data presentation in biostatistics

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• v.21(4); Oct-Dec 2018

Scales of Measurement and Presentation of Statistical Data

Prabhaker mishra.

Department of Biostatistics and Health Informatics, Sanjay Gandhi Post Graduate Institute of Medical Sciences, Lucknow, Uttar Pradesh, India

Uttam Singh

Anshul gupta.

1 Department of Haematology, Sanjay Gandhi Post Graduate Institute of Medical Sciences, Lucknow, Uttar Pradesh, India

Measurement scale is an important part of data collection, analysis, and presentation. In the data collection and data analysis, statistical tools differ from one data type to another. There are four types of variables, namely nominal, ordinal, discrete, and continuous, and their nature and application are different. Graphs are a common method to visually present and illustrate relationships in the data. There are several statistical diagrams available to present data sets. However, their use depends on our objectives and data types. We should use the appropriate diagram for the data set, which is very useful for easily and quickly communicating summaries and findings to the audience. In the present study, statistical data type and its presentation, which are used in the field of biomedical research, have been discussed.

Introduction

Statistics is a branch of mathematics dealing with the collection, analysis, presentation, interpretation, and conclusion of data, while biostatistics is a branch of statistics, where statistical techniques are used on biomedical data to reach a final conclusion.[ 1 ] Measurement scale (data type) is an important part of data collection, analysis, and presentation. In the data collection, the type of questionnaire and the data recording tool differ according to the data types. Similarly, in the data analysis, statistical tests/methods differ from one data type to another.

Data presentation is an important step to communicate our information and findings to the audience and readers in an effective way. If done properly, they not only reduce word count but also convey an important message in a meaningful way so that the readers can grasp it easily.[ 2 ] There are various tabulation and graphical methods used to present the data, which are not possible without proper knowledge of data types.

The objective of this paper is to discuss the statistical data type (Section A) and its presentation (Section B), which is an important part of biomedical research.

Scales of measurement

As data are the heart of the statistics, and at the time of data analysis and presentation, many people are confused about what type of statistical tools to be used on a set of data and the relevant forms of presentation or data display. Its decision is taken by looking the types of data and the objectives of the research.

Data are a collection of facts such as values or measurements. It can be numbers, words, measurements, observations, or even just descriptions of things. Basically, data are two types: constant and variable. Constant is a situation/value that does not change, while a characteristic, number, or quantity that increases or decreases over time or takes different values in different situations is called variable. Due to unchangeable property, constant is not used and only variable is used for summary measures and analysis.[ 1 , 3 , 4 ]

Types of variables

There are four types of variables: nominal, ordinal, discrete, and continuous. The first two are called qualitative data and the last two are quantitative data. The first two (nominal and ordinal) are assessed in terms of words or attributes called qualitative data, whereas discrete and continuous variables are part of the quantitative data.[ 5 ]

Qualitative variable

Qualitative variable (also called categorical variable) shows the quality or properties of the data. It is represented by a name, a symbol, or a number code. These scales are mutually exclusive (no overlap) and none of them have any numerical significance. It is two types: nominal and ordinal.

Nominal variable : Nominal data are simply names or properties having two or more categories, and there is no intrinsic ordering to the categories, i.e., data have no natural ranking or ordering. For example, gender (male and female) and marital status (married/unmarried) have two categories, but these categories have no natural order or ranking.

Ordinal variable : An ordinal variable is similar to a nominal variable. The difference between the two is that there is a clear ordering in the data, i.e., ordinal data, unlike nominal data, have some order. For example, ordinal scales are seen in questions that call for ratings of quality (very good, good, fair, poor, very poor), agreement (strongly agree, agree, disagree, strongly disagree), economic status (low, medium, and high), etc. All the ranking data including Likert scales, Bristol stool scale, and all the other scales which are ranked between 0 and 10 are also called ordinal data.

Quantitative variable

Quantitative variable is the data that show some quantity through numerical value. Quantitative data are the numeric variables (e.g., how many, how much, or how often). Age, blood pressure, body temperature, hemoglobin level, and serum creatinine level are some examples of quantitative data. It is also called metric data. It is two types: discrete and continuous.

