case study about function

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• v.24(6); 2019 Sep

Lessons learnt: examining the use of case study methodology for nursing research in the context of palliative care

Paula brogan.

School of Communication and Media, University of Ulster, Northern Ireland, UK

Felicity Hasson

Institute of Nursing Research, University of Ulster, Northern Ireland, UK

An empirical social research approach, facilitating in-depth exploration of complex, contemporary contextualised phenomena, case study research has been used internationally in healthcare studies across clinical settings, to explore systems and processes of care delivery. In the United Kingdom, case study methods have been championed by nurse researchers, particularly in the context of community nursing and palliative care provision, where its applicability is well established. Yet, dogged by conceptual confusion, case study remains largely underutilised as a research approach.

Drawing on examples from nursing and palliative care studies, this paper clarifies case study research, identifies key concepts and considers lessons learned about its potential for nursing research within the unique and complex palliative and end of life context.

A case study approach offers nurse researchers the opportunity for in-depth, contextualised understanding of the systems and processes which influence their role in palliative care delivery across settings. However, philosophical and conceptual understandings are needed and further training in case study methodology is required to enable researchers to articulate and conduct case study.

Introduction

An empirical social research approach, facilitating in-depth exploration of a contemporary phenomenon ( Yin, 2009 ), case study research has been used internationally in healthcare studies ( Anthony and Jack, 2009 ) to explore systems of palliative care ( Lalor et al., 2013 ), diverse contexts for palliative care delivery ( Sussman et al., 2011 ), roles of professional groups such as pharmacy ( O’Connor et al., 2011 ), the impact of services such as complementary therapy ( Maddalena et al., 2010 ) and nursing (Kaasalainen et al., 2013). In the United Kingdom, case study methods have been championed by nurse researchers ( Payne et al., 2006 ), particularly in the context of community nursing and palliative care provision ( Kennedy, 2005 ; Walshe et al., 2004 , 2008 ) and its applicability to palliative and end-of-life care research is established ( Goodman et al., 2012 ). Suited to the study of complex processes ( Walshe, 2011 ), case study methodology is embedded in professional guidance on the development of complex interventions ( Medical Research Council, 2008 ). Yet, case study is dogged by conceptual confusion (Flyvberg, 2006), and, despite sporadic use, remains underutilised as a research approach in healthcare settings ( Froggatt et al., 2003 ).

Illustrated by examples from nursing and palliative care studies, this paper aims to clarify conceptual understanding and identify key lessons for its application within these unique and complex contexts and, more broadly, for nursing research.

Origins and definitions

French sociologist Frederic Le Play (1806–1882) is associated with the origin of the case study approach ( Hamel et al., 1993 ). Using a purposive sample of working class families and fieldwork methods of observation and individual interview, he sought a contextualised and in-depth understanding of their individual experiences. Each family case study uncovered the unique experience of that family, but each additional family studied was another ‘ case of the lived experience’ of working class families in mid-18th century France. Thereby, Le Play used the lens of individual experience ( Yin, 2013 ) to build comparisons across families and enrich overall understanding of that complex society.

This early glimpse of the case study approach showed it to be a straightforward ‘field investigation’ ( Hamel et al., 1993 ); epistemologically pragmatic as it generated knowledge through data drawn from diverse sources, such as family members, and used the best available data collection methods then, to inform a holistic and contextualised understanding of how people operated within a complex social system ( Stake, 1995 ).

However, defining case study has become increasingly challenging since its expansion into North America in the 1800s ( Platt, 1992 ), and its use across a range of disciplines such as politics ( Gerring, 2004 ), social science ( George and Bennett, 2005 ), education ( Merriam, 1998 ) and healthcare ( Yin, 2013 ). Variously characterised as a case report, data collection method and methodology ( Anthony and Jack, 2009 ), the development of case histories as illustrations in health and social care and in education ( Merriam, 1998 ) has contributed to further confusion for researchers and readers of case study research ( Gomm et al., 2000 ). Critiques of case study note that it lacks a single definition, such that a plethora of discipline dependant interpretations ( Simons, 2009 ) and loose use of the term case study ( Tight, 2010 ) have contributed to confusion and undermined case study credibility. However, Simons ( 2009 , p. 63) advises researchers that case study must be seen within the complex nexus of political, methodological and epistemological convictions that constitute the field of enquiry, and variations of these may be glimpsed in Table 1 as definitions from four eminent and frequently cited case study authors illustrate philosophical and discipline-influenced differences in emphasis. Consequently, the case study definition selected, with its underpinning ontology and epistemology has important implications for the coherent outworking of the overall research design. It is therefore notable that many of the palliative care case studies contained in Table 2 fail to identify any such definition and this may have implications for interpretation of the quality of studies.

Definitions of case study by four key authors, showing the variation in meaning and interpretation.

Examples of Case Studies (CS) conducted in palliative care contexts.

Case study as a philosophy for the epistemology of knowledge generation

Although frequently linked to naturalistic inquiry ( Lincoln and Guba, 1986 ), interpretative/constructivist philosophy and qualitative methodology ( Stake, 1995 ), case study is not in fact bound to any single research paradigm ( Creswell, 2013 ). It is philosophically pragmatic, such that the case study design should reflect the ontological positions and epistemological considerations of the researchers and their topic of interest ( Luck et al., 2006 ). In practice, this means that case study research may pragmatically employ both qualitative and quantitative methods independently or together in order to respond to the research objectives ( Cooper et al., 2012 ; Simons, 1987 ; Stake, 2006 ). So whilst Table 2 shows that qualitative case studies are common in palliative care, epistemological variation is evident and reflects the study topic, purpose and context of the research. For example, Maddalena et al. (2010) used in-depth interview and discourse analysis to understand individual patient meaning-making; Brogan et al. (2017) used focus groups and thematic analysis as part of an embedded element of a multiple case study, to contrast the diverse perspectives of multi-disciplinary healthcare practitioners on end-of-life decision-making; Sussman et al. (2011) incorporated survey data into a mixed methods multiple case study which explored health system characteristics and quality of care delivery for cancer patients across four regions of Canada. Consequently, it is useful to ‘conceptualise (case study) as an approach to research rather than a methodology in its own right’ ( Rosenberg and Yates, 2007 , p. 448), so that a non-standardised approach exists and the case study design, its boundaries, numbers of cases and methods are guided by the stated underpinning ontological perspectives of the researcher and their topic of interest. The study then flexibly adopts the best methods to gain an in-depth, holistic and contextualised understanding of the phenomenon of interest – the latter objectives being at the core of any definition of case study research.

Key case study concepts and lessons for practice

When considering the utility of a case study approach, research conducted in complex palliative care contexts offers several insights into how central concepts translate to practice.

Contextualised understanding

Drawing on the definitions in Table 1 , Stake emphasised the particularity and intrinsic value of each individual case ( Stake, 1995 ), to emphasise the usefulness of multiple cases to increase insight ( Stake, 2006 ), analyse patterns ( Gerring, 2004 ; George and Bennett, 2005 ) and develop causal hypotheses ( Yin, 2013 ). Yet, whatever the purpose, all case studies are concerned with the crucial relationship between a phenomenon and the environment in which it has occurred. In practice therefore, case study researchers must be concerned with understanding the background systems, structures and processes that influence and interact with the phenomenon under study. This capacity for contextualised and holistic understanding is underpinned by use of multiple data collection methods, such as observation, interview and document review, used simultaneously or sequentially ( Stake, 2006 ; Scholz and Tietje, 2002 ), to mine multiple sources of data, such as participant experience ( Brogan et al., 2017 ; Kaasalainen et al., 2012 ), documents (Lalor et al., 2003) service evaluations ( Walshe et al., 2008 ), and diaries ( Skilbeck and Seymour, 2002 ). This is exemplified in a study by Walshe et al. (2011) , who investigated referral decisions made by community palliative care nurses in the UK, by capturing interview data on the self-reported perspectives of healthcare professionals, in combination with observed team meetings in which decisions were influenced, and review of the written referral policies, protocols and palliative healthcare strategies specific to those decisions. This comprehensive and complex data enabled comparison of decisional processes and their influencing factors both within and across three Primary Care Trusts, thus providing a contemporaneous understanding of the complex relationship between individual nurse's referral decisions and the impact of the organisational and professional systems that underpinned them. Enhancing rigor, such methodological triangulation importantly contributed to the richness of data analysis and the development of assertions which might be drawn from the findings ( Cooper et al., 2012 ; Stake, 2006 ).

Process-focused

Flexible data collection methods, linked to the research purpose, enables case study researchers to gather both historical and real-time data in a variety of ways. For example, Kennedy’s longitudinal case study ( Kennedy, 2002 ) observed snapshots of the initial and follow-up assessment conducted by 11 district nurses over the subsequent 12 months, enabling an exploration of the outcome and impact of their decision-making, demonstrating the usefulness of case study to understand complex roles and processes which are fluid and elusive ( Yin, 2013 ), or otherwise difficult to capture, particularly in the intimate interpersonal contexts where nursing happens.

Analytic frame

Palliative care studies reviewed frequently report the use of thematic analysis. However, whilst this approach is certainly useful to process data generated in qualitative case studies, the approach to analysis must be congruent with the research design and reflect the purpose of the research and methods used. Moreover, beyond decisions about use of thematic analysis or descriptive statistics etc., in case study, important decisions must be made about the analytic frame of the research. Gerring’s definition (2004) set out the analytic frame in which the cases studied might be understood, explaining that each unit of analysis (or case), sheds light on other units (or cases). Thus defined, an individual case offers intrinsically valuable information about a phenomenon ( Stake, 1995 ) and the purposeful selection of cases is central to case study design. This is because, viewed from a certain angle, each case is also a case of something else, such that the findings have broader implications ( Gerring, 2004 ; Simons, 2009 , 1987 ; Yin, 2013 ). In practice, this means that the case and what it is a case of, must be clearly identified and well defined at the outset of a study, since this has implications for the relevance of findings. This can be seen in a study by O’Connor et al., (2011) , who considered the perceived role of community pharmacists in palliative care teams in Australia. Each unique case included multi-disciplinary healthcare team members, such as pharmacists, doctors and nurses working in localities, whose perspectives were sought. Each locality group was a case of community pharmacy provision in palliative care settings in Australia, and findings had implications for the planning of community services overall. So, insight development was possible at an individual, group and organisational level, and inferences were made directly in relation to the parameters of that case study.

The addition of several carefully selected cases, as in multiple case studies, offers the opportunity to analyse data gained within and across cases ( Stake, 2006 ). Case selection may be made in order to explore similarities and contrasting perspectives ( Brogan et al., 2017 ), understand the various impacts of geographical differences ( Sussman et al., 2011 ), and different organisational influences ( Walshe et al., 2008 ). However, whilst repetition of data across cases may reinforce propositions made at the outset of a study, the purpose of increasing the number of cases in case study research is primarily about increasing insight development into the complexity of a phenomenon ( Stake, 2006 ). Since case study is the study of a boundaried phenomenon ( Yin, 2013 ), establishing the analytic frame then underpins the selection criteria for potentially useful cases. Such clarification is essential since it provides the lens through which to focus research ( Gerring, 2004 ; Scholz and Tietje, 2002 ; Stake, 2006 ) and permits key decisions to be made about data which may be included and that which is not applicable.

However, significantly, this information is rarely articulated within published case studies in palliative care. This is an important issue for the quality of case study research, since description of the process of refining case study parameters, establishing clear boundaries of the case, articulating propositions based on existing literature, identifying the sources of data (people, records, policies, etc.) and the ways in which data would be captured, establishes clarity and underpins a rigorous, systematic and comprehensive process ( Gibbert et al., 2008 ), which can usefully contribute to practice and policy development ( George and Bennett, 2005 ).

