and sleep quality included 4 studies, with 14,837 participants; the category of general smartphone use and sleep quality included 10 studies, with 5011 participants; and the category of general social media use and sleep quality included 6 studies, with 1746 participants.

These studies came from the following countries or areas: Germany, Serbia, Indonesia, India, China, Italy, Saudi Arabia, New Zealand, the United Kingdom, the United States, Spain, Qatar, Egypt, Argentina, and Portugal. The most frequently used measure of electronic media use was the time spent on it. The most frequently used measure of sleep was the Pittsburgh Sleep Quality Index.

In 35 studies, 20,122 participants were included in the analysis of the problematic use of electronic media and sleep quality. The average age of the sample ranged from 14.76 to 65.62 years. The category of problematic online gaming and sleep quality included 5 studies, with 1874 participants; the category of problematic internet use and sleep quality included 2 studies, with 774 participants; the category of problematic smartphone use and sleep quality included 18 studies, with 12,204 participants; and the category of problematic social media use and sleep quality included 11 studies, with 5270 participants. There was a study that focused on both social media and online gaming, which led to its inclusion in the analysis. These studies came from 14 countries or areas: Turkey, the United States, Indonesia, China, France, Taiwan, India, South Korea, Hong Kong, Iran, Poland, Israel, Hungary, and Saudi Arabia. The most frequently used measures of problematic electronic media use were the Internet Gaming Disorder Scale-Short Form, Smartphone Addiction Scale-Short Form, and Bergen Social Media Addiction Scale.

With respect to study quality, the 56 papers were published in 50 journals, 41 of which were indexed in Journal Citation Reports 2022 , while the remaining 9 journals were rated based on their citation counts as reported in Google Scholar. As a result, of the 56 papers included in the study, 22 papers were assigned a high rating, 18 papers were assigned a middle rating, and 16 papers were assigned a low rating. More information about the included studies is listed in Multimedia Appendix 3 [ 20 - 74 ].

Meta-Analysis

The results of the meta-analysis of the relationship between general electronic media use and sleep quality showed that electronic media use was associated with a significant decrease in sleep quality ( P <.001). The pooled effect size was 0.28 (95% CI 0.21-0.35; k =20), indicating that individuals who used electronic media more frequently were generally associated with more sleeping problems.

The second meta-analysis showed that problematic electronic media use was associated with a significant increase in sleep problems ( P ≤.001). The pooled effect size was 0.33 (95% CI 0.28-0.38; k =36), indicating that participants who used electronic media more frequently were more likely to have more sleep problems.

Moderator Analyses

At first, we conducted subgroup analyses for different media or devices. The results are shown in Tables 1 and 2 . The effect of the relationship between general online gaming and sleep problems was r =0.14 (95% CI 0.06-0.22); the effect of the relationship between general smartphone use and sleep problems was r =0.33 (95% CI 0.27-0.40); and the effect of the relationship between general social media use and sleep problems was r =0.28 (95% CI 0.21-0.34). There are significant differences among these groups ( Q between =14.46; P =.001).

The effect of the relationship between problematic gaming and sleep problems was r =0.49, 95% CI 0.23-0.69; the effect of the relationship between problematic internet use and sleep problems was r =0.51 (95% CI 0.43-0.59); the effect of the relationship between problematic smartphone use and sleep problems was r =0.25 (95% CI 0.20-0.30); and the effect of the relationship between problematic social media use and sleep problems was r =0.35 (95% CI 0.29-0.40). There are significant differences among these groups ( Q between =27.37; P <.001).

We also used age, gender, and culture as moderators to conduct meta-regression analyses. The results are shown in Tables 3 and 4 . Only cultural difference in the relationship between Eastern and Western culture was significant ( Q between =6.694; P =.01). All other analyses were not significant.

a Not applicable.

All funnel plots of the analyses were symmetrical, showing no evidence of publication bias ( Figures 2 - 5 ). We also conducted p -curve analyses to see whether there were any selection biases. The results also showed that there were no biases.

Principal Findings

This study indicated that electronic media use was significantly linked with decreased sleep quality and increased sleep problems with varying effect sizes across subgroups. General use was associated with a significant decrease in sleep quality. Problematic use was associated with a significant increase in sleep problems. A significant cultural difference was also observed by the meta-regression analysis.