Discrete variable : Discrete variable is the quantitative data, but its values cannot be expressed or presented in the form of a decimal; for example, number of males, number of females, number of patients, and family size cannot expressed in decimal in meaningful way.

Continuous data : Data are measured in values and can be quantified and presented in decimals. Age, height, weight, body mass index, serum creatinine, heart rate, systolic blood pressure, and diastolic blood pressure are some examples.

The variables such as heart rate, platelet count, respiration rate, systolic blood pressure, and diastolic blood pressure are in fact discrete (measuring in complete number) but are considered continuous because of large number of possible values. Only those variables which can take a small number of values, say, <10, are generally considered discrete.[ 6 , 7 ] Summary is that if discrete variables values are at least 10 or more, then discrete variables can be considered as continuous variable and we analyze them as per the methods applicable on continuous data.

Data presentation

Data presentation plays a crucial role in research. The researchers can convince their research to the reader by the effective data presentation. Basically, there are two types of data presentation: numerical and graphical.

Numerical presentation

There are various types of numerical presentation of the data including arranging them into ascending order, descending order, and classification of the data in the tabular form.

Graphical presentation

Graphs are a common method to visually illustrate relationships in the data. A chart, also called a graph, is a graphical representation of the data, in which the data are represented by symbols, such as bars in a bar chart, lines in a line chart, or slices in a pie chart. Graphs enable us in studying the cause-and-effect relationship between two variables. Graphs help measure the extent of change in one variable when another variable changes by a certain amount.[ 8 , 9 ]

There are various types of graphical presentation given below.[ 10 , 11 ]

A bar graph is the presentation of data using rectangular bars, with heights or lengths proportional to the values that they represent. The reader can easily compare the quantity by observing the length of the bar. In bar graph, the bars may be plotted either horizontally or vertically. In the x-axis, use categorical variable, while in y-axis, use numerical values. Bar graph is three types: simple, adjacent, and cumulative. The last two are also called multiple bar graph. In simple bar graph, maximum two variables (one categorical and one quantitative) are used, while in multiple bar diagram, maximum three variables (two categorical and one quantitative) are used. Multiple bar graphs are useful when a researcher wants to compare figures of two or more different data [Figure ​ [Figure1a 1a and ​ andb b ].

(a) Simple bar graph showing mean age between sex, (b and c) multiple bar graph and line graph showing mean age and BMI between sex, (d) sex distribution of the data, (e) histogram showing nature of the BMI distribution, (f) error bar graph showing mean BMI as per sex, (g) box plot showing age distribution as per sex, (h) scatter diagram showing linear relationship between age and BMI, (i) Bland–Altman plot showing relationship between SBP difference and their average values, (j) Forest plot showing relative risk and associated confidence intervals observed from five different studies for the exposure group as compared to nonexposure group. BMI: Body mass index, SBP: Systolic blood pressure

It is alternative graph of the bar graph. A line graph is a kind of graph which represents data in a way that a series of points are to be connected by segments of straight lines. Difference between bar and line graph is that bar represented by rectangle while line graph showing by line, although both used for the same purpose [ Figure 1c ].

A pie chart is defined as a graph which contains a circle and is divided into sectors. The arc lengths of the sectors are proportional to the numerical value they represent. It is used only for the categorical data [ Figure 1d ].

Histogram and frequency polygon

A histogram represents the frequency distribution of a continuous variable whose areas are proportional to the corresponding frequencies. A histogram is quite similar to the bar graph and both are made up of rectangular bars. The difference is that there is no gap between any two bars in the histogram. The histogram is used to check the normal distribution of continuous data and have only one continuous variable, and no categorical variables are used to plot it, while in bar graph, we have required at least two variables including one quantitative and one categorical variables. Frequency polygons serve the same purpose as histograms but are particularly helpful for comparing sets of data. Frequency polygons are also a good choice for displaying cumulative frequency distributions. When the midpoints of tops of the rectangular bars in histogram are joined together, the frequency polygon is made [ Figure 1e ].