Shaped by organisational systems, intimate settings and significant life stage contexts, the interconnection between context and participant experience of palliative care is one example of a process of healthcare provision that is often complex, subtle and elusive ( Walshe et al., 2011 ). Case studies conducted in these swiftly changing contexts illustrate several characteristics of case study research, which make it an appropriate methodological option for nurse researchers, providing the opportunity for in-depth, contextualised understanding of the systems and processes which influence their role in palliative care delivery across settings ( Walshe et al., 2004 ) and many others who seek a contextualised, contemporaneous understanding of any complex role or process ( Yin, 2013 ; Simons, 2009 ). This fieldwork-based approach has the potential to achieve depth and breadth of insight through the pragmatic, but carefully planned and articulated, use of multiple methods of data collection in order to answer the research question ( Stake, 2006 ) when analysed systematically within a frame determined at the outset by the definition of the case and its boundaries ( Gerring, 2004 ). Yet, the methodological flexibility that is advantageous in complex contexts, may be misunderstood ( Hammersley, 2012 ), particularly where terminology is unclear ( Lather, 1996 ) or where description of the systematic and rigorous application of the approach is missing from the report ( Morrow, 2005 ). Taken as an example of one area of healthcare research, evidence suggests that palliative care studies that deal meaningfully with underpinning philosophical perspectives for their selected case study approach, or which articulate coherent links between the defined case, its boundaries and the analytical frame are rare. The impact of such omissions may be the perpetuation of confusion and out-dated perceptions about the personality and quality of case study research ( King et al., 1994 ), with implications for its wider adoption by nurses in healthcare research. Further training in case study methodology is required to promote philosophical and conceptual understanding, and to enable researchers to fully articulate, conduct and report case study, to underpin its credibility, relevance and future use ( Hammersley et al., 2000 ; Stake and Turnbull, 1982).

Key points for policy, practice and/or research

• Case study is well suited to nursing research in palliative care contexts, where in-depth understanding of participant experience, complex systems and processes of care within changing contexts is needed.
• Not bound to any single paradigm, nor defined by any methodology, case study’s pragmatism and flexibility makes it useful for studies in palliative care.
• Training is needed in the underpinning philosophical and conceptual basis of case study methodology, in order to articulate, conduct and report credible case study research, and take advantage of the opportunities it offers for the conduct of palliative and end-of-life care research.

Paula Brogan is a Lecturer in counselling and communication in the School of Communication and Media, and was recently appointed as Faculty Partnership Manager, University of Ulster. Dual qualified as a Registered Nurse with specialism in District Nursing and as a Counsellor/couple psychotherapist (Reg MBACPaccred), she has over 30 years’ clinical practice experience in community palliative care nursing and the provision of psychological care to patients and families dealing with palliative and chronic illness. Having worked across statutory, voluntary and private sectors, her PhD focused on multi-disciplinary decision-making at the end of life with patients and families in the community setting. Currently secretary of the Palliative Care Research Forum for Northern Ireland (PCRFNI), Paula’s ongoing research interests include communication and co-constructed decision-making in palliative and chronic illness, and the psychological support of individuals, couples, patient-family groups and multi-disciplinary staff responding to challenges of advanced progressive illness.

Felicity Hasson is a Senior Lecturer in the Institute of Nursing Research at the University of Ulster with 20 years’ experience in research. A social researcher by background, she has extensive experience and knowledge of qualitative, quantitative and mixed method research and has been involved in numerous research studies in palliative and end-of-life care. She completed her MSc in 1996 and her PhD from University of Ulster in 2012. Felicity sits on the Council of Partners for the All Ireland Institute of Hospice and the Palliative Care Palliative Care Research Network (PCRN) and is an executive board member for the UK Palliative Care Research Society. She holds an editorial board position on Futures and Foresight Science. Felicity has an established publication track recorded and successful history of grant applications. Her research interests include nurse and assistant workforce, workforce training, palliative care and chronic illness (malignant and non-malignant with patients, families and multi-disciplinary health care professionals) and public awareness of palliative care and end of life issues.

Sonja McIlfatrick is a Professor in Nursing and Palliative Care and has recently been appointed as the Head of School of Nursing at University of Ulster. She is an experienced clinical academic with experience in nursing and palliative care practice, education and research. She previously worked as the Head of Research for the All Ireland Institute of Hospice and Palliative Care (2011-2014) and led the establishment of the All Ireland Palliative Care Research Network (PCRN) and is the current Chair of the Strategic Scientific Committee for the PCRN (AIIHPC). Sonja is an Executive Board member for the UK, Palliative Care Research Society and is member of the Research Scientific Advisory Committee for Marie Curie, UK. Sonja holds an Editorial Board position on the International Journal of Palliative Nursing and Journal of Research in Nursing. Professor McIlfatrick has published widely in academic and professional journals focused on palliative care research and has a successful history of grant acquisition. Sonja has a keen interest in doctoral education and is the current President of the International Network of Doctoral Education in Nursing (INDEN). Her research interests include, palliative care in chronic illness, decision making at end of life; public awareness of palliative care and psychosocial support for family caregivers affected by advanced disease.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics statement

Ethical permission was not required for this paper.

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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5.2.1: Function Case Study (Lambert)

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• Page ID 87676

• Carey Smith
• Oxnard College

By Adam Lambert, Zero to MATLAB, 8.1 Basic Functions

Generally, when we make a function we will be using two separate m-files. One m-file will contain the code for the function. A 2nd file (the test file) will call the function.

Two notes of caution:

1. Do not try to run a function file by itself. A function file is different from a script file. If you do try to run a function file, MATLAB or Octave will usually complain that the inputs are not defined. You need to call the function from the test script file.

2. Do not "clear all" inside the function. That would clear your inputs and the function will fail. Only "clear all" in the test script file.

The function syntax can be confusing at first. In simple problems it can seem pointless to implement a function, but  you want to practice creating functions with simple problems. As you begin to write more complex programs, functions become a valuable tool. Take the time to learn the operation with these simple examples.

The syntax required to build a function is the most complex that we have encountered. It takes some practice to get it organized in your head. Let's dive into a simple example and take some time to discuss all of the pieces.

Example \(\PageIndex{1}\) times_two function

This is a function which will accept a number as input, multiply it by two, and return the result of that calculation as output. This code should be saved in an m-file called times_two.m. The name of the function must be the same as the m-file where it is stored.

function y = times_two(x)     y = 2*x; end

On the first line we see the function command, followed by the expression y = times_two(x). We call this line the declaration. (Some authors call this the function declaration; others call it the function signature. Both declaration and signature mean the same thing.) The function command tells MATLAB that this code is a function. It must be the first command in the file.

The variable x is the input variable for the function. Whatever number that we pass to the function will be assigned to the variable x which can then be used in the calculations inside the function. The variable y to the left of the assignment operator is the output variable. This value must be assigned during the execution of the function. In this simple case, the assignment is the only expression inside the function. As long as the variable is assigned within the function, then the value of the variable will be returned once the code inside the function completes.

The name of the function, times_two, is also the command that we use to execute the function. When we execute a function, we say that we call the function. A line of code in a script that calls a function is often referred to as a function call. In order to call a function, the m-file must be saved in the current directory.

If you look at the structure of the declaration, you can see that it mimics the structure of the code which is used to call it. The output variable is in the position to be assigned a value, and the input variable is in the position to pass a value into the function. Consider this similar expression using a built-in command:

>>z = sin(pi)

The value of pi is passed into the sin function and the result is assigned to the variable z. The declaration of this function would look like this.

function y = sin(x)

Inside there would be an algorithm to calculate the sine of the value of x and assign it to the variable y.

Now that we've had an overview of how functions are made and implemented, let's practice with this simple example to learn more about the behavior.

1. Open up a new m-file and save it in the current directory as times two.m.

2. Type the code from the times two example into the script and save it. Note that the file name and the function name are the same.

3. Now go to the Command Window and call the function at the prompt. We need to input a number, just like if we used one of the trigonometric functions.

>>times two(4)

The function will return the value 8. Note that the variable y is not saved in the Workspace and the value is assigned to the default variable name ans. If you do have a variable y from a previous calculation then clear the Workspace and try again. This is important, because the function only returns a value, not a variable. We'll discuss this in more detail in the next section.

4. We can use a variable to pass the input value into the function. We can also use a variable to store the returned results. Try the following sequence in the Command Window.

>>a = 4; >>b = times two(a);

Note that the variable names are not the same as the names inside the function. They do not have to be, because they are simply passing values in and out of the function. The external variables never interact with the code inside the function.

Let's look back at the code in times two.m and walk through the whole process. First, the input value is assigned to the variable x. This can occur with a number or a variable. If the input to the function is a variable, then MATLAB will look up the value and assign that value to the variable x. Once the variable x is defined, then the code will execute. In this case, x will be multiplied by 2 and the result assigned the to variable y. Then, because all of the code inside the function has completed, the value of the output variable will be returned.

This is the most complex topic that we have covered, so don't be discouraged if this is confusing the first time through. As we move through the chapter and you get more experience, the flow of information will be easier to see.

Add example text here.

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What the Case Study Method Really Teaches

• Nitin Nohria

Seven meta-skills that stick even if the cases fade from memory.

It’s been 100 years since Harvard Business School began using the case study method. Beyond teaching specific subject matter, the case study method excels in instilling meta-skills in students. This article explains the importance of seven such skills: preparation, discernment, bias recognition, judgement, collaboration, curiosity, and self-confidence.

During my decade as dean of Harvard Business School, I spent hundreds of hours talking with our alumni. To enliven these conversations, I relied on a favorite question: “What was the most important thing you learned from your time in our MBA program?”

• Nitin Nohria is the George F. Baker Professor of Business Administration, Distinguished University Service Professor, and former dean of Harvard Business School.

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Production function for modeling hospital activities. The case of Polish county hospitals

Contributed equally to this work with: Agata Sielska, Ewelina Nojszewska

Roles Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Visualization, Writing – original draft, Writing – review & editing

* E-mail: [email protected]

Affiliation Department of Applied Economics, Collegium of Finance and Management, SGH Warsaw School of Economics, Warsaw, Poland

Roles Conceptualization, Methodology, Visualization, Writing – original draft, Writing – review & editing

• Agata Sielska, 
• Ewelina Nojszewska

• Published: May 12, 2022
• https://doi.org/10.1371/journal.pone.0268350
• Reader Comments

The aim of the article is to present the use of production function as a source of knowledge for managers of county hospitals to make rational decisions so as to achieve economic efficiency, including naturally the financial efficiency. The healthcare sector in each country differs from other sectors of the economy. The economically effective operation of county hospitals in Poland is very difficult due to all their determinants. Therefore, all economic analyses should be used to help hospital managers achieve this goal, and production function remains underestimated as a source of knowledge. The Cobb-Douglas and translog production functions were used as sources of knowledge for decision-making by county hospitals. Total number of patient-days was a dependent variable; and the total number of beds, the number of doctors and nurses (in full time equivalents, FTEs) and costs (of materials, electricity, services) were a set of explanatory variables. The significance of explanatory variables most often appeared in models accounting for the workload of nurses. On the other hand, the greatest fit measured with the residual standard error was characterised by models accounting for the number of beds. For each type of production function, the diversified results obtained show the properties of production function. This kind of knowledge is not provided by analyses which are not based on production functions.

Citation: Sielska A, Nojszewska E (2022) Production function for modeling hospital activities. The case of Polish county hospitals. PLoS ONE 17(5): e0268350. https://doi.org/10.1371/journal.pone.0268350

Editor: Maurizio Naldi, LUMSA: Libera Universita Maria Santissima Assunta, ITALY

Received: December 10, 2021; Accepted: April 27, 2022; Published: May 12, 2022

Copyright: © 2022 Sielska, Nojszewska. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: Data comes from a third party: Polish Association of Employers of Poviat Hospitals (Ogólnopolski Zwiazek Pracodawców Szpitali Powiatowych - abbr. OZPSP) and were transferred to the Author for conducting quantitative analysis of financial situation in Polish poviat hospitals. After the analysis was finished, the corresponding author received special access privileges to the data that others would not have. The corresponding author was allowed to use the data for her further research under confidentiality agreement. Data cannot be shared publicly because of the confidentiality agreement between the Author and OZPSP. However, interested parties may contact OZPSP via: http://ozpsp.pl and [email protected] (chair). The dataset is known as the "data on county (poviat) hospitals coming from the survey conducted in 2019". No other names or ID numbers/codes apply.

Funding: The author(s) received no specific funding for this work.

Competing interests: I have read the journal’s policy and the authors of this manuscript have the following competing interests: Authors were conducting quantitative analysis for Polish Association of Employers of Poviat Hospitals (OZPSP – Ogólnopolski Związek Pracodawców Szpitali Powiatowych) who provided data for the study. This does not alter our adherence to PLOS ONE policies on sharing data and materials.

Introduction

Goals of the research.

Hospitals play a significant role in the treatment process and at the same time constitute a group of healthcare providers which take a significant part of health spending [ 1 ]. Production function is used to analyse the effectiveness of operation of hospitals, helping in this way to effectively manage hospital’s resources, and thus to properly care for the state of health. The issue of such an application of this function is presented on the basis of the literature, primarily articles, the review of which was based first of all on the PubMed, JSTOR and Springer Link databases.