First, there is a distinction in the impact on sleep quality between problematic use and general use, with the former exhibiting a higher correlation strength. However, both have a positive correlation, suggesting that the deeper the level of use, the more sleep-related issues are observed. In addressing this research question, the way in which electronic media use is conceptualized and operationalized may have a bearing on the ultimate outcomes. Problematic use is measured through addiction scales, while general use is predominantly assessed by duration of use (time), leading to divergent results stemming from these distinct approaches. The key takeaway is that each measurement possesses unique strengths and weaknesses, and the pathways affecting sleep quality differ. Consequently, the selection of a measurement approach should be tailored to the specific research question at hand. The duration of general use reflects an individual’s comprehensive involvement with electronic media, and its impact on sleep quality is evident in factors such as an extended time to fall asleep and reduced sleep duration. The addiction scale for problematic use illuminates an individual’s preferences, dependencies, and other associations with electronic media. Its impact on sleep quality is evident through physiological and psychological responses, including anxiety, stress, and emotional reactions.

Second, notable variations exist in how different types of electronic media affect sleep quality. In general, the positive predictive effects of smartphone, social media, and online gaming use durations on sleep problems gradually decrease. In the problematic context, the intensity of addiction to the internet and online gaming has the most significant positive impact on sleep problems, followed by social media, while smartphones exert the least influence. On one hand, longitudinal comparisons within the same context reveal that the content and format of electronic media can have varying degrees of negative impact on sleep quality, irrespective of whether it involves general or problematic use. On the other hand, cross-context comparisons suggest that both general and problematic use play a role in moderating the impact of electronic media types on sleep quality. As an illustration, problematic use reinforces the positive impact of online gaming and social media on sleep problems, while mitigating the influence of smartphones. Considering smartphones as electronic media, an extended duration of general use is associated with lower sleep quality. However, during problematic use, smartphones serve as the platform for other electronic media such as games and social media, resulting in a weakened predictive effect on sleep quality. Put differently, in the context of problematic use, the specific type of electronic media an individual consumes on their smartphones becomes increasingly pivotal in shaping sleep quality.

Third, cultural differences were found to be significant moderators of the relationship between electronic media use and sleep problems in both our study and Carter et al [ 16 ]. Kristensen et al [ 17 ], however, did not specifically address the role of cultural differences but revealed that there was a strong and consistent association between bedtime media device use and sleep outcomes across the studies included. Our findings showed that the association between problematic social media use was significantly larger in Eastern culture. We speculate that the difference may be attributed to cultural differences in social media use patterns, perceptions of social norms and expectations, variations in bedtime routines and habits, and diverse coping mechanisms for stress. These speculations warrant further investigation to understand better the underlying factors contributing to the observed cultural differences in the relationship between social media use and sleep quality.

Fourth, it was observed that gender and age had no significant impact on sleep quality. The negative effects of electronic media use are not only confined to the sleep quality of adults, and the association with gender differences remains unclear. Recent studies point out that electronic media use among preschoolers may result in a “time-shifting” process, disrupting their sleep patterns [ 75 ]. Similarly, children and adolescent sleep patterns have been reported to be adversely affected by electronic media use [ 76 - 78 ]. These findings underscore the necessity of considering age group variations in future research, as electronic media use may differently impact sleep quality across age demographics.

In conclusion, our study, Carter et al [ 16 ], and Kristensen et al [ 17 ] collectively emphasize the importance of understanding and addressing the negative impact of electronic media use, particularly problematic online gaming and smartphone use, on sleep quality and related issues. Further research is warranted to explore the underlying mechanisms and specific factors contributing to the relationship between electronic media use and sleep problems.

Strengths and Limitations

Our study, supplemented with research by Carter et al [ 16 ] and Kristensen et al [ 17 ], contributes to the growing evidence supporting a connection between electronic media use and sleep quality. We found that both general and problematic use of electronic media correlates with sleep issues, with the strength of the correlation varying based on the type of electronic media and cultural factors, with no significant relationship observed with age or gender.

Despite the vast amount of research on the relationship between electronic media use and sleep, several gaps and limitations still exist.