Error bars are graphical representations of the variability of data and used on graph to indicate the error or uncertainty (standard deviation/standard error/confidence interval) in a reported measurement (mean). They give a general idea of how precise a measurement is or conversely, how far from the reported value [ Figure 1f ].

Box plots characterize a sample using the minimum, 25 th , 50 th , and 75 th percentiles, maximum values. The interquartile range (IQR = Q3 − Q1, where Q1 is first quartile or 25 th percentile while Q3 is third quartile or 75 th percentile) which covers the central 50% of the data. Quartiles are insensitive to outliers and preserve information about the center and spread (variation). If a data point is below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR, it is viewed as being too far from the central values (median), which are called outliers [ Figure 1g ].

Scatter plot

A scatter plot (also called scatter diagram) is a graph in which the values of two quantitative variables are plotted along two axes, the pattern of the resulting points revealing any correlation present between variables for a set of data. Scatter plots show how much one variable is affected by another. The relationship between two variables is called their correlation. If the data points make a straight line going from the origin out to high x- and y-values, then the variables are said to have a positive correlation. If the line goes from a high value on the y-axis down to a high value on the x-axis, the variables have a negative correlation. In case no trend was shown, it is called no correlation [ Figure 1h ].

Bland–Altman plot

A Bland–Altman plot (difference plot) is a method of data plotting used in analyzing the agreement between two different assays. In the Bland–Altman plot, the differences (between the two methods) are plotted against the averages of the two methods. Alternatively, we can choose to plot the differences (between the two methods) against one of the two methods, if this is a reference method of both methods [ Figure 1i ].

Forest plot

A forest plot, also known as a blobbogram, is a graphical display of estimated results from a number of scientific studies addressing the same question, along with the overall results. It is a graphical representation of a meta-analysis. It is usually accompanied by a table listing references (author and date) of the studies with their estimated result included in the meta-analysis[ 12 ] [ Figure 1j ].

Other graphical methods

Besides above, there are some other graphical methods, used in the research studies, although they are less popular including stem and leaf plot, area chart, polar plot, youden plot, and high-low graph.

Relationship between Scales of Measurement, Statistical Methods, and Graphical Presentation of Statistical Data

Statistical methods are varying according to the scales of measurements. For example, when the data are a continuous variable, then we can use the parametric methods (including t -test, ANOVA test, linear regression, and Pearson correlation). When the data are a discrete variable/qualitative variable, we cannot use parametric testing and only nonparametric methods (including Mann–Whitney U-test, Kruskal–Wallis H-test, Wilcoxon test, Friedman test, Chi-square test, logistic regression, and Spearman correlation) are used. Similarly, graphical methods are varying according to the scales of measurements. For example, histogram, error bar graph, scatter plot, boxplot, and Bland–Altman graph can be drawn for continuous variables, but not for qualitative variables. In contrast, the pie chart is a graph that is only for qualitative data. There are many diagrams those are used for either categorical variable(s) or mix of the categorical and quantitative variables including bar graph and line graph. In brief, it is not possible to use appropriate statistical method and graphical presentation without proper knowledge of the concepts and properties of data types.

Conclusions

Data type is an important concept of statistics, which should be understand to implement statistical tools correctly. Proper knowledge of data types is necessary to analyze data sets with appropriate statistical methods. This not only enhances our ability to decide its summary measures but helps us to analyze data sets with proper statistical methods. There are several statistical diagrams available to display summaries and finding of data sets. There are several statistical diagrams available to display summaries and finding of data sets, although their use depends on our objectives and data types. We should use appropriate diagrams for our data sets, which is very much useful to communicate the summary and findings to the viewers with easily and quickly.

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Conflicts of interest.

There are no conflicts of interest.