Hospitals play a special role in the treatment process, i.e. in achieving clinical effectiveness, which translates into the health status of individual patients and the entire society. They implement the most expensive treatment procedures while encountering budgetary constraints, which makes it impossible to meet all health needs and the total demand for health services. Looking from the perspective of striving for clinical effectiveness in the face of shortages of financial resources, material capital and, above all, human capital, striving for the effective use of all these resources is of particular importance. Researching the effectiveness of hospitals is particularly difficult due to the specific nature of their operations. That is why it is so important to use all tools for this purpose. The production function is precisely the tool which—in the opinion of the authors—is used the least frequently. Therefore, in the presented article, attention was focused on demonstrating the possibility of gaining knowledge through the analysis of the production function of hospitals by decision-makers at the hospital and healthcare system level. The aim of the study is to show that the empirical analysis of the production functions of hospitals provides quantitative and qualitative information allowing for making decisions regarding hospital management, its organization and financing. In the current paper we focus on the possibilities presented by the production functions, our goal is not to study the efficiency of the hospitals. The study also analyses which inputs are mostly useful for the modelling of hospital performance.

Previous studies

The literature review shows that relatively few researchers have used the production functions to analyse the functioning of hospitals and their efficiency. Moreover, the research conducted so far is varied and therefore incomparable, but each point of view brings a new aspect to the knowledge obtained through the analysis of the production function. Therefore, it is worth quoting the results obtained in the previous research.

Authors of some papers focus on the usefulness of using the production function to analyse the functioning of service providers, and above all hospitals. The microeconomic concept of production function links products with the factors employed to produce them. It is used in health economics, and in empirical research this function is estimated with econometric tools. The creator of this analytical approach, which contributes to the understanding of the effectiveness of provision of health services, is Feldstein [ 2 ]. According to his approach, a hospital is an enterprise for which costs, productivity and economies of scale can be analysed primarily on the basis of the estimated production function. It is possible and also necessary to get acquainted with the efficient use of resources and production capacity by hospitals. Properly defined hospital products are linked to the factors of production selected for the study using different kinds of functions, but primarily the Cobb-Douglas function [ 2 ]. The knowledge of results of this kind of research is of great importance when making decisions with regard, for example, to the allocation of human capital, the training of medical staff (first of all doctors), the size of investment in hospital infrastructure or the distribution of limited hospital capacity among its wards. Using the production function and knowledge of costs, it is possible to determine the different types of costs per unit of product, and this is of particular importance when this kind of unit is a disease case. Thanks to this, it is possible to create benchmarking of hospitals or wards regarding cost effectiveness or quality of treatment in relation to each case mix [ 2 ]. Comparing health services on account of the products themselves is not appropriate, because the failure to account for the factors employed to produce them may create a false picture. Thanks to the use of production function for a full analysis of health services, it is also possible to formulate expectations regarding them, deviations from them and from the patterns, which translates into a worse or better quality of services as well as effectiveness of their provision. Owing to the full knowledge gained from production function, indicators can be constructed to measure and evaluate the activities of healthcare providers [ 3 ]. An example of such a use of production function can be maternity hospitals due to a certain homogeneity of services, and it is in their case that attempts were made to explain the quality and efficiency of their products with production function. For example, such a study was conducted for 193 English maternity hospitals with the Cobb-Douglas and logarithmic-square functions. It turned out that the most important factors were nurses and the number of beds, although their employment did not achieve technical efficiency, and economies of scale were constant [ 4 ].

A large part of the literature is devoted to the possibility of using the production function to study the effectiveness of hospitals. It seems that efficiency is the best concept/tool for operation analysis of enterprises, including healthcare providers which transform factors into products. Production function is a fundamental tool for efficiency analysis; it models the maximum production volume for an employment combination of production factors. It is the function of production that is a critical factor to determine which entrepreneurs are better than others in transforming factors into products [ 5 ]. Therefore, some researchers analyse what forms of production function should be used to analyse efficiency, and also formulate new proposals, e.g. flexible form of production function derived from the Generalized Additive Models and tested on data from public hospitals in Spanish Galicia during the period 2002–2008 [ 6 – 8 ]. In another example of attempt to improve the analytical tool, which is the form of estimated production function, researchers seek to identify a form which will not only allow to study the inefficiency of hospitals, but also draw economic conclusions through the knowledge of scale elasticity, scale efficiency and which will be serve an effective allocation of resources [ 9 ]. The authors’ aim is to provide decision-makers in hospitals with an administrative tool based on the analysis of the stochastic production function, which will enable the identification of non-standard production conditions as well as the determination of a set of corrective actions in the form of proper reallocation of resources. In another study, researchers focused on determining the best form of production function, which the examination of the hospital costs is based on [ 10 ]. In their study, they used data from the Washington State hospitals for 1988–1993 to construct long-term cost functions and concluded that the Leontief production function works best, especially when compared to, for example, the translog function. In the next example, attention is focused on the method of determination of the optimal production function to investigate the effect of nurse staffing on patient mortality in acute-care hospitals under Taiwan universal health insurance system [ 11 ]. The Random Effect Zero-Inflated Poisson model incorporating a first order autoregressive structure was used for this purpose. The problem of choosing the right analytical tools was also addressed in the next article [ 12 ]. The authors focused on creating a new flexible hospital production function using the Generalized Additive Model (GAM) and on the comparison of the results obtained with those provided by the classic Cobb-Douglas model. The databases of public hospitals of the Galician health service for the 2012–2018 time series were used for the calculations made with the use of both tools. The authors of another study used the empirical production function to present the technology used by recipients and living donors on Kidney Exchange platforms to explain the productivity of these platforms due to productivity factors identification [ 13 ].

Continuing the topic of efficiency research in the next part of the articles, the production function is a tool for a fuller understanding of its activities by hospitals. In such studies, the problem is the selection of an appropriate functional form. They are usually related to the search for the drivers of ineffectiveness. For example, econometric and linear programming tools are used for this purpose. Production function is a tool for exhaustive analyses, and thus for gaining further knowledge of the performance of such enterprises as hospitals. Particularly interesting results are provided by the model of effects of technical inefficiency, which is one of the most commonly used in the analysis of stochastic frontier function. This is because it provides the ability to estimate technical efficiency specific to each firm, and also combines changes in the functioning of the company with changes in exogenous or conditional variables (e.g. forms of ownership or socio-economic characteristics). In addition, in the panel approach, this model enables the identification of the effects of technical changes and technical efficiency changing over time [ 14 ]. Such models of technical inefficiency effects for the stochastic frontier of production function and panel data are used in the analyses of various sectors of the economy and, according to the authors, should also be applied to hospitals [ 15 ]. Stochastic frontier analyses are used to study the efficiency of hospitals by using the production as well as cost functions [ 16 ]. The use of the cost function also enables a simultaneous estimation of both technical and allocative efficiency, since the cost function is a dual function in relation to production function (under certain conditions) [ 17 ]. For example, production function was used in the study of the technical efficiency of private and public hospitals in Turkey [ 18 ]. The technical and cost effectiveness of German hospitals was investigated using SFA (Stochastic Frontier Analysis) for production function (Cobb-Douglas) [ 19 ]. Many examples could be given of using production function to measure efficiency with SFA. The study of the technical and cost efficiency of Nordic hospitals is an example of using production function through SFA and DEA (Data Envelopment Analysis) [ 20 ]. Another example of the use of both of these tools is the study of the effectiveness of government hospitals in Palestine [ 21 ]. The calculations revealed that the technical efficiency of these hospitals varied greatly (from 28% to 91%), and in addition, the production process was characterised by declining economies of scale, so the results obtained enable the determination of directions of changes in hospital management; the benchmarkings drawn up should be an incentive to improve the efficiency of Palestinian hospitals. This analysis is particularly important because it concerns the public sector, where the market mechanism does not work and due to it, it is possible to compare best practices in the provision of health services. It is about the improvement of the quality of these services as well as the reduction in their costs down to the necessary minimum—according to the microeconomic definition of the cost function. It is possible thanks to the application of production function, which, thanks to its complexity, contains information about all hospital activities related to health services. This approach is particularly important for university hospitals, which also deal with medical education, clinical research and implementation innovative technologies.

The production function can also be used for cost analysis as shown by some articles. It is worth emphasising that production function may be used to introduce activities to curb the increase in the costs of operations of healthcare providers, primarily hospitals. The exponential increase in these costs, as well as the related forecasts, already in 2010 alarmed the WHO and prompted the encouragement of policymakers and politicians to take action to hinder the adverse trend [ 22 ]. In addition, the report shows that up to 40% of healthcare spending is wasted and therefore, it focuses on 10 ways to improve efficiency. Among other things, the emphasis was put on the significance of effective use of all resources in the process of production of health services. All kinds of cost functions are used to analyse hospital costs and attempts to achieve efficiency. The microeconomic cost function shows all the volumes of production made at minimum, i.e. necessary costs. Using a dual approach, it can be concluded that cost functions describe the axial volume of production which is possible to be made at a specific cost level. This position/locus of efficiency is derived from production function as well as from the prices of production factors employed [ 23 ]. Thus, cost analyses of hospitals are possible by the isolation of cost function from production function. Cost function can also be used to study efficiency, and therefore some research deals with improving and testing different forms of production functions to obtain the best efficiency results for the cost function derived from them [ 17 ].

Many articles [ 16 , 24 – 27 ] focus on estimating the productivity of hospitals (thanks to the knowledge of production function) as well as their costs is a fundamental issue in making decisions concerning, for example, how to finance hospitals or introduce appropriate incentives both to reward and punish those who have a positive or negative impact on the hospital performance. In an example of such a study, the aim of the analysis was to find out the determinants of the temporary as well as permanent effectiveness of hospitals [ 28 ]. 133 hospitals in Lombardy were examined between 2008 and 2013 to find out that the average total inefficiency was almost 25% higher than shown in the former estimates. This was possible thanks to the distinction between temporary and permanent effectiveness, determination of their meaning and changes.

Investments in IT systems are a prerequisite for the improvement of the quality of health services and therefore their impacts should be diagnosed in detail. The growth rate of spending on it reaches the growth rate of healthcare spending in the US [ 29 , 30 ]. In the studies devoted to the analysis of this issue, hospital production functions are used, accounting for two types of IT systems: the first of them used in the treatment process and the other in administrative activities [ 31 ]. The analysis shows the significance of the implementation itself of IT innovations as well as the ways of implementation; thus, it should all be done in the right order and in the right places. Since a properly implemented information technology (IT) affects the increase in hospital productivity, the next article is devoted to the examination of it and assesses a value-added hospital production function parameters [ 32 ]. Endogenous choices of manufacturing factors, i.e. labour, capital, health IT labour, health IT capital were taken into account in order to determine the returns that hospitals obtain from the introduction of health IT. The calculations based on data from almost all hospitals in California from 1997 to 2007 show that thanks to investments in IT, hospitals obtained high marginal products.

The challenge for hospitals is to implement new, lower-value technologies to replace those of greater value, which forces hard budgetary constraints [ 33 ]. Out of concern for the quality of services, each country wants to control the implementation of technologies of a lower value, e.g. by imposing cost-effectiveness thresholds. The authors of this article focused on calculating the threshold for Dutch hospitals.

The knowledge gained from the analysis of hospital production function is used to properly manage the resources that the hospital possesses. The approach basing management on the knowledge obtained from production function is pragmatic and serves reduction in the waste of resources [ 34 ]. The authors of this article determined a short- and long-term production function in relation to 64 Iranian hospitals in the years 2007–2009 as well as the elasticity of production factors (showing a percentage increase in products due to a 1% increase in the employment of the analysed factors). The results obtained form the basis for the management improvement. Production function was treated as a tool to improve the efficiency of the use of resources in hospitals operating under social security, i.e. it was also about the efficiency of spending public money. This study showed that hospitals should change medical staff management so that this most important factor is employed in an optimal way. The issue of the effectiveness of hospitals in Iran operating under social security was discussed in an article using SFA based on the Cobb-Douglas estimated production function for the years 2008–2015 [ 35 ]. The coefficients of elasticity for the selected factors, their marginal products and the marginal rate of technical substitution (MRTS) were also calculated. MRTS between nurses and doctors showed that the burden on hospital costs caused by doctors’ earning can be reduced by increasing the employment of nurses. The calculations obtained show that production in these hospitals is capital-intensive and achieves increasing economies of scale. Inefficiency was reduced to a minimal extent over time, and the knowledge of its causes gave rise to improved efficiency through a properly conducted reform. The next article also estimated the production functions of 67 Iranian public hospitals with the Cobb-Douglas function in order to obtain the knowledge of productivity of employed factors in order to effectively manage them [ 36 ]. The flexibility of hospital services in relation to medical staff and beds as well as technical efficiency coefficients were recalculated again. The calculations confirmed the existence of inefficiency, and the knowledge of their carriers should be used to reduce it.