First, the inclusion criteria were restricted to English-language, peer-reviewed empirical studies published between January 2018 and October 2023. This may have led to the exclusion of relevant studies published in other languages or before 2018, potentially limiting the generalizability of our findings. Furthermore, the exclusion of non–peer-reviewed studies and conference abstracts may have introduced publication bias, as significant results are more likely to be published in peer-reviewed journals.

Second, although we used a comprehensive search strategy, the possibility remains that some relevant studies may have been missed. Additionally, the search strategies were not linked with Medical Subject Headings headers and may not have captured all possible electronic media types, resulting in an incomplete representation of the effects of electronic media use on sleep quality.

Third, the studies included in our meta-analysis exhibited considerable heterogeneity in sample characteristics, electronic media types, and measures of sleep quality. This heterogeneity might have contributed to the variability in effect sizes observed across studies. Although we conducted moderator analyses to explore potential sources of heterogeneity, other unexamined factors may still have influenced the relationship between electronic media use and sleep quality.

Fourth, our meta-analysis relied on the correlation coefficient ( r ) as the primary effect size measure, which may not fully capture the complex relationships between electronic media use and sleep quality. Moreover, the conversion of other reported statistics into correlation coefficients could introduce additional sources of error. The correlational nature of the included studies limited our ability to draw causal inferences between electronic media use and sleep quality. Experimental and longitudinal research designs would provide stronger evidence for the directionality of this relationship.

Given these limitations, future research should aim to include a more diverse range of studies, examine additional potential moderators, and use more robust research designs to better understand the complex relationship between electronic media use and sleep quality.

Conclusions

In conclusion, our updated meta-analysis affirms the consistent negative impact of electronic media use on sleep outcomes, with problematic online gaming and smartphone use being particularly impactful. Notably, the negative effect of problematic social media use on sleep quality appears more pronounced in Eastern cultures. This research emphasizes the need for public health initiatives to increase awareness of these impacts, particularly for adolescents. Further research, including experimental and longitudinal studies, is necessary to delve deeper into the complex relationship between electronic media use and sleep quality, considering potential moderators like cultural differences.

Acknowledgments

This research was supported by the Journalism and Marxism Research Center, Renmin University of China (MXG202215), and by funds for building world-class universities (disciplines) of Renmin University of China (23RXW195).

A statement on the use of ChatGPT in the process of writing this paper can be found in Multimedia Appendix 4.

Data Availability

The data sets analyzed during this study are available from the corresponding author on reasonable request.

Conflicts of Interest

None declared.

PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) 2020 checklist.

Search strategies.

Characteristics of included studies.

Large language model statement.