Acknowledgment

We would like to express their deep and sincere gratitude to Dr. Prabhat Tiwari, Professor, Department of Anaesthesiology, Sanjay Gandhi Postgraduate Institute of Medical Sciences, Lucknow, for his encouragement to write this article. His critical reviews and suggestions were very useful for improvement in the article

Radiopharmaceutical Chemistry pp 531–539 Cite as

An Introduction to Biostatistics

• Kristen M. Cunanan 4 &
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• First Online: 03 April 2019

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In this chapter, we discuss the basics of what you need to know about biostatistics in order to statistically analyze and interpret the data from your in vitro and preclinical in vivo experiments. Experiments are conducted to answer one or more specific scientific questions, and they must be designed so that they are likely to provide answers with minimal bias and appropriate measures of variability and significance. Here, we discuss different methods of analysis and their accompanying assumptions. In addition, we cover several different experimental design considerations as well as the subsequent interpretation and graphical presentation of data and statistical findings. Furthermore, we provide insight on both sides of the debates surrounding controversial issues such as testing multiple hypotheses in a single study and addressing outliers in the data. We conclude with a discussion of the future of biostatistics for in vitro and preclinical experiments, highlighting the importance of learning biostatistical software in your training. We suggest you read this chapter before you begin performing experiments and collecting data.

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Houghton JL, Membreno R, Abdel-Atti D, Cunanan KM, Carlin S, et al. Establishment of the in vivo efficacy of pretargeted radioimmunotherapy utilizing inverse electron demand Diels-Alder click chemistry. Mol Cancer Ther. 2017;16(1):124–33.

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Sharma SK, Pourat J, Abdel-Atti D, Carlsin SD, Piersigilli A, et al. Noninvasive interrogation of DLL3 expression in metastatic small cell lung cancer. Cancer Res. 2017;77(14):3931–41.

Casella G, Berger R. Statistical inference. Pacific Grove: Duxbury; 2002.

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Vardi Y, Ying Z, Zhang CH. Two-sample tests for growth curves under dependent right censoring. Biometrika. 2001;88(4):949–50.

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Cunanan, K.M., Gönen, M. (2019). An Introduction to Biostatistics. In: Lewis, J., Windhorst, A., Zeglis, B. (eds) Radiopharmaceutical Chemistry. Springer, Cham. https://doi.org/10.1007/978-3-319-98947-1_30

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Role of Biostatistics

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Our first course objective will be addressed throughout the semester in that you will be adding to your understanding of biostatistics in an ongoing manner during the course.

CO-1: Describe the roles biostatistics serves in the discipline of public health.

What is Biostatistics?

Learning objectives.

LO 1.1: Define statistics and biostatistics.

Biostatistics is the application of statistics to a variety of topics in biology. In this course, we tend to focus on biological topics in the health sciences as we learn about statistics.

In an introductory course such as ours, there is essentially no difference between “biostatistics” and “statistics” and thus you will notice that we focus on learning “statistics” in general but use as many examples from and applications to the health sciences as possible.

Statistics is all about converting data into useful information . Statistics is therefore a process where we are:

• collecting data,
• summarizing data, and
• interpreting data.

The following video adapted from material available from Johns Hopkins – Introduction to Biostatistics provides a few examples of statistics in use.

Statistics Examples (3:14)

The following reading from the online version of Little Handbook of Statistical Practice contains excellent comments about common reasons why many people feel that “statistics is hard” and how to overcome them! We will suggest returning to and reviewing this document as we cover some of the topics mentioned in the reading.

Is Statistics Hard? (≈ 1500 words)

Steps in a Research Project

LO 1.2: Identify the steps in a research project.

In practice, every research project or study involves the following steps .

• Planning/design of study
• Data collection
• Data analysis
• Presentation
• Interpretation

The following video adapted from material available at Johns Hopkins – Introduction to Biostatistics provides an overview of the steps in a research project and the role biostatistics and biostatisticians play in each step.