Production function is also used to study the quality of performance of primary health care. In one of the articles, researchers analysed the effectiveness of primary healthcare in Denmark as a result of shortages of GPs within the healthcare system [ 37 ]. They tried to identify organisational factors affecting the production of GPs as well as its effectiveness. The calculations showed that it was necessary to introduce thoroughly checked organisational changes, especially with regard to the relationship between nurses and doctors.

The impact of doctors on the production of two types of hospitals, namely those dealing with teaching and those having nothing to do with it, was the subject of another article many years ago [ 38 ]. The analysis showed that doctors had a strong and positive impact on the productivity of other factors, and that there was a substitution relationship between them and other resources.

Production function may also be used to study a trade off between the quality of services provided and their number. An example to cite may be an article analysing this problem on the basis of dialysis centres financed by Medicare [ 39 ]. Dialyses are increasingly costly procedures, and therefore the knowledge gained from the analysis of the production function accounting for exogenous quality decisions allows for a better solution to the problem of dialysis centres regarding their development and combining a growing number of patients with the safety and quality of dialysis.

Another example of using hospital production function is shown in the article in which the subject of study is the impact of diffusion of technological progress on productivity growth in the treatment of heart attacks [ 40 ]. The authors, thanks to hospital production function, built a macroeconomic model to analyse the data of 2.8 million Medicare patients between 1986 and 2004. They proved that hospitals which quickly implement cost-effective innovations achieve significantly better health results of their patients. On the other hand, with a constant, deferred adoption of new technologies, the marginal rate of return on expenses is poor. To sum up, even small differences in the propensity to implement innovative effective technologies lead to a significant diversification in productivity between hospitals.

Production function may also be used to determine the TFP of hospitals [ 41 ]. In this way, Japanese hospitals were analysed with panel data from 47 prefectures for hospitals and data from the Secondary Medical Area levels from 1998–2007. The analysis confirmed the existence of economies of scale, as a greater productivity was recorded in larger hospitals.

The analysis of production function may also be used to gain knowledge and opportunities to improve the quality of hospital administration activities [ 42 ]. The authors focused on the importance of the stochastic factors they selected, i.e. the transfer of patients between wards caused by the diversity of diseases, the time of reaching the appropriate hospital unit, the number of patients leaving hospital for the efficiency of administration work.

Contribution

The literature review presented above shows that the range of possibilities of using the production function to analyse the functioning of hospitals is very wide. Current paper contributes to the literature because it is the first study of this type conducted for Polish county hospitals. It shows which inputs contribute to the best fit in such a research and shows estimation results for different production functions. It presents production function as a useful tool for hospital managers and owners interested in gaining knowledge that may allow for making effective decisions regarding hospital organization, management and financing.

Since the aim of the article is to present the rationality of the behaviour of producers, such as county hospitals, using the Cobb-Douglas production function and translog function for calculations, it is worth showing what management information can be obtained from these functions.

When examining the properties of production function, the characteristics of the production process should be taken into account, i.e. marginal productivity (the pace of production growth and its rate), elasticity, the marginal rate of substitution.

For a producer, an important piece of information is the pace of production growth caused by the change in the employment of i-th factor, which is called marginal product (marginal productivity), presented by formula ( 1 ).

A producer knows how the volume of production will increase/decrease/remain unchanged with an increase in employment of i -th factor by a "unit" (this is an ideal approximation within the frontier, i.e. this "unit" tends to zero), ceteris paribus . In microeconomics, the assumption of producer’s rationality implies non-negativity of the marginal product. The producer will not increase the input of the factors of production (which is associated with an increase in costs) if this causes a decrease in the volume of production. Acting in this way would be ineffective. Additional information is provided by the production growth rate in relation to i -th factor, defined by formula ( 2 ).

Being aware of it, the producer knows by how many percent the production will increase/decrease or remain unchanged with an increase in employment of i -th factor by a "unit", ceteris paribus . Another tool for the entrepreneur is the elasticity of production in relation to the increase in employment of i -th factor, which is presented by the expression ( 3 ).

This elasticity indicates by how many percent the production will increase/decrease or remain unchanged with an increase in employment of i -th factor by 1%, ceteri s paribus . The expression shows that this elasticity is a dimensionless marginal productivity.

The elasticity of production with respect to the increase in employment of i -th factor can be calculated with the logarithmic derivative ( 4 ).

This elasticity shows by how many percent the employment of the second factor should be increased, while the employment of the first is reduced by 1% with the volume of production unchanged. It can be seen that the elasticity of substitution is the elasticity of the marginal rate of substitution relative to the quotient of production factors.

In the examination of the production function of county hospitals, two types of production function were used, namely the Cobb-Douglas function (which is a special case of the power function of production with a degree of homogeneity equal to 1) and the translog function.

The Cobb-Douglas function for m production factors can be written with an expression ( 8 ).

Once logarithmed, it takes the form ( 9 ).

Thus, the elasticity of production in relation to the increase in employment of i -th factor is presented by the expression ( 10 ), which shows that this elasticity does not depend on the size of the employment of factors.

The marginal rate of technical substitution, which is the quotient of the marginal products, is presented by the expression ( 12 ), from which it follows that it depends on the size relations of the factors employed.

The elasticity of substitution can be derived as shown in expression ( 13 ); thus, the elasticity of substitution does not depend on the employment of factors and equals 1.

The second functional form used was the translog function, given by the formula ( 14 ), often occurring in a logarithmed form, facilitating estimation ( 15 ).

Marginal products are defined by the expression ( 16 ).

Each of the 2 functions mentioned was estimated in a form that accounted for two and three independent variables (factors of production). Every time, the dependent variable was the total number of patient-days, while the set of regressors accounted for the total number of beds, the employment of doctors and nurses (both in FTEs) and the costs of materials, electricity and outsourced services. For each model, it is assumed that the set of explanatory variables (consisting of two or three elements) must account for at least one of the following factors: total number of beds, employment of doctors or employment of nurses.

Production functions were estimated with the R version 4.0.2 (2020-06-22)–"Taking Off Again [ 47 ] using the least squares method, while robust regression has been done using MASS package [ 48 ]. A further analysis was carried out with an MS Excel spreadsheet.

The data used in the study are from 2018. The sample included 94 county (powiat) hospitals, i.e. hospitals whose founding body is the powiat (the second-level unit of local government and administration in Poland). Hospitals come from all over the country. Data used in the current study were provided by the Polish Association of Employers of Powiat Hospitals (OZPSP—Ogólnopolski Związek Pracodawców Szpitali Powiatowych).

The sample used in the analysis includes hospitals of different types. There are both public and non-public hospitals, hospitals which have an Emergency Department or an Intensive Care Unit in their structure as well as those which do not run such units. Functioning of a hospital likely depends on such characteristics, which in turn may lead to the estimates being biased, but the authors decided not to subset the sample due to the following reasons. Firstly, imposing other conditions on the dataset would result in the number of observations decreasing rapidly. When we include only relatively big (i.e. hospitals which have the number of beds between the first and the third quartile) public hospitals with an Emergency Department and an Intensive Care Unit the number of units is below 30. Secondly, our main goal is to show the properties of production function which may prove useful in the analysis of hospitals and their functioning. Aiming for the consistency of this paper, we do not intend to analyse differences between various groups of hospitals which is an interesting and important sphere of future analysis. It is also important for us to analyse, which inputs are mostly useful for modelling. We use robust regression in order to neutralize the effect of potential outliers in the dataset. The values of descriptive statistics for the analysed sample are presented in Table 1 . Hospitals in the sample had the number of beds within the range of 57–599, which translates into patient-days in the range of 14.25–154.38. The average employment of doctors and nurses amounted to 121.71 and 383.63 FTEs respectively. On average, the value of materials was 86.389; electricity 10.076, and outsourced services 160.95. It is worth noting that in the case of all variables, the average values were higher than the medians, which indicates the occurrence of right-sided asymmetry and outlaying observations characterised by relatively large values of the analysed variables. Based on the comparison of averages and standard deviations, it can be concluded that the variables were most diverse due to the employment of doctors and nurses and least diverse due to the number of beds.

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https://doi.org/10.1371/journal.pone.0268350.t001

In the analysis, we assume the level of significance of α equal to 0.05.

The results of the estimation of two-factor Cobb-Douglas function are presented in Table A in S1 Appendix . The results show that the model with the costs of electricity and the workload of nurses as explanatory variables can be mentioned as the best description of the operation of hospitals as in this case, both explanatory variables were significant, and the parameter estimates had positive signs. The only other model with two significant inputs has higher residual standard error. It is worth mentioning that some of the models, such as the model accounting for the workload of doctors and nurses as well as the model with the total number of beds and the cost of outsourced services, did not meet the assumptions of production function (negative elasticity, and consequently negative values of marginal productivity). This can be interpreted as inefficiency caused by the employment of such a combination of these factors. In addition to fragments of the production function illustrating the efficient use of production factors, negative marginal products appear, which indicates the need to control the relations of the employed factors in order to avoid hospital operation inefficiency.

The results of the estimation of three-factor Cobb-Douglas function are presented in Table B in S1 Appendix . They show that the best fit assessed by the residual standard error was achieved in the case of a model that accounts for the number of beds, the workload of doctors and the material costs. However, not all variables are significantly different from zero in this case. There are also models which do not meet the assumptions of production function due to the negative elasticity of production in relation to some of the inputs. This means a reduction in the hospital production—the total number of patient-days. Thus, the availability of health services for patients is becoming limited. The results of the estimation of two-factor translog function are presented in Table C in S1 Appendix . Based on the residual standard error value, the model with the number of beds and doctors as explanatory variables can be considered the best description of the operation of hospitals. Unfortunately, only one estimate is statistically significant in this case.

The results of the estimation of three-factor translog function are presented in Table D in S1 Appendix . The best fit evaluated with residual standard error was achieved with a model which accounts for the number of beds, costs of electricity and workload of doctors. Unfortunately, in this model, only two estimates of inputs were statistically significant, and in addition, this model does not meet the assumptions of production function due to the negative marginal productivity of the employment of doctors, and thus also a negative elasticity of the production function.

Table A in S2 Appendix presents additional sources of knowledge resulting from the two-factor Cobb-Douglas function. For all types of models we will provide sample interpretations for the models characterized by the greatest number of significant parameters (providing it satisfies all the conditions for the production function, such as positive productivities). For the two-factor estimations of the Cobb-Douglas function, we will discuss the values of marginal productivity and other functions for the model with electricity and nurses as explanatory variables. According to the principles of economic analysis, in the interpretation, we use the principle of ceteris paribus , which means that we abstract from the standards that may be applicable in a specific healthcare system (e.g. the relation of the number of medical staff to the number of beds). It should be emphasised that data from county hospitals also result from the regulations of the Ministry of Health in (e.g. the relation of the number of medical staff to the number of beds). It appears that when comparing the results of health systems in different countries, it should be borne in mind that they are to some extent incomparable. The standards introduced by law create conditions to achieve efficiency, and their diversity between countries is an obstacle to modelling their own organisational, management and financial solutions, because these detailed legal regulations must be followed. This is a necessary simplification in order to illustrate the possibilities offered by the production function for the analysis of the situation in the entity and when making decisions. The results indicate that the electricity marginal productivity for the average and median amounted to 3.0993 and 3.1562 respectively. This means that 1 extra unit of money spent on the electricity would allow for an increase in patient service of about 3 patient-days, with other factors unchanged. The marginal products of FTEs for nurses are equal to 0.0342 and 0.0517 (again for averages and medians respectively),which means that an increase in nurse employment by 1 FTE would allow, with other factors unchanged, for an increase in patient service of about 0.03–0.05 patient-day. Production growth rates mean that the capacity to serve patients calculated in patient-days will increase by around 0.05%-0.06% if the cost of electricity is increased by a unit, and by 0.0005%-0.0011% if the employment of nurses is increased by 1 FTE. The elasticity of production in relation to the increase in the employment of manufacturing factors means that a one-percent increase in the costs of electricity translates into an increase in the capacity to serve patients (in patient-days) by 0.48%, and a one-percent increase in the number of FTEs by 0.2%. Economies of scale for the discussed function do not exceed 1, which means that a 1% increase in outlays in both factors will result in less than 1% more patient service capacity. The marginal substitution rate calculated for average values of 0.011 informs about the need to increase the employment of nurses by nearly 0.011 FTEs in the situation of reducing the electricity costs by 1 unit and the intention to maintain patient service at the current level. In the case of medians, the necessary increase in employment amounts to about 0.016 FTEs. The elasticity of substitution indicates that for both factors of production the required changes are at the level of about 0.42%.