• Brink-Kjaer A, Leary EB, Sun H, Westover MB, Stone KL, Peppard PE, et al. Age estimation from sleep studies using deep learning predicts life expectancy. NPJ Digit Med. 2022;5(1):103. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Killgore WDS. Effects of sleep deprivation on cognition. Prog Brain Res. 2010;185:105-129. [ CrossRef ] [ Medline ]
• Lee S, Mu CX, Wallace ML, Andel R, Almeida DM, Buxton OM, et al. Sleep health composites are associated with the risk of heart disease across sex and race. Sci Rep. 2022;12(1):2023. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Prather AA. Sleep, stress, and immunity. In: Grandner MA, editor. Sleep and Health, 1st Edition. Cambridge. Academic Press; 2019;319-330.
• Scott AJ, Webb TL, Martyn-St James M, Rowse G, Weich S. Improving sleep quality leads to better mental health: a meta-analysis of randomised controlled trials. Sleep Med Rev. Dec 2021;60:101556. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Guttmann A. Statista. 2023. URL: https://www.statista.com/topics/1536/media-use/#topicOverview [accessed 2023-06-10]
• Hysing M, Pallesen S, Stormark KM, Jakobsen R, Lundervold AJ, Sivertsen B. Sleep and use of electronic devices in adolescence: results from a large population-based study. BMJ Open. Feb 02, 2015;5(1):e006748. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Lavender RM. Electronic media use and sleep quality. Undergrad J Psychol. 2015;28(1):55-62. [ FREE Full text ]
• Exelmans L, Van den Bulck J. Bedtime mobile phone use and sleep in adults. Soc Sci Med. 2016;148:93-101. [ CrossRef ] [ Medline ]
• Twenge JM, Krizan Z, Hisler G. Decreases in self-reported sleep duration among U.S. adolescents 2009-2015 and association with new media screen time. Sleep Med. 2017;39:47-53. [ CrossRef ] [ Medline ]
• Exelmans L. Electronic media use and sleep: a self-control perspective. Curr Sleep Med Rep. 2019;5:135-140. [ CrossRef ]
• Jniene A, Errguig L, El Hangouche AJ, Rkain H, Aboudrar S, El Ftouh M, et al. Perception of sleep disturbances due to bedtime use of blue light-emitting devices and its impact on habits and sleep quality among young medical students. Biomed Res Int. 2019;2019:7012350. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Munezawa T, Kaneita Y, Osaki Y, Kanda H, Minowa M, Suzuki K, et al. The association between use of mobile phones after lights out and sleep disturbances among Japanese adolescents: a nationwide cross-sectional survey. Sleep. 2011;34(8):1013-1020. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Smith LJ, Gradisar M, King DL, Short M. Intrinsic and extrinsic predictors of video-gaming behaviour and adolescent bedtimes: the relationship between flow states, self-perceived risk-taking, device accessibility, parental regulation of media and bedtime. Sleep Med. 2017;30:64-70. [ CrossRef ] [ Medline ]
• Alimoradi Z, Lin CY, Broström A, Bülow PH, Bajalan Z, Griffiths MD, et al. Internet addiction and sleep problems: a systematic review and meta-analysis. Sleep Med Rev. 2019;47:51-61. [ CrossRef ] [ Medline ]
• Carter B, Rees P, Hale L, Bhattacharjee D, Paradkar MS. Association between portable screen-based media device access or use and sleep outcomes: a systematic review and meta-analysis. JAMA Pediatr. 2016;170(12):1202-1208. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Kristensen JH, Pallesen S, King DL, Hysing M, Erevik EK. Problematic gaming and sleep: a systematic review and meta-analysis. Front Psychiatry. 2021;12:675237. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Moher D, Liberati A, Tetzlaff J, Altman DG, PRISMA Group. Preferred reporting items for systematic reviews and meta-analyses: the PRISMA statement. PLoS Med. 2009;6(7):e1000097. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Page MJ, McKenzie JE, Bossuyt PM, Boutron I, Hoffmann TC, Mulrow CD, et al. The PRISMA 2020 statement: an updated guideline for reporting systematic reviews. BMJ. 2021;372:n71. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Akçay D, Akçay BD. The effect of computer game playing habits of university students on their sleep states. Perspect Psychiatr Care. 2020;56(4):820-826. [ CrossRef ] [ Medline ]