Role of Biostatistics in the Steps of a Research Project (5:23)

(Optional) Outside Reading : Role of Biostatistics in Modern Medicine (≈ 1000 words)

Basic Concepts for Biostatistics

Lisa Sullivan, PhD, Professor of Biostatistics, Boston University School of Public Health

Introduction

Biostatistics is the application of statistical principles to questions and problems in medicine, public health or biology. One can imagine that it might be of interest to characterize a given population (e.g., adults in Boston or all children in the United States) with respect to the proportion of subjects who are overweight or the proportion who have asthma, and it would also be important to estimate the magnitude of these problems over time or perhaps in different locations. In other circumstances in would be important to make comparisons among groups of subjects in order to determine whether certain behaviors (e.g., smoking, exercise, etc.) are associated with a greater risk of certain health outcomes. It would, of course, be impossible to answer all such questions by collecting information (data) from all subjects in the populations of interest. A more realistic approach is to study samples or subsets of a population. The discipline of biostatistics provides tools and techniques for collecting data and then summarizing, analyzing, and interpreting it. If the samples one takes are representative of the population of interest, they will provide good estimates regarding the population overall. Consequently, in biostatistics one analyzes samples in order to make inferences about the population. This module introduces fundamental concepts and definitions for biostatistics.

Learning Objectives

After completing this module, the student will be able to:

• Define and distinguish between populations and samples.
• Define and distinguish between population parameters and sample statistics.
• Compute a sample mean, sample variance, and sample standard deviation.
• Compute a population mean, population variance, and population standard deviation.
• Explain what is meant by statistical inference.

----------- 

Population Parameters versus Sample Statistics

As noted in the Introduction, a fundamental task of biostatistics is to analyze samples in order to make inferences about the population from which the samples were drawn .  To illustrate this, consider the population of Massachusetts in 2010, which consisted of 6,547,629 persons. One characteristic (or variable) of potential interest might be the diastolic blood pressure of the population. There are a number of ways of reporting and analyzing this, which will be considered in the module on Summarizing Data. However, for the time being, we will focus on the mean diastolic blood pressure of all people living in Massachusetts. It is obviously not feasible to measure and record blood pressures for of all the residents, but one could take samples of the population in order estimate the population's mean diastolic blood pressure.

Despite the simplicity of this example, it raises a series of concepts and terms that need to be defined. The terms population , subjects , sample , variable , and data elements are defined in the tabbed activity below.

It is possible to select many samples from a given population, and we will see in other learning modules that there are several methods that can be used for selecting subjects from a population into a sample. The simple example above shows three small samples that were drawn to estimate the mean diastolic blood pressure of Massachusetts residents, although it doesn't specify how the samples were drawn. Note also that each of the samples provided a different estimate of the mean value for the population, and none of the estimates was the same as the actual mean for the overall population (78 mm Hg in this hypothetical example). In reality, one generally doesn't know the true mean values of the characteristics of the population, which is of course why we are trying to estimate them from samples. Consequently, it is important to define and distinguish between:

• population size versus sample size
• parameter versus sample statistic.

Sample Statistics

In order to illustrate the computation of sample statistics, we selected a small subset (n=10) of participants in the Framingham Heart Study. The data values for these ten individuals are shown in the table below. The rightmost column contains the body mass index (BMI) computed using the height and weight measurements. We will come back to this example in the module on Summarizing Data, but it provides a useful illustration of some of the terms that have been introduced and will also serve to illustrate the computation of some sample statistics.

Data Values for a Small Sample

The first summary statistic that is important to report is the sample size. In this example the sample size is n=10. Because this sample is small (n=10), it is easy to summarize the sample by inspecting the observed values, for example, by listing the diastolic blood pressures in ascending order:

62        63        64        67        70        72        76        77        81        81

Simple inspection of this small sample gives us a sense of the center of the observed diastolic pressures and also gives us a sense of how much variability there is. However, for a large sample, inspection of the individual data values does not provide a meaningful summary, and summary statistics are necessary.  The two key components of a useful summary for a continuous variable are:

• a description of the center or 'average' of the data (i.e., what is a typical value?) and
• an indication of the variability in the data.   