The significance of explanatory variables most often appeared in models accounting for the workload of nurses. And the best fit measured with the residual standard error was characterised by models accounting for the number of beds, the worst—the cost of outsourced services. Adjustments by explanatory variables in the discussed production function are shown in Table 2 .

https://doi.org/10.1371/journal.pone.0268350.t002

For three-factor estimations of the Cobb-Douglas function, we present the interpretation of the model with nurses, outsourced services, and electricity (M19) (Table B in S2 Appendix ). As above, in the interpretation we use the principle of ceteris paribus and disregard the standards which may be applicable in a specific healthcare system. In the case of the three-factor Cobb-Douglas function given in the M19 model, the marginal productivities of factors amounted to (for averages): 0.0233 (nurses), 2.2275 (electricity) and 0.1082 (outsourced services). This means that the increase in outlays of these variables by an additional unit would increase the capacity to serve patients from 0.0233 patient-day in the case of employment of nurses, up to 2.2275 in the case of electricity costs. For medians, these values are 0.0985 (outsourced services), 0.2358 (electricity) and 0.0367 (nurses). In both cases, the largest changes in patient-days would result from a unit increase in electricity costs, and the smallest from an increase in the employment of nurses of 1 FTE. The same relationships occur in the production growth rates determined for individual factors. Patient service capacity in patient-days will increase by about 0.002% if the costs of outsourced services rises by a unit, and by 0.0351%-0.0478% if electricity costs rise by a unit and 0.0004%-0.0007% in the case of increase in the employment of nurses by 1 FTE.

A one-percent increase in the cost of outsourced services is related to an increase in patient-days by about 0.27%, in the case of a one-percent increase in electricity, the increase in patient-days is about 0.35%, and in case of the change in nurses’ FTEs by 0.14%. As in the case of the two-factor function discussed earlier, the benefit from economies of scale does not exceed 1, which means that increasing the outlay of all factors by 1% will result in an increase in the capacity to serve patients by less than 1%. The marginal substitution rate calculated for the nurses and electricity indicates that the reduction of workload of nurses by 1 FTE would require an increase in electricity outlay of 0.011–0.016 unit while maintaining the same level of patient-days. At first glance, this interpretation may seem irrational, because the reduction of FTE should result in a reduction in costs, but it should be remembered that despite this reduction, the number of patient-days should remain at the same level. This may mean, for example, the need for additional medical procedures for patients, which is connected with higher electricity costs. The same reduction in the FTEs would require, ceteris paribus , an increase in the costs of outsourced services by about 0.21–0.37 units, while reducing electricity costs by a unit would require, ceteris paribus , an increase in the costs of outsourced services of 20.58–23.94 units. A one-percent reduction in the workload of nurses would require, ceteris paribus , either a 0.399% increase in electricity costs or an 0.514% increase in the cost of outsourced services; and for the same percentage reduction in electricity costs, it would be necessary to increase the cost of outsourced services by nearly 1.3%.

The median residual standard error is the lowest for models in which total number of beds is used as an explanatory variable. Differences in median residual standard error for all explanatory variables except for the total number of beds are relatively small. Significant variables were most often found in models which included nurses, doctors, electricity costs and costs of outsourced services. Adjustments by explanatory variables for the discussed production function are shown in Table 3 .

https://doi.org/10.1371/journal.pone.0268350.t003

Despite the reservations raised above in relation to the results obtained for the two-input translog function, to make the considerations complete, its interpretation and analysis of the significance of variables and residual standard error are presented in this part due to the variables included in the model, similar to those of the Cobb-Douglas type function.

In the case of the two-factor translog function, we present the interpretation on the example of the M10 model, in which the explanatory variables are nurses’ workload and material costs. For this model, a relatively low residual standard error value was obtained, and also estimates of nearly all parameters remained significantly different from zero. The results presented in Table C in S2 Appendix indicate that marginal productivity of nurses’ FTEs, for averages and medians are 0.119 and 0.244 respectively. This means that increasing the employment of nurses by 1 FTE would enable the increase in patient service of 0.119–0.244 patient-day, with other factors unchanged. Increasing the employment of nurses by 1% would result in an increase in patient service by 0.48% (calculations for averages) and by 0.82% (for medians).

As indicated by the values of the marginal product of the cost of materials, increasing these costs by a unit would result, ceteris paribus , in increased patient service by approximately 0.26 and 0.08 (for averages and medians, respectively). On the other hand, an increase in the level of material costs by 1% would result in an increase in patient service by 0.24% as calculated for averages and by 0.08% for medians. The determined growth rates lead to the conclusion that the patient service capacity calculated in patient-days will increase by about 0.0013% and 0.0043% for averages and medians, respectively if the number of nurse FTEs rises by 1. The corresponding values for the cost of materials amount to 0.0028% and 0.0013%.

In the case of the discussed function, like in the Cobb-Douglas functions interpreted before, the benefits from the economies of scale do not exceed 1, which means that a 1% increase in the input of both factors will result in a relatively smaller increase in the number of patient-days. The marginal substitution rate indicates the need to increase material costs by 0.45–3.22 (for averages and medians respectively), in the event of the liquidation of 1 nurse FTE and the desire to maintain patient service at the current level. In the case of a 1% reduction in the workload of nurses, the change in the cost of materials required to maintain the current number of patient-days is, for averages, close to 2%, and for medians 10.196%.

Table 4 compares the significance of variables and residual standard error by factors of production. It can be noted that the significance of explanatory variables most often appeared in models accounting for the workload of nurses. On the other hand, the greatest fit measured with the residual standard error was characterised by models accounting for the number of beds, and the lowest adjustment was recorded for models accounting for the workload of doctors.

https://doi.org/10.1371/journal.pone.0268350.t004

Below, there is an interpretation of the estimations of the three-factor translog function, in which the explanatory variables are: the workload of nurses and the costs of outsourced services and electricity (M19). On the basis of the marginal productivity of the factors (for averages) shown in Table D in S2 Appendix , it can be concluded that an increase in the workload of nurses by 1 FTE would entail an increase in the capacity of patient service by about 0.08 patient-day. If the cost of outsourced services or electricity were increased by a unit, it would be about 0.1 or 2.74, respectively. If the case of change of outlays of subsequent factors of 1%, ceteris paribus , the increases in the number of patient-days would amount to 0.3641 (nurses), 0.3198 (electricity) and 0.1783 (outsourced services). The values calculated for medians vary, from 0.0358 to 0.718 in the case of elasticity (percentage change in the number of patient-days caused by a one-percent change in the input of a given factor) to 0.014–1.58 in the case of marginal productivity (change in the number of patient-days caused by a unit change in the outlay of a given factor).

Production growth rates are highest for electricity costs, which means that an increase in these costs by a unit will enable the largest (in terms of percentages) increase in the number of patient-days.

Like in the case of the two-factor function, the benefits from the economies of scale do not exceed 1, and therefore an increase in the outlays of all factors by 1% will result in the increase in patient-days below 1 percent.

The marginal substitution rate calculated for the workload of nurse and costs of electricity indicates that a reduction of 1 FTE would entail an increase in the costs of electricity of 0.0299–0.1276 (for averages and medians, respectively), In the case of substitution of the workload of nurses by the cost of outsourced services, the obtained substitution rates indicate the need to increase the cost by 0.8 for averages or 14.56 units for medians which is a relatively large discrepancy compared to the results of calculations obtained with regard to the previous pair of production factors. And in the case of reducing the cost of electricity by a unit, increase in the costs of outsourced services should amount to from 28.65 unit for averages to 114.06 unit for medians.

Analogous relationships can be seen when considering changes of 1%. For example, calculating on the basis of averages, one percent reduction in FTEs would require, ceteris paribus , either an increase in electricity costs by 1.14%, or an increase in costs of outsourced services by 2.04%. In the case of the same percentage reduction in electricity costs, it would be necessary to increase costs of outsourced services by 1.8%. After determining these changes based on medians, we will get 3.27%, 20.07% and 6.14%, respectively.

Among the estimations of the three-factor translog models, the best fit was once again characterised by models accounting for the total number of beds. Significant variables were found most commonly in models which included nurses and electricity costs. Adjustments by explanatory variables for this function are included in Table 5 .

https://doi.org/10.1371/journal.pone.0268350.t005

An interesting problem for the interpretation of results and the formulation of conclusions based on them is the question the impact on them of the assumptions necessary for the analytical tool, which is the production function. Thus, the obtained result shows the overlap of both the actual determinants in which the hospital operates as well as the analytical assumptions to be met to follow the requirements of production function.

The study presented in the paper has several limitations. First of all, as mentioned previously, the dataset we includes hospitals of different types (both public and non-public hospitals, with an without an Emergency Department or an Intensive Care Unit in their structure) which may lead to the OLS estimates being biased. Firstly, imposing other conditions on the dataset would result in the number of observations decreasing rapidly. When we include only relatively big (i.e. hospitals which have the number of beds between the first and the third quartile) public hospitals with an Emergency Department and an Intensive Care Unit in order to guarantee the greatest similarity of the units in the study, the number of hospitals is falls to 23. In our opinion this number of observations is too low to provide an important insight. Secondly, one of our goals has been to show the properties of production function which may prove useful in the analysis of hospitals and their functioning. Table 6 presents comparison of adjustment of two- and three-factor translog and Cobb-Douglas functions estimated by OLS on the subsample of 23 hospitals of similar characteristics by explanatory variables. Apart from some differences, especially in case of the number of significant variables, these results lead to similar conclusions to the ones discussed previously.

https://doi.org/10.1371/journal.pone.0268350.t006

For all the models the total number of beds contributed to the best fit measured with residual standard error, which is in line with the results reported previously for the sample of 94 hospitals. For the two- and three-factor Cobb-Douglas functions the mean and median significance of explanatory variables was equal to 1 in all cases. In case of the translog models, significant variables were found most commonly in models which included nurses and electricity costs. This result is also similar to the one drawn for the whole sample of 94 hospitals.

Aiming for the consistency of this paper, we do not intend to analyse differences in estimates between various groups of hospitals which is an interesting and important sphere of future analysis. We believe, that introducing dynamics or implementing panel models in the future studies will provide much needed additional insight, especially in the light of the healthcare system reform which took place in Poland in 2017.

In the current study it was important for us to analyse, which inputs are mostly useful for the modelling. We compare however the consistency of our results with the results achieved implementing robust regression and regression on the smaller subset of hospitals with similar characteristics (relatively big public hospitals with an Emergency Department and an Intensive Care Unit within their structures), finding little differences.

Supporting information

S1 appendix. estimation results..

https://doi.org/10.1371/journal.pone.0268350.s001

S2 Appendix. Additional sources of knowledge.

https://doi.org/10.1371/journal.pone.0268350.s002

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Class 12 Maths: Case Study of Chapter 1 Relations and Functions PDF Download

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In Class 12 Boards there will be Case studies and Passage Based Questions will be asked, So practice these types of questions. Study Rate is always there to help you. Free PDF Download of CBSE Class 12 Mathematics Chapter 1 Relations and Functions Case Study and Passage Based Questions with Answers were Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Relations and Functions  to know their preparation level.

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In CBSE Class 12 Maths Paper, There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Relations and Functions Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 12 Mathematics  Chapter 1 Relations and Functions

Case Study/Passage-Based Questions

Case Study 1:

A general election of the Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever.

Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows: R = {(𝑉1, 𝑉2) ∶ 𝑉1, 𝑉2 ∈ 𝐼 and both use their voting right in the general election – 2019}

• Two neighbors X and Y∈ I. X exercised his voting right while Y did not cast her vote in general election – 2019. Which of the following is true? a. (X,Y) ∈R b. (Y,X) ∈R c. (X,X) ∉R d. (X,Y) ∉R
• Mr.’𝑋’ and his wife ‘𝑊’both exercised their voting right in general election -2019, Which of the following is true? a. both (X,W) and (W,X) ∈ R b. (X,W) ∈ R but (W,X) ∉ R c. both (X,W) and (W,X) ∉ R d. (W,X) ∈ R but (X,W) ∉ R
• Three friends F1, F2, and F3 exercised their voting right in the general election 2019, then which of the following is true? a. (F1,F2 ) ∈R, (F2,F3) ∈ R and (F1,F3) ∈ R b. (F1,F2 ) ∈ R, (F2,F3) ∈ R and (F1,F3) ∉ R c. (F1,F2 ) ∈ R, (F2,F2) ∈R but (F3,F3) ∉ R d. (F1,F2 ) ∉ R, (F2,F3) ∉ R and (F1,F3) ∉ R
• The above-defined relation R is __ a. Symmetric and transitive but not reflexive b. Universal relation c. Equivalence relation d. Reflexive but not symmetric and transitive
• Mr. Shyam exercised his voting right in General Election – 2019, then Mr. Shyam is related to which of the following? a. All those eligible voters who cast their votes b. Family members of Mr.Shyam c. All citizens of India d. Eligible voters of India

Answer: 1. (d) (X,Y) ∉R 2. (a) both (X,W) and (W,X) ∈ R 3. (a) (F1,F2 ) ∈R, (F2,F3) ∈ R and (F1,F3) ∈ R 4. (c) Equivalence relation 5. (a) All those eligible voters who cast their votes

Case Study 2:

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belonging to set {1, 2, 3, 4, 5, 6}. Let A be the set of players while B be the set of all possible outcomes. A = {S, D}, B = {1, 2, 3, 4, 5, 6}

(i) Let R : B –> B be defined by R = {(x, y) : y is divisible by x} is (a) Reflexive and transitive but not symmetric (b) Reflexive and symmetric but not transitive (c) Not reflexive but symmetric and transitive (d) Equivalence

Answer: (a) Reflexive and transitive but not symmetric

(ii) Raji wants to know the number of functions from A to B. How many number of functions are possible? (a) 6 2 (b) 2 6 (c) 6! (d) 2 12

Answer: (a) 62

(iii) Let R be a relation on B defined by R = {(1, 2), (2, 2), (1, 3), (3, 4), (3, 1), (4, 3), (5, 5)}. Then R is (a) Symmetric (b) Reflexive (c) Transitive (d) None of these three

Answer: (d) None of these three

(iv) Raji wants to know the number of relations possible from A to B. How many numbers of relations are possible? (a) 6 2 (b) 2 6 (c) 6! (d) 2 12

Answer: (d) 212

(v) Let R : B –> B be defined by R = {(1, 1), (1, 2), (2, 2)(3, 3), (4, 4), (5, 5), (6, 6)}, then R is (a) Symmetric (b) Reflexive and Transitive (c) Transitive and symmetric (d) Equivalence

Answer: (b) Reflexive and Transitive

Hope the information shed above regarding Case Study and Passage Based Questions for Class 12 Maths Chapter 1 Relations and Functions with Answers Pdf free download has been useful to an extent. If you have any other queries of CBSE Class 12 Mathematics Relations and Functions Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible. By Team Study Rate

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CBSE Case Study Questions for Class 12 Maths Relations and Functions Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 12 Maths Relations and Functions  in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 12 Maths Relations and Functions PDF

Mcq set 1 -, mcq set 2 -, checkout our case study questions for other chapters.

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• Chapter 5 Continuity and Differentiability Case Study Questions

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

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Conversation makes a big difference in study of isolated older people

Tracy Hampton

MGH Communications

Just talking to other people can stimulate different brain functions among socially isolated older adults, even when the interactions are internet-based, according to a new clinical trial out of Massachusetts General Hospital.

The  results  are published in  The Gerontologist , a flagship journal of the Gerontological Society of America.

“We initiated the first proof of concept behavioral intervention study in 2010, nearly a decade prior to the COVID-19 pandemic drawing attention to the detrimental effects of social isolation on our overall health,” explained lead author Hiroko H. Dodge, the principal investigator of the National Institutes of Health–funded trials.

The 186-participant phase 2 randomized trial, called  I-CONECT , used the internet and webcams to allow for conversational interactions between trained interviewers and socially isolated individuals aged 75 years and older who had normal cognition or mild cognitive impairment.

Investigators rotated conversation partners assigned to each participant to enhance the novelty of the experience, provided user-friendly devices allowing participants without any internet/webcam experience to easily engage in video-based conversations, and encouraged conversations with standardized daily themes and picture prompts.

Thirty-minute conversations were conducted four times per week for six months and then twice per week for an additional six months. A control group of similar individuals did not participate in such conversations, but both the intervention and control groups received weekly 10-minute telephone check-ins.

After the initial six-month period, the intervention group had a higher global cognitive test score compared with the control group with a large effect size among those with mild cognitive impairment. Also, intervention group participants with normal cognition had scores indicating higher language-based executive function.

At the end of final six-month period, intervention group participants with mild cognitive impairment had test scores indicating better memory-related brain function than those in the control group. Measures of emotional well-being improved in both control and intervention groups, suggesting that emotion can be boosted by brief weekly telephone calls while improving cognitive function requires frequent conversational engagement.

Also, brain imaging tests showed that the intervention group had increased connectivity within the dorsal attention network—a region important for the maintenance of visuospatial attention—relative to the control group, although this finding must be interpreted carefully because of the limited number of participants assessed due to COVID-19–related research restrictions.

Upon requests from former trial participants asking to continuously have conversations, Dodge and her colleagues have established a nonprofit organization, the  I-CONNECT Foundation . The foundation has been providing social interactions to isolated older individuals in the community free of charge, using the same materials used in the trial.

“Our next goal is to extend these activities to reach more isolated individuals in need, as well as to delve into the biological mechanisms underlying the impact of social interactions on our brain functions,” said Dodge. “Providing frequent stimulating conversational interactions via the internet could be an effective home-based dementia risk-reduction strategy against social isolation and cognitive decline. We plan to extend this therapy to geriatric outpatient populations, for which we are currently fundraising, and also examine its effectiveness for mild to moderate depressive symptoms.”

The team is also exploring the possibility of providing conversational interactions via chatbot — an artificial intelligence – trained robot that provides stimulating conversations as a cost-effective intervention. “We are aware that human contacts are critically important for our emotional well-being, but for cognitive stimulations, chatbots might work as effectively as humans, which we are currently investigating,” said Dodge, who serves as the director of Research Analytics at the recently inaugurated Interdisciplinary Brain Center at MGH and is a faculty member of the Harvard Medical School.

Funding was provided by the National Institute on Aging.

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Function of Beauty uses Pitney Bowes Designed Delivery solutions to meet customer delivery expectations

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Function of Beauty is the world leader in customizable beauty, with hair, skin, and body care products made for you (and only you).

"When we started experiencing exponential growth, we knew we needed a delivery solution that would match our values–putting the needs of our customers first –while supporting our continued growth.”

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When Function of Beauty , an innovative, digitally native beauty brand, started experiencing exponential growth, the demand for its made-to-order beauty products created a backlog that slowed delivery. Initially, an expedited-only delivery solution helped clear the backlog and drove customer satisfaction—resulting in a 92% volume increase—but it also created a cost burden for the growing brand. Function of Beauty ’s personalized beauty products are primarily available through a custom subscription catered to each of their customers. To continue to provide this high level of customer experience, the company identified two types of delivery needs: first-time buyers who–after having a unique product designed just for their needs–are eager to get their order quickly, and refill customers whose orders are less time sensitive. Function of Beauty needed a solution that could meet the expectations of their new customers while maintaining a cost-effective approach for predictable refill orders.

Rather than using a one-size-fits-all solution, Pitney Bowes designed a blended, customer-driven delivery solution for Function of Beauty’s unique challenge. Their designed solution balances speed and cost by triggering expedited delivery for new customers and standard delivery for repeat customers. The hybrid solution meets Function of Beauty’s customer expectations—no matter who they are—while also aiding in their goals for new customer acquisition and delivery cost savings. Additionally, the Pitney Bowes BOXtour solution empowers Function of Beauty to know where and how their packages are being handled, giving them the power to make the best decisions and pivot when needed.

"Our company was born from the belief that there is no one size fits all and that each person deserves a product just for them. We appreciate that Pitney Bowes treats us with the same care we treat our customers, consulting with us to meet our unique delivery needs rather than limiting us into a one-size solution.”

Function of Beauty’s highly personalized beauty offerings and varying customer needs called for a flexible delivery solution. Pitney Bowes Designed Delivery approach—from configuring a bespoke delivery solution to collaborating on innovative features—allowed Function to continue to grow with peace of mind that Pitney Bowes will continue to flex and grow with them as a long-term partner. Pitney Bowes and  Function of Beauty  look forward to continuing this strong partnership and collaborating hand-in-hand to ensure that we are evolving to meet their needs, sharing ideas and input on new features that will continue to improve the customer experience and enable growth.

Case Study on Executive Function

by Neuron Learning Team | May 27, 2022 | Case Studies , Free Resources | 0 comments

Mark’s Literacy Struggles

From an early age, Mark had difficulty reading. Like other struggling readers, he had trouble decoding and comprehending and received intensive direct phonics instruction during second grade. Mark also completed a computer-based supplemental reading program. Yet, he continued to read slowly and effortfully, and comprehension problems persisted even when he decoded accurately.

Toward the end of third grade, a school psychologist diagnosed him with attentional problems and verbal and nonverbal working memory issues. The psychologist found that Mark had learned to decode accurately, but his distractibility caused him to lose his place frequently. His poor working memory meant he forgot what he’d read, further compounding his comprehension problems. As a result, he repeatedly re-read texts with little to no benefit and became frustrated by the effort required to complete his assignments.

At this point, Mark was demoralized, his parents were concerned, and his teachers weren’t sure what to do next. Since reading well is one of the   major predictors of academic success , not to mention a stepping stone to   greater confidence , everyone wanted Mark to succeed.

Mark’s Literacy Successes

As soon as Mark was referred to me, I suggested he begin participating in a different computer-based intervention than the one he’d been doing. The program included the decoding and comprehension lessons he was used to, but the reading tasks included training in building attention and working memory as they pertained to reading. It also had literacy-specific components designed to build other EF skills, such as cognitive flexibility and self-regulation. Lastly, the program was highly  adaptive , meaning that it addressed Mark’s specific challenges and prioritized the skill-building Mark needed most. 

So what was this reading program that provided EF skills embedded in literacy training? It’s called   Fast ForWord .  

And did it work? Absolutely.

By the middle of fourth grade, Mark was an avid reader. He enjoyed reading so much that, according to his mother, he now read independently on nights and weekends. Sometimes Mark became so mesmerized by books that he would get annoyed when his parents interrupted his reading. Although very social, he often ignored texts from his friends until he finished a chapter.

When his parents asked Mark why he now liked reading so much, he said, “I’m really good at it. My teacher says I’m one of her best readers.”

Although Mark is an exceptional example of the power of Fast ForWord, many clinicians like me have seen students like Mark make a U-turn in as little time as a year. Of the hundreds of students I’ve worked with, the vast majority improved significantly using Fast ForWord. Several moved out of special education, and others stopped requiring supplemental services altogether. One of my Fast ForWord users recently became a licensed pediatric clinical psychologist, another a well-respected software engineer.

The Fast ForWord exercise Flying Fish provides an example of an activity that embeds EF skill-building into literacy instruction.

Learning from Mark’s Literacy Experience

Circling back to Mark, our struggling reader turned literacy all-star, Fast ForWord was the right program for him because his reading struggles were as tied to EF issues as they were to basic literacy skills. The EF tasks embedded in Fast ForWord augmented Mark’s other reading instruction and helped him overcome both his literacy and EF challenges.

What’s the lesson in all this?

Struggling readers can become our best readers if we combine direct reading instruction with supplemental training that builds literacy-specific EF skills. Teaching these essential EF skills as they are used in reading might be the missing people of the puzzle needed to help all struggling readers thrive.

Check out our Blog Post

Have a look at our home courses and learn more about fast forword, learn more about our summer programs, for more information please  contact us.

Dr Martha Burns / Director of Neuroscience Education /Carnegie Learning, Inc.

Dr. Martha Burns is an Adjunct Associate Professor at Northwestern University and has authored four books and over 100 journal articles on the neuroscience of language and communication. Dr. Burns’ expertise is in all areas related to the neuroscience of learning, such as language and reading in the brain, the bilingual brain, the language to literacy continuum, and the adolescent brain. Dr. Martha Burns is a Fellow of the American Speech-Language-Hearing Association and the Director of Neuroscience Education for Carnegie Learning.

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• Study Protocol
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• Published: 25 April 2024

The ‘PSILAUT’ protocol: an experimental medicine study of autistic differences in the function of brain serotonin targets of psilocybin

• Tobias P. Whelan 1 , 2 ,
• Eileen Daly 1 ,
• Nicolaas A. Puts 1 , 3 ,
• Paula Smith 4 ,
• Carrie Allison 4 ,
• Simon Baron-Cohen 4 ,
• Ekaterina Malievskaia 2 ,
• Declan G. M. Murphy 1 , 3 , 5 &
• Grainne M. McAlonan 1 , 3 , 5  

BMC Psychiatry volume  24 , Article number:  319 ( 2024 ) Cite this article

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The underlying neurobiology of the complex autism phenotype remains obscure, although accumulating evidence implicates the serotonin system and especially the 5HT 2A receptor. However, previous research has largely relied upon association or correlation studies to link differences in serotonin targets to autism. To directly establish that serotonergic signalling is involved in a candidate brain function our approach is to change it and observe a shift in that function.