• Alahdal WM, Alsaedi AA, Garrni AS, Alharbi FS. The impact of smartphone addiction on sleep quality among high school students in Makkah, Saudi Arabia. Cureus. 2023;15(6):e40759. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Alam A, Alshakhsi S, Al-Thani D, Ali R. The role of objectively recorded smartphone usage and personality traits in sleep quality. PeerJ Comput Sci. 2023;9:e1261. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Almeida F, Marques DR, Gomes AA. A preliminary study on the association between social media at night and sleep quality: the relevance of FOMO, cognitive pre-sleep arousal, and maladaptive cognitive emotion regulation. Scand J Psychol. 2023;64(2):123-132. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Alshobaili FA, AlYousefi NA. The effect of smartphone usage at bedtime on sleep quality among Saudi non-medical staff at King Saud University Medical City. J Family Med Prim Care. 2019;8(6):1953-1957. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Alsulami A, Bakhsh D, Baik M, Merdad M, Aboalfaraj N. Assessment of sleep quality and its relationship to social media use among medical students. Med Sci Educ. 2019;29(1):157-161. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Altintas E, Karaca Y, Hullaert T, Tassi P. Sleep quality and video game playing: effect of intensity of video game playing and mental health. Psychiatry Res. 2019;273:487-492. [ CrossRef ] [ Medline ]
• Asbee J, Slavish D, Taylor DJ, Dietch JR. Using a frequentist and Bayesian approach to examine video game usage, substance use, and sleep among college students. J Sleep Res. 2023;32(4):e13844. [ CrossRef ] [ Medline ]
• Bae ES, Kang HS, Lee HN. The mediating effect of sleep quality in the relationship between academic stress and social network service addiction tendency among adolescents. J Korean Acad Community Health Nurs. 2020;31(3):290-299. [ FREE Full text ] [ CrossRef ]
• Chatterjee S, Kar SK. Smartphone addiction and quality of sleep among Indian medical students. Psychiatry. 2021;84(2):182-191. [ CrossRef ] [ Medline ]
• Chung JE, Choi SA, Kim KT, Yee J, Kim JH, Seong JW, et al. Smartphone addiction risk and daytime sleepiness in Korean adolescents. J Paediatr Child Health. 2018;54(7):800-806. [ CrossRef ] [ Medline ]
• Demir YP, Sumer MM. Effects of smartphone overuse on headache, sleep and quality of life in migraine patients. Neurosciences (Riyadh). 2019;24(2):115-121. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Dewi RK, Efendi F, Has EMM, Gunawan J. Adolescents' smartphone use at night, sleep disturbance and depressive symptoms. Int J Adolesc Med Health. 2018;33(2):20180095. [ CrossRef ] [ Medline ]
• Eden A, Ellithorpe ME, Meshi D, Ulusoy E, Grady SM. All night long: problematic media use is differentially associated with sleep quality and depression by medium. Commun Res Rep. 2021;38(3):143-149. [ CrossRef ]
• Ellithorpe ME, Meshi D, Tham SM. Problematic video gaming is associated with poor sleep quality, diet quality, and personal hygiene. Psychol Pop Media. 2023;12(2):248-253. [ CrossRef ]
• Elsheikh AA, Elsharkawy SA, Ahmed DS. Impact of smartphone use at bedtime on sleep quality and academic activities among medical students at Al -Azhar University at Cairo. J Public Health (Berl.). Jun 15, 2023.:1-10. [ FREE Full text ] [ CrossRef ]
• Gaya AR, Brum R, Brites K, Gaya A, de Borba Schneiders L, Duarte Junior MA, et al. Electronic device and social network use and sleep outcomes among adolescents: the EHDLA study. BMC Public Health. 2023;23(1):919. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Gezgin DM. Understanding patterns for smartphone addiction: age, sleep duration, social network use and fear of missing out. Cypriot J Educ Sci. 2018;13(2):166-177. [ CrossRef ]
• Graham S, Mason A, Riordan B, Winter T, Scarf D. Taking a break from social media improves wellbeing through sleep quality. Cyberpsychol Behav Soc Netw. 2021;24(6):421-425. [ CrossRef ] [ Medline ]
• Guerrero MD, Barnes JD, Chaput JP, Tremblay MS. Screen time and problem behaviors in children: exploring the mediating role of sleep duration. Int J Behav Nutr Phys Act. 2019;16(1):105. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Hamvai C, Kiss H, Vörös H, Fitzpatrick KM, Vargha A, Pikó BF. Association between impulsivity and cognitive capacity decrease is mediated by smartphone addiction, academic procrastination, bedtime procrastination, sleep insufficiency and daytime fatigue among medical students: a path analysis. BMC Med Educ. 2023;23(1):537. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Herlache AD, Lang KM, Krizan Z. Withdrawn and wired: problematic internet use accounts for the link of neurotic withdrawal to sleep disturbances. Sleep Sci. 2018;11(2):69-73. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Huang Q, Li Y, Huang S, Qi J, Shao T, Chen X, et al. Smartphone use and sleep quality in chinese college students: a preliminary study. Front Psychiatry. 2020;11:352. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Hussain Z, Griffiths MD. The associations between problematic social networking site use and sleep quality, attention-deficit hyperactivity disorder, depression, anxiety and stress. Int J Ment Health Addict. 2021;19:686-700. [ FREE Full text ] [ CrossRef ]