Sample Mean

There are several statistics that describe the center of the data, but for now we will focus on the sample mean, which is computed by summing all of the values for a particular variable in the sample and dividing by the sample size. For the sample of diastolic blood pressures in the table above, the sample mean is computed as follows:

To simplify the formulas for sample statistics (and for population parameters), we usually denote the variable of interest as "X".  X is simply a placeholder for the variable being analyzed.  Here X=diastolic blood pressure. 

The general formula for the sample mean is:

The X with the bar over it represents the sample mean, and it is read as "X bar". The Σ indicates summation (i.e., sum of the X's or sum of the diastolic blood pressures in this example). 

When reporting summary statistics for a continuous variable, the convention is to report one more decimal place than the number of decimal places measured.  Systolic and diastolic blood pressures, total serum cholesterol and weight were measured to the nearest integer, therefore the summary statistics are reported to the nearest tenth place. Height was measured to the nearest quarter inch (hundredths place), therefore the summary statistics are reported to the nearest thousandths place. Body mass index was computed to the nearest tenths place, summary statistics are reported to the nearest hundredths place.  

Sample Variance and Standard Deviation 

If there are no extreme or outlying values of the variable, the mean is the most appropriate summary of a typical value, and to summarize variability in the data we specifically estimate the variability in the sample around the sample mean. If all of the observed values in a sample are close to the sample mean, the standard deviation will be small (i.e., close to zero), and if the observed values vary widely around the sample mean, the standard deviation will be large.  If all of the values in the sample are identical, the sample standard deviation will be zero.

When discussing the sample mean, we found that the sample mean for diastolic blood pressure = 71.3. The table below shows each of the observed values along with its respective deviation from the sample mean.

Table - Diastolic Blood Pressures and Deviations from the Sample Mean

The deviations from the mean reflect how far each individual's diastolic blood pressure is from the mean diastolic blood pressure. The first participant's diastolic blood pressure is 4.7 units above the mean while the second participant's diastolic blood pressure is 7.3 units below the mean. What we need is a summary of these deviations from the mean, in particular a measure of how far, on average, each participant is from the mean diastolic blood pressure.  If we compute the mean of the deviations by summing the deviations and dividing by the sample size we run into a problem.  The sum of the deviations from the mean is zero.  This will always be the case as it is a property of the sample mean, i.e., the sum of the deviations below the mean will always equal the sum of the deviations above the mean. However, the goal is to capture the magnitude of these deviations in a summary measure. To address this problem of the deviations summing to zero, we could take absolute values or square each deviation from the mean.  Both methods would address the problem.  The more popular method to summarize the deviations from the mean involves squaring the deviations (absolute values are difficult in mathematical proofs). The table below displays each of the observed values, the respective deviations from the sample mean and the squared deviations from the mean.

The squared deviations are interpreted as follows. The first participant's squared deviation is 22.09 meaning that his/her diastolic blood pressure is 22.09 units squared from the mean diastolic blood pressure, and the second participant's diastolic blood pressure is 53.29 units squared from the mean diastolic blood pressure. A quantity that is often used to measure variability in a sample is called the sample variance, and it is essentially the mean of the squared deviations. The sample variance is denoted s 2 and is computed as follows:

 In this sample of n=10 diastolic blood pressures, the sample variance is s 2 = 472.10/9 = 52.46. Thus, on average diastolic blood pressures are 52.46 units squared from the mean diastolic blood pressure. Because of the squaring, the variance is not particularly interpretable. The more common measure of variability in a sample is the sample standard deviation, defined as the square root of the sample variance:

A sample of 10 women seeking prenatal care at Boston Medical center agree to participate in a study to assess the quality of prenatal care. At the time of study enrollment, you the study coordinator, collected background characteristics on each of the moms including their age (in years).The data are shown below:

24        18        28        32        26        21        22        43        27        29

A sample of 12 men have been recruited into a study on the risk factors for cardiovascular disease. The following data are HDL cholesterol levels (mg/dL) at study enrollment:

50        45        67        82        44        51        64        105      56        60        74        68 

Population Parameters

The previous page outlined the sample statistics for diastolic blood pressure measurement in our sample. If we had diastolic blood pressure measurements for all subjects in the population, we could also calculate the population parameters as follows:

Population Mean

Typically, a population mean is designated by the lower case Greek letter µ (pronounced 'mu'), and the formula is as follows:

where "N" is the populations size.