We will use psilocybin as a pharmacological probe of the serotonin system in vivo. We will directly test the hypothesis that serotonergic targets of psilocybin – principally, but not exclusively, 5HT 2A receptor pathways—function differently in autistic and non-autistic adults.

The ‘PSILAUT’ “shiftability” study is a case–control study autistic and non-autistic adults. How neural responses ‘shift’ in response to low doses (2 mg and 5 mg) of psilocybin compared to placebo will be examined using multimodal techniques including functional MRI and EEG. Each participant will attend on up to three separate visits with drug or placebo administration in a double-blind and randomized order.

This study will provide the first direct evidence that the serotonin targets of psilocybin function differently in the autistic and non-autistic brain. We will also examine individual differences in serotonin system function.

Conclusions

This work will inform our understanding of the neurobiology of autism as well as decisions about future clinical trials of psilocybin and/or related compounds including stratification approaches.

Trial registration

NCT05651126.

Peer Review reports

Autism spectrum disorder (hereafter referred to as ‘autism’) is a neurodevelopmental condition characterised by differences in social interaction and communication, repetitive or restricted patterns of behaviour, and sensory differences [ 1 ]. Although the neurobiological underpinnings of the diverse autistic phenotype remain obscure, accumulating evidence strongly supports involvement of the serotonin system. Identifying differences in the serotonin system in autistic individuals may reveal novel mechanisms to be targeted pharmacologically to benefit those who seek support.

The serotonin system in autism

There is increasing evidence from association and/or correlation studies linking serotonin to autism. First, polymorphisms in genes for serotonin synthesis, transporters and receptors are associated with autism [ 2 , 3 ]. Second, elevated whole blood serotonin levels are also reported in one-third of autistic individuals [ 4 , 5 ]. Third, our team has previously reported that acutely elevating serotonin levels with a single dose of selective-serotonin reuptake inhibitor (SSRI) citalopram differentially affects autistic brain function. For example, citalopram produces sustained activation of brain regions associated with facial expression processing in autistic adults, but not in controls [ 6 ].

More specifically, there is also evidence implicating specific serotonin receptors in autism, especially the 5HT 2A receptor. This receptor is involved in dendritic maturation, neuronal differentiation and the regulation of brain-derived neurotrophic factor levels during development [ 7 ]. At the circuit level, 5HT 2A receptor signalling is thought to enhance neural plasticity [ 8 ] and increases cortical glutamate and thalamic GABA levels [ 9 ]. The receptor is expressed throughout the cortex but especially in regions related to sensorimotor integration [ 10 ] and the so-called default mode network responsible for “self” and “other” processing [ 11 ]. Thus, through these key processes that shape neuronal architecture and neurotransmission, serotonin influences lower-order systems (e.g. sensory) through to higher-order processes (e.g. whole-brain connectivity) as they emerge. As a result, early perturbations in the serotonin system, such as alterations in 5HT 2A receptor-signalling, may influence subsequent brain developmental outcomes. Indeed the HT2RA gene is a candidate gene associated with autism [ 12 , 13 , 14 , 15 ]. However, although lower cortical 5HT 2A receptor binding has been reported to correlate with social communication differences in autism [ 16 ], to date there have been no studies that have directly tested whether 5HT 2A receptor pathways function differently in autistic and non-autistic people.

Measuring ‘Shift’ in the serotonin system in autism

To do this, we have developed a ‘“shiftability” paradigm [ 17 ] to examine how ‘foundational’ mechanisms of brain function such as neural responses to sensory stimuli or whole-brain network connectivity captured using electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) are modulated by targeted pharmacological probes. These measures are biologically informative and may be used across a wide range of ages and, in many cases, also back-translate to animal models to inform future target identification and engagement studies [ 18 , 19 , 20 , 21 , 22 , 23 ].

The range of measures used to capture ‘shift’ and their target level of brain organisation is shown in Fig.  1 .

The organisational levels of information processing in the brain and methodologies that probe each level. Methodologies used to detect ‘shift’ that are included in our ‘PSILAUT’ protocol and discussed here are shown in bold. Bidirectional arrows represent interaction between organisation levels (adapted from Ahmad & Ellis, 2022 [ 24 ])

Targeting 5HT 2A receptor in autism using psilocybin

The only way to directly test if a neurosignalling system functions differently in one group of individuals compared to another is to experimentally manipulate it (for example using a pharmacological probe) and observe a ‘shift’ in function. In humans unlike preclinical model systems, it is of critical importance that the choice of pharmacological probe is safe and has minimal side effects. However, few (if any) neuropsychiatric drugs used in people are entirely specific in their biological effects. With this caveat in mind, in this protocol we selected psilocybin (4-phosphoryloxy- N.N -dimethyltryptamine), as a pharmacological probe of the 5HT 2A receptor in autistic and non-autistic adults.

Psilocybin is a classic psychedelic compound produced by several species of mushrooms, including so-called “magic mushrooms”. Psilocybin is rapidly metabolised into its active component psilocin [ 25 ]. Psilocin is a 5HT 2A receptor agonist but also binds several serotonin receptors, including 5HT 7 , 5HT 2B , 5HT 1D , 5HT 6 , 5HT 5 , 5HT 2C & 5HT 1B receptors in decreasing order of reported affinity [ 26 ]. Prior studies have used relatively high doses of psilocybin to explore the effects of psychedelics on the brain. However, in the planned study we will use lower doses (2 mg and 5 mg) in our “shiftability” protocol to assess brain responses so as not to cause a marked psychedelic experience. This dose range is expected to generate a ‘shift’ in brain function based on evidence using positron emission topography that similar doses of psilocybin engage 5HT 2A receptors [ 27 ]; and low dose psilocybin has been shown to be sufficient to alter cognition and obsessive–compulsive behaviour [ 28 , 29 ]. Low doses of the serotonergic psychedelic lysergic acid diethylamide (LSD) and psilocybin-containing mushrooms also acutely alter brain resting-state fMRI and EEG indices in the non-autistic population [ 30 , 31 ], as well as neural responses to sensory stimuli [ 32 ]. Therefore, we expect that 2 mg and 5 mg of psilocybin will expose functional differences in the serotonin system targeted by psilocybin in autistic and non-autistic individuals using the experimental medicine approach outlined in this protocol.

Overall design of the ‘PSILAUT’ study

The study is an Investigator-Initiated Study sponsored by King’s College London and co-Sponsored by South London and Maudsley NHS Foundation Trust (SLaM). It is part funded by COMPASS Pathfinder Ltd with infrastructure support from the NIHR-Maudsley Biomedical Research Centre at South London and Maudsley NHS Foundation Trust and King’s College London. COMPASS Pathfinder Ltd are donating psilocybin (as “COMP360”). The study is a case–control study with a pseudo-randomised, double-blind, placebo-controlled, cross-over design. We have capacity to recruit up to 70 adult participants to accommodate participant drop-out and/or data quality screening with the goal of n  = 30 autistic adults (half female) and n  = 30 non-autistic adults (half female), who will be matched by age and sex. All participants will provide written informed consent. Participants will be asked to attend 3 visits in total and on each visit they will receive either placebo or one of two single doses (2 mg or 5 mg) of oral synthetic COMP360 psilocybin. Participants and the researchers accompanying the visit will be blind to allocation. The order of administration of placebo and psilocybin will also be pseudo-randomised by the Chief Investigator using a randomisation tool to help generate a list (e.g. Random.org, Randomness and Integrity Services Ltd.) then modified manually to ensure a reasonable balance of individuals in each cell are allocated each of the 3 possible administration orders throughout the duration study (for example, to avoid a ‘run’ of placebo first visits, should different groups/sexes be harder to recruit and result in different cell sizes). Thus, there are 3 possible orders of administration allocated:

Visit 1, placebo; Visit 2, 2 mg psilocybin; Visit 3, 5 mg psilocybin

Visit 1, 2 mg psilocybin; Visit 2, 5 mg psilocybin; Visit 3, placebo

Visit 1, 2 mg psilocybin; Visit 2, placebo; Visit 3 5 mg psilocybin

The lowest dose of psilocybin will always precede the higher dose. This allows us to unblind in the case of unwanted side effects (such as a significant increase in blood pressure) or unwanted experience and potentially omit the higher dose visit. We also explain that there will be more chance of side effects with the higher dose in our informed consent process and if a participant only wishes to attend for the placebo and lower dose visit, we can exclude the higher dose from the randomisation (i.e. they would attend a total of 2 visits only). Thus, a ‘drop-out’ would be considered a participant that did not attend all 3 visits and has missing data for at least one condition.

Ethical considerations

This study will take place at the Institute of Psychiatry, Psychology and Neuroscience (IoPPN) at De Crespigny Park, SE5 8AF, London, United Kingdom. Our study does not address safety or clinical efficacy and the UK Medicines and Health Regulatory Authority (MHRA) has confirmed that our protocol is therefore not a clinical trial of an Investigational Medicinal Product (IMP) as defined by the EU Directive 2001/20/EC.

The authors assert that all procedures contributing to this work comply with the ethical standards of the relevant national and institutional committees on human experimentation and with the Helsinki Declaration of 1975, as revised in 2013. All procedures involving human participants were approved by Dulwich Research Ethics Committee (Reference: 21/LO/0795) and the study protocol was peer reviewed during the ethical review process. As clinicaltrials.gov accepts a range of study designs, because definitions of study types using pharmacological probes differ in different jurisdictions, and in the interest of transparency, we have preregistered the study (Identifier: NCT05651126). We emphasize that in this study, to ensure individuals can provide full informed consent, we will be recruiting autistic and non-autistic adults without intellectual disability and the doses of psilocybin used will be low to limit likelihood of marked psychedelic experiences.

Community engagement

Community engagement was led by the Autism Research Centre at Cambridge University in 2019, prior to designing the study. Three hundred and thirty-one autistic adults were asked about their attitudes to psilocybin research in autism. It was made clear that the research team were not aiming to ‘treat’ autism itself and that the research would not proceed if there was not clear support for it from the autism community. The majority of respondents supported exploratory studies using psilocybin.

Of the 331 autistic adult respondents, 41% were ‘very interested’ and 28% were ‘somewhat interested’. For example: “I am very interested in helping with pioneering new approaches… and feel it is high time proper research was done in this area”. There was also caution however as 25% were ‘not interested’ or ‘not at all interested’. Therefore, rather than proceed immediately to a conventional clinical trial, this study was designed to provide further information on the brain functions targeted by low dose psilocybin and understand any differences between autistic and non-autistic adults. Our hope is that this study will establish a firmer neurobiological evidence base to inform potential opportunities for the development of psilocybin as a pharmacological support option.

Stakeholder engagement also included a press release by King’s College London, South London and Maudsley NHS Foundation Trust and COMPASS Pathways ( https://ir.compasspathways.com/news-releases/news-release-details/compass-pathways-fund-study-comp360-psilocybin-autistic-adults ), as well as articles and interviews across several platforms including The Economist ( https://www.economist.com/psychedelics-pod ), Psychology Today [ 33 ], Technology Networks [ 34 ] and The BBC ( https://www.bbc.co.uk/programmes/m001j45x ), which received positive feedback. Study findings will be continue to be widely disseminated in forums, publications and presentations involving stakeholders in the autistic community, study participants, researchers, industry and clinicians (Fig.  2 ).