• Imani V, Ahorsu DK, Taghizadeh N, Parsapour Z, Nejati B, Chen HP, et al. The mediating roles of anxiety, depression, sleepiness, insomnia, and sleep quality in the association between problematic social media use and quality of life among patients with cancer. Healthcare (Basel). 2022;10(9):1745. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Jeong CY, Seo YS, Cho EH. The effect of SNS addiction tendency on trait-anxiety and quality of sleep in university students'. J Korean Clin Health Sci. 2018;6(2):1147-1155. [ CrossRef ]
• Karaş H, Küçükparlak İ, Özbek MG, Yılmaz T. Addictive smartphone use in the elderly: relationship with depression, anxiety and sleep quality. Psychogeriatrics. 2023;23(1):116-125. [ CrossRef ] [ Medline ]
• Kater MJ, Schlarb AA. Smartphone usage in adolescents: motives and link to sleep disturbances, stress and sleep reactivity. Somnologie. 2020;24(4):245-252. [ CrossRef ]
• Kharisma AC, Fitryasari R, Rahmawati PD. Online games addiction and the decline in sleep quality of college student gamers in the online game communities in Surabaya, Indonesia. Int J Psychosoc Rehabil. 2020;24(7):8987-8993. [ FREE Full text ] [ CrossRef ]
• Kumar VA, Chandrasekaran V, Brahadeeswari H. Prevalence of smartphone addiction and its effects on sleep quality: a cross-sectional study among medical students. Ind Psychiatry J. 2019;28(1):82-85. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Lee Y, Blebea J, Janssen F, Domoff SE. The impact of smartphone and social media use on adolescent sleep quality and mental health during the COVID-19 pandemic. Hum Behav Emerg Technol. 2023;2023:3277040. [ FREE Full text ] [ CrossRef ]
• Li L, Griffiths MD, Mei S, Niu Z. Fear of missing out and smartphone addiction mediates the relationship between positive and negative affect and sleep quality among Chinese university students. Front Psychiatry. 2020;11:877. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Li Y, Mu W, Sun C, Kwok SYCL. Surrounded by smartphones: relationship between peer phubbing, psychological distress, problematic smartphone use, daytime sleepiness, and subjective sleep quality. Appl Res Qual Life. 2023;18:1099-1114. [ CrossRef ]
• Luo X, Hu C. Loneliness and sleep disturbance among first-year college students: the sequential mediating effect of attachment anxiety and mobile social media dependence. Psychol Sch. 2022;59(9):1776-1789. [ CrossRef ]
• Luqman A, Masood A, Shahzad F, Shahbaz M, Feng Y. Untangling the adverse effects of late-night usage of smartphone-based SNS among university students. Behav Inf Technol. 2021;40(15):1671-1687. [ CrossRef ]
• Makhfudli, Aulia A, Pratiwi A. Relationship intensity of social media use with quality of sleep, social interaction, and self-esteem in urban adolescents in Surabaya. Sys Rev Pharm. 2020;11(5):783-788. [ CrossRef ]
• Ozcan B, Acimis NM. Sleep quality in Pamukkale university students and its relationship with smartphone addiction. Pak J Med Sci. 2021;37(1):206-211. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Peltz JS, Bodenlos JS, Kingery JN, Abar C. Psychological processes linking problematic smartphone use to sleep disturbance in young adults. Sleep Health. 2023;9(4):524-531. [ CrossRef ] [ Medline ]
• Pérez-Chada D, Bioch SA, Schönfeld D, Gozal D, Perez-Lloret S, Sleep in Adolescents Collaborative Study Group. Screen use, sleep duration, daytime somnolence, and academic failure in school-aged adolescents. PLoS One. 2023;18(2):e0281379. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Przepiorka A, Blachnio A. The role of Facebook intrusion, depression, and future time perspective in sleep problems among adolescents. J Res Adolesc. 2020;30(2):559-569. [ CrossRef ] [ Medline ]
• Rudolf K, Bickmann P, Froböse I, Tholl C, Wechsler K, Grieben C. Demographics and health behavior of video game and eSports players in Germany: the eSports study 2019. Int J Environ Res Public Health. 2020;17(6):1870. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Sami H, Danielle L, Lihi D, Elena S. The effect of sleep disturbances and internet addiction on suicidal ideation among adolescents in the presence of depressive symptoms. Psychiatry Res. 2018;267:327-332. [ CrossRef ] [ Medline ]