Population Variance and Standard Deviation

Statistical inference.

We usually don't have information about all of the subjects in a population of interest, so we take samples from the population in order to make inferences about unknown population parameters .

An obvious concern would be how good a given sample's statistics are in estimating the characteristics of the population from which it was drawn. There are many factors that influence diastolic blood pressure levels, such as age, body weight, fitness, and heredity.

We would ideally like the sample to be representative of the population . Intuitively, it would seem preferable to have a random sample , meaning that all subjects in the population have an equal chance of being selected into the sample; this would minimize systematic errors caused by biased sampling.

In addition, it is also intuitive that small samples might not be representative of the population just by chance, and large samples are less likely to be affected by "the luck of the draw"; this would reduce so-called random error. Since we often rely on a single sample to estimate population parameters, we never actually know how good our estimates are. However, one can use sampling methods that reduce bias, and the degree of random error in a given sample can be estimated in order to get a sense of the precision of our estimates.

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April 23 @ 1:00 pm - 2:00 pm.

Seunggeun ‘Shawn’ Lee

Adjunct Professor, Biostatistics University of Michigan

Rare variants significantly impact complex diseases. This presentation will first introduce SAIGE-GENE and SAIGE-GENE+, methodologies extending SAIGE to gene/region-based rare variant tests. These methods efficiently utilize mixed effects models to adjust for sample relatedness and saddlepoint approximations to account for case-control imbalance. SAIGE-GENE+ additionally incorporates functional annotations and collapsing of ultra-rare variants that can help to improve type I error control and power. In the second part of the talk, I will introduce our recent work to estimate effect sizes of rare variants. The method, RareEffect, uses an empirical Bayesian approach that estimates gene/region-level heritability and then an effect size of each variant. We also show the effect sizes obtained from our model can be leveraged to improve the performance of polygenic scores.

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News from the School

Bethany Kotlar, PhD '24, studies how children fare when they're born to incarcerated mothers

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Depression May Lead to Faster Cognitive Decline among Black, Latino Adults

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Sph snapshot: spring 2024 ..

SPH Snapshot: Spring 2024

Scenes from the arrival of spring, including the solar eclipse, Giving Day, Shine Lecture, and more.

Solar eclipse.

Talbot Green was a prime viewing spot for the solar eclipse, luring hundreds outside to view the celestial spectacle. Students, faculty, and staff clustered on the lawn to watch the progression of the moon across the sun, the last time the US will experience a total solar eclipse until a brief 3-minute passage over Alaska in 2033.

Giving Day 2024

Giving Day offered a chance for the SPH community to support the School during the BU-wide fundraising challenge. Nearly 12,000 donors raised just under $4M to accelerate the mission of BUSPH and help shape the future of public health. While Giving Day has passed, there are still opportunities to help support SPH’s strategic priorities .

Cupples Award Presentation

Nandita Mitra, professor of biostatistics at the Perelman School of Medicine, University of Pennsylvania, was the recipient of the 2024 L. Adrienne Cupples Award for Excellence in Teaching, Research, and Service in Biostatistics. The  L. Adrienne Cupples Award  is presented each year by the Department of Biostatistics at Boston University School of Public Health to recognize a biostatistician whose academic achievements reflect the contributions to biostatistics exemplified by  the late L. Adrienne Cupples , an emeritus professor of biostatistics and epidemiology and the award’s first recipient. Mitra was selected for her substantial achievements in each of these areas; she is currently vice chair of education and co-director of the Center for Causal Inference in the Department of Biostatistics, Epidemiology and Informatics at Penn.