• Scott H, Woods HC. Fear of missing out and sleep: cognitive behavioural factors in adolescents' nighttime social media use. J Adolesc. 2018;68:61-65. [ CrossRef ] [ Medline ]
• Spagnoli P, Balducci C, Fabbri M, Molinaro D, Barbato G. Workaholism, intensive smartphone use, and the sleep-wake cycle: a multiple mediation analysis. Int J Environ Res Public Health. 2019;16(19):3517. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Stanković M, Nešić M, Čičević S, Shi Z. Association of smartphone use with depression, anxiety, stress, sleep quality, and internet addiction. empirical evidence from a smartphone application. Pers Individ Differ. Jan 2021;168:110342. [ CrossRef ]
• Tandon A, Kaur P, Dhir A, Mäntymäki M. Sleepless due to social media? investigating problematic sleep due to social media and social media sleep hygiene. Comput Hum Behav. Dec 2020;113:106487. [ FREE Full text ] [ CrossRef ]
• Wang PY, Chen KL, Yang SY, Lin PH. Relationship of sleep quality, smartphone dependence, and health-related behaviors in female junior college students. PLoS One. 2019;14(4):e0214769. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Wang Q, Zhong Y, Zhao G, Song R, Zeng C. Relationship among content type of smartphone use, technostress, and sleep difficulty: a study of university students in China. Educ Inf Technol. Aug 02, 2022;28(2):1697-1714. [ CrossRef ]
• Wong HY, Mo HY, Potenza MN, Chan MNM, Lau WM, Chui TK, et al. Relationships between severity of internet gaming disorder, severity of problematic social media use, sleep quality and psychological distress. Int J Environ Res Public Health. 2020;17(6):1879. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Xie X, Dong Y, Wang J. Sleep quality as a mediator of problematic smartphone use and clinical health symptoms. J Behav Addict. 2018;7(2):466-472. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Yang SY, Chen KL, Lin PH, Wang PY. Relationships among health-related behaviors, smartphone dependence, and sleep duration in female junior college students. Soc Health Behav. 2019;2(1):26-31. [ FREE Full text ] [ CrossRef ]
• Yıldırım M, Öztürk A, Solmaz F. Fear of COVID-19 and sleep problems in Turkish young adults: mediating roles of happiness and problematic social networking sites use. Psihologija. 2023;56(4):497-515. [ FREE Full text ] [ CrossRef ]
• Zhai X, Ye M, Wang C, Gu Q, Huang T, Wang K, et al. Associations among physical activity and smartphone use with perceived stress and sleep quality of Chinese college students. Mental Health and Physical Activity. Mar 2020;18:100323. [ CrossRef ]
• Zhang MX, Wu AMS. Effects of smartphone addiction on sleep quality among Chinese university students: the mediating role of self-regulation and bedtime procrastination. Addict Behav. 2020;111:106552. [ CrossRef ] [ Medline ]
• Zhang MX, Zhou H, Yang HM, Wu AMS. The prospective effect of problematic smartphone use and fear of missing out on sleep among Chinese adolescents. Curr Psychol. May 24, 2021;42(7):5297-5305. [ CrossRef ]
• Beyens I, Nathanson AI. Electronic media use and sleep among preschoolers: evidence for time-shifted and less consolidated sleep. Health Commun. 2019;34(5):537-544. [ FREE Full text ] [ CrossRef ] [ Medline ]
• Mazurek MO, Engelhardt CR, Hilgard J, Sohl K. Bedtime electronic media use and sleep in children with autism spectrum disorder. J Dev Behav Pediatr. 2016;37(7):525-531. [ CrossRef ] [ Medline ]
• King DL, Delfabbro PH, Zwaans T, Kaptsis D. Sleep interference effects of pathological electronic media use during adolescence. Int J Ment Health Addict. 2014;12:21-35. [ CrossRef ]
• Kubiszewski V, Fontaine R, Rusch E, Hazouard E. Association between electronic media use and sleep habits: an eight-day follow-up study. Int J Adolesc Youth. 2013;19(3):395-407. [ FREE Full text ] [ CrossRef ]

Abbreviations

Edited by G Eysenbach, T Leung; submitted 20.04.23; peer-reviewed by M Behzadifar, F Estévez-López, R Prieto-Moreno; comments to author 18.05.23; revised version received 15.06.23; accepted 26.03.24; published 23.04.24.

©Xiaoning Han, Enze Zhou, Dong Liu. Originally published in the Journal of Medical Internet Research (https://www.jmir.org), 23.04.2024.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work, first published in the Journal of Medical Internet Research, is properly cited. The complete bibliographic information, a link to the original publication on https://www.jmir.org/, as well as this copyright and license information must be included.