Cathy Shine Lecture

The  Center for Health Law, Ethics & Human Rights  presented the annual Cathy Shine lecture to honor the memory of Cathy Shine and her dedication to the rights of all those in need of care.  This year’s event featured Cheryl Clark, MD, ScD, who serves as the inaugural executive director and senior vice president of the Institute for Health Equity Research, Evaluation & Policy at the Massachusetts League of Community Health Centers. The lecture was moderated by George Annas, William Fairfield Warren Distinguished Professor and director of the Center for Health Law, Ethics & Human Rights.

Internship & Practicum Expo

Hundreds of students connected with potential employers to explore opportunities for internships and their practicum experience , the required graduate-level internship that allows MPH students to apply the knowledge gained in the classroom in a real-world public health setting.

Arrival of spring

Just a few days after winter’s last blast of wind-driven sleet and rain, the campus came alive with the sights and sounds of spring. New plantings brightened walkways, students gathered to study and relax on Talbot Green, and robins patrolled the grass looking for a meal.

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Does a USC-designed wearable device accurately measure daily activity and sleep for children? A new series of studies will tell

April 12, 2024  | Erin Bluvas,  [email protected]

Exercise science assistant professor Bridget Armstrong has been awarded $3.5 million from the National Heart Lung and Blood Institute. She will use the five-year R01 grant to test the effectiveness of PATCH (Platform for Accurate Tracking of Children’s Health). The wearable device was designed by exercise science and electrical engineering faculty in 2020 to measure children’s routine activities (e.g., physical activity, sedentary time, sleep etc.).

“Assessing children’s 24-hour movement behaviors can reveal the complex and interdependent ways energy expenditure and sleep are related to health outcomes,” Armstrong says. “However, assessing these activities among children in free-living conditions is inherently difficult, and every available method has its own limitations.”

Our long-term goal is to give scientists better tools to measure kids' energy expenditure and sleep when they are outside the lab, going about their daily lives; doing so is essential if we want to understand how kids grow, move and develop.

Previous research has shown that devices that measure both heart rate and accelerometry offer the most precise estimates of activity and sleep. Yet those that do measure both (e.g., ActiHeart, Fitbit) are not designed for children. They can be distracting, uncomfortable and inaccurate. Further, most commercially available trackers use proprietary algorithms that do not allow access to the raw data that researchers need to analyze.

Enter PATCH. This small (only one inch by one inch), open-source wearable device integrates multiple sensors that accurately capture everyday activities. Custom-made to meet the needs of scientists and the comfort of kids, PATCH is designed to be unobtrusive, water resistant and worn for many hours/days (important for scientific studies) .

The team has already conducted a pilot study funded by the National Institute of Diabetes and Digestive and Kidney Diseases. Using a $420K R21 grant, Armstrong and members of the Arnold Healthy Kids Initiative and Research Center for Child Well-Being invited 60 children (ages three to eight years old) to test drive an early version of the device with promising results.

With this study, the team will conduct a series of studies to establish PATCH’s validity in both laboratory and free-living conditions. If their research establishes its effectiveness, this device (made from off-the-shelf parts) and its open-source software could be a game-changer for scientists working to combat the childhood obesity epidemic.

“Our long-term goal is to give scientists better tools to measure kids' energy expenditure and sleep when they are outside the lab, going about their daily lives; doing so is essential if we want to understand how kids grow, move and develop,” Armstrong says. “The results from this project will help other researchers to build their own PATCH device and independently process the data, thereby overcoming issues related to proprietary hardware and algorithms that currently limit the field of wearable devices.”

Participate in a Study

Learn more about opportunities to participate in a PATCH study (or another children's physical activity/health study) by completing a survey or texting 803-768-5652.

Find Out More

The Arnold Healthy Kids Initiative is a multidisciplinary group of researchers working  to fight childhood obesity by studying related factors  (i.e., physical activity, sedentary behaviors, sleep, diet).

Focusing on Children's Well-Being

The Research Center for Child Well-Being conducts prevention research impacting the well-being of children ages 2 to 10, with the goals of reducing the risk for social, emotional, and behavioral problems and decreasing unhealthy lifestyle behaviors.

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Challenge the conventional. Create the exceptional. No Limits.