'PSILAUT' recruitment and study procedures. Autistic and non-autistic participants will be recruited from existing local research databases, advertising on the King’s College London website and wider dissemination of study information. Participants are welcome to self-refer. Autistic participants will also be recruited from clinical contacts from South London and Maudsley NHS trust, local and national support groups and via the Cambridge Autism Research Database (CARD), managed by our collaborators at the Autism Research Centre, University of Cambridge. Interested participants will be sent an information sheet and screened via video call or phone for eligibility according to the inclusion and exclusion criteria prior to the first visit. Written consent will be sought after inclusion criteria are confirmed and the participant is then assigned to a study schedule. Participants will be provided with login details to an online platform (Delosis Ltd., London) to complete a battery of questionnaires remotely. Participants will visit the study site on three separate occasions. A blood sample will be collected on one of the three visits for quantification of whole blood serotonin levels. Each participant will complete an MRI scan session to acquire a structural, resting-state functional MRI scan and a face emotion processing task. The EEG paradigm will include resting-state and functional activation during a face processing, auditory oddball and visual processing. Psychophysical tasks will be collected prior to a cognitive battery which will include the ‘reading the mind in the eyes’ (RMET), probabilistic reversal learning (PRT), both of which will be delivered using PsyTools (Delosis Ltd., London) and a semantic verbal fluency task. The 5-dimensional altered states of consciousness (5D-ASC) questionnaire will then be completed to quantify any subjective effects experienced by participants

‘PSILAUT’ protocol measures

Each study visit will last approximately 4–5 h in total. Although given the number of measures, the data collected is time permitting and cognitive tasks at the end of the protocol may be omitted, for example. We will aim to collect spectroscopy and resting-state MRI at 60min and 70min post-dose at T max [ 27 ], respectively; EEG at ~ 2 h post-dose & psychophysics at ~ 3 h post-dose. We have established the tolerability and feasibility of this study design in autistic adults as we have conducted similar studies previously with several different pharmacological probes [ 6 , 21 , 35 , 36 , 37 , 38 ]. Indeed, many of our participants have also attended our studies in the past and are well-informed about the visit procedures.

Inclusion & exclusion criteria

A comprehensive baseline characterisation will be obtained. An expert clinical diagnosis of autism from a recognised UK assessment service will be accepted. This may be supported by the Autism Diagnostic Interview-Revised [ 39 ] where an appropriate informant is available. An Autism Diagnostic Observation Schedule [ 40 ] will be used to support diagnosis, but if it has already been used to inform the diagnostic assessment in adulthood, it will not be repeated. Participants with ASD of a known genetic cause (e.g. Fragile X syndrome) were excluded. Other inclusion criteria include being over 18 years old; the ability to provide informed consent; no cooccurring psychiatric illness such as major mood disorder or psychotic illness; no history of seizures or diagnosis of epilepsy and no physical illness such as high blood pressure. Participants taking medications known to affect serotonin (such as selective serotonin-reuptake inhibitors) will be excluded. Those taking stimulants will be eligible and asked to ideally exclude on the day of testing or else ensure they take it the same way on each visit. These and any other potential medication use will be included as covariates in analyses and/or statistical analyses rerun excluding data from individuals taking medication to establish the extent to which medication use drives any potential findings.

Baseline characterisation

Additional baseline questionnaires will quantify autistic traits (e.g. social behaviour or sensory differences), relevant cognitive domains (e.g. intolerance of uncertainty and behavioural flexibility) and the symptomology of co-occurring psychiatric conditions.

Neurometabolites

Magnetic resonance spectroscopy (mrs).

An MRS Hadamard Encoding and Reconstruction of MEGA-Edited Spectroscopy (HERMES) sequence [ 41 ] will be collected during the MRI scan for the dorsal medial prefrontal cortex region. HERMES permits the quantification of levels of metabolites in the living brain and is focused on estimating GABA and Glutamate-glutamine markers of E/I balance. For the purposes of our study, given the evidence that E-I pathways are modulated by 5HT 2A receptor action in animal models [ 9 ], we will be able to examine the impact of psilocybin on these tissue level measures of E-I balance.

Local circuits

Resting-state.

High-density (64-channel) EEG data will be collected during the resting-state, metrics from which local circuit activity can be derived such as beta and gamma band power/frequency [ 24 ]. Oscillations in the beta frequency band at rest, for example, are associated with inhibitory neurotransmitter levels in sensorimotor cortex [ 42 ]. This, and other EEG-derived metrics such as aperiodic activity, are considered a proxy measure for E/I balance in vivo [ 24 ]. Hence, we will be able to examine the impact of psilocybin on these dynamic measures of E/I balance.

Passive sensory tasks

Visual domain.

A visual processing task (contrast saturation) in which steady-state evoked potentials (SSVEPs) are elicited by passive surround suppression stimuli will be conducted. We have shown that SSVEPs during this task are altered in autism [ 21 ]. 5HT 2A receptors are particularly highly expressed in the primary visual cortex [ 11 ], and their agonism alters visual response amplitudes and surround suppression in mouse primary visual cortex [ 43 ]. In humans, we expect visual processing to be altered by 5HT 2A receptor activation given that the marked visual perceptual changes robustly induced with higher doses of psychedelics are blocked by pretreatment with the 5HT 2 receptor antagonist, ketanserin [ 44 ].

Auditory domain

A conventional auditory oddball paradigm of mismatch negativity (MMN) [ 45 ] will be used to passively measure ‘repetition suppression’ (or habituation) to repetitive auditory stimuli and response to an unexpected ‘deviant’ stimulus (the event-related mismatch negativity MMN response). We and others have observed less repetition suppression in both eight-month-old infants who go on to receive a diagnosis or autism, and adults with a diagnosis of autism [ 19 , 46 ]. Thus, this signal appears linked to autism across infancy to maturity. The impact of autism on the event-related MMN is less consistent and varies with age [ 47 , 48 , 49 ]. The latter may in part be due to differences in the serotonin system, as the MMN response can be modulated by acute elevation of serotonin levels by the highly selective SSRI escitalopram [ 50 ]. In this study we will test the prediction that psilocybin alters both sensory suppression and MMN in autism differently compared to controls.

Global networks

Oscillatory power will be assessed across multiple frequency bands during the resting-state. This will include electrodes over key brain regions implicated in autism such as those belonging to the default mode network (DMN) [ 51 ]. Reduced oscillatory power over DMN regions using electrophysiological approaches following 5HT 2A receptor activation by psilocybin has been reported previously [ 52 ]. Functional connectivity analyses (e.g. within and between brain networks) can also be derived from EEG, and this will complement connectivity analyses from resting-state fMRI.

Participants will undergo a structural and functional MRI scan. Scans will be acquired on a 3.0 Tesla MR Scanner (General Electric Premier). A fMRI scan with a multiband 4 sequence will be acquired during the resting-state, multiband 4 is preferable for connectivity analyses [ 53 ]. In addition, multiband sequences will considerably reduce the repetition time (TR), therefore they have the advantage of allowing dynamic functional connectivity analyses. Autistic differences in both ‘averaged’ functional connectivity and dynamic functional connectivity have been reliably reported across different datasets [ 20 , 54 ]. Functional connectivity of brain networks in neurotypical individuals has also be shown to be acutely modulated by 5HT 2A receptor activation [ 55 ]. Notably, psilocybin alters dynamic functional connectivity, mediated by 5HT 2A receptor agonism [ 56 ]. It facilitates state transitions and more temporally diverse brain activity in neurotypical individuals[ 57 ]. Our study will be the first to examine the effects of psilocybin on conventional and dynamic functional metrics in autistic individuals.

Task-dependent MRI and EEG

fMRI studies of face emotion processing in autism have produced inconsistent results. In the largest study to date, no differences between autistic and non-autistic individuals in fMRI response to facial expressions of emotion were observed [ 58 ]. However, we have recently examined the fMRI response to facial expressions of emotion in a social brain network before and after administration of the SSRI, citalopram. We reported that the dynamics of the response to faces is different in autism, in that serotonin reuptake inhibition slows habituation [ 6 ]. Consistent with this, blockade of 5HT 2A receptors causes an ‘opposite’ effect and reduces neural responses to emotional faces during fMRI in neurotypical individuals [ 59 ]. Therefore, we expect that psilocybin will alter the dynamics of face emotion processing, but differently in autistic individuals.

Event-related potentials (ERPs) in response to face stimuli will also be assessed during EEG. The N170 component, a neural response present at 170ms following the presentation of facial stimuli and can be modulated by 5HT 2A receptor activation [ 44 , 60 , 61 ]. An altered N170 response is associated with social communication differences in autism and may have utility as a stratification marker that is amenable to support [ 62 ]. It is also going to be the first prognostic biomarker for autism (or any neurodevelopmental or psychiatric condition) to be approved by regulatory agencies [ 62 ]. The incorporation of this task in our protocol therefore will be an important test of whether an autism biomarker can be modified pharmacologically.

Psychophysical approaches are structured approaches in which stimulus characteristics are tightly controlled, and they provide robust, objective measures of sensory sensitivity by estimating perceptual metrics [ 63 , 64 ]. Serotonin has been directly implicated in tactile perception, such as in affective touch, by studies using tryptophan depletion (which acutely reduces central serotonin levels) alongside psychophysical approaches [ 65 ]. Tactile detection threshold and amplitude discrimination will be assessed, as differences in tactile thresholds have already been reported in autism and are associated with outcomes [ 66 ]. As processing of tactile stimuli is also known to be perturbed by 5HT 2A receptor agonism with psilocybin [ 67 ], we also expect to elicited functional differences following psilocybin in autistic and non-autistic individuals in this paradigm.

Additional measures

Questionnaires.

The 5-dimensional altered states of consciousness (5D-ASC) questionnaire [ 68 ] will be completed on each visit following the completion of study procedures to quantify the subjective effects of psilocybin, which are primarily mediated by the 5HT 2A receptor [ 69 ].

Cognitive battery

‘Theory of mind’ (i.e. cognitive empathy, the ability to understand and take into account the mental state of another individual) can be investigated using the ‘reading the mind in the eyes’ (RMET) task [ 70 ]. Other cognitive processes in which differences are observed in autism such as language and executive and reward-related functioning (e.g. flexible choice behaviour) will be assessed with a verbal fluency task and probabilistic reversal learning task, respectively [ 71 , 72 ].

Peripheral biochemistry

Participants will be asked to provide a blood sample on one visit prior to placebo/drug administration (their preference). Whole blood serotonin levels will be determined for each individual, given that elevated levels are present in one-third of individuals with autism [ 4 , 5 ]. This will allow us to explore whether any ‘shift’ in brain function in response to psilocybin depends on overall serotonin ‘tone’ as indexed by proxy.

Data analyses

The overarching goal of our analyses is to assess whether we see a ‘shift’ by psilocybin in autistic and non-autistic individuals for each modality. Both parametric and nonparametric statistical analyses will be used to test hypotheses that the serotonergic targets of psilocybin functioning differently in autistic individuals. Given the heterogeneity of the autistic population and our prior observations that there is a wide range of pharmacological responses in both autistic and non-autistic individuals, we will calculate individual ‘shift’ for each modality, and what characteristics (e.g. clinical scores, questionnaire responses, whole blood serotonin) these are associated with. Although we will generate and analyse data from single modalities, post-hoc we will also explore multimodal metrics (i.e. associations between modalities) to understand how ‘shifts’ detected across multiple organisational levels are inter-related.

Power analyses

We will use a within-subject, repeated-measures design with a placebo condition so that each subject is their own control, thus increasing statistical power. Results from our prior neuroimaging studies using pharmacological challenge were successful in detecting group differences in MRI metrics with sample sizes of n  =  < 20 [ 6 , 35 , 36 , 37 , 38 , 73 , 74 , 75 ]. This implies an effects size (expressed as Cohen’s d) in excess of 1.2. In sensory tasks a sample size of n  = 16 per cell is estimated to achieve 80% power to detect a medium effect (0.5) at a = 0.05; this has been achieved even in mixed sex groups of 20 participants or fewer. This reflects the literature in which significant group differences are evident even in mixed sex groups of 20 participants or fewer (e.g. n  = 16) [ 76 , 77 , 78 ]. Nevertheless, we aim for n  = 30 per group (approximately half female in both groups). Our design relies upon participants attending for repeat test sessions. Thus, there is a chance that participants may ‘drop-out’ and need to be replaced, this is accommodated with our ethically approved total sample size of n  = 70.

Limitations

Our protocol requires active participation despite the passive nature of several of our tasks. For example, participants will wear an EEG cap and will be asked to remain focused on the screen during the presentation of sensory stimuli. This may limit generalisability across ages or to autistic individuals with higher support needs.

Even in the proposed adult cohort, participants may get restless or become distracted. Hence, we have included concurrent eye tracking during EEG to control for the potential confound of participant variability in fixation on the screen. However, many of our tasks require minimal or no response from participants and so they are less likely to be impacted by confounds such as individual cognitive difficulties. We hope that this way, should our indices prove worthy of further investigation and/or incorporation in (for example) clinical trials, they will be more accessible for individuals who may otherwise be excluded from drug development studies.

Our “shiftability” paradigm aims to determine how different organisational scales of brain function are modulated by the serotonin system, in particular the 5HT 2A receptor pathway when activated by psilocybin. It will test the hypothesis that the serotonin system targeted by psilocybin is different in autistic and non-autistic people. The results will expand our understanding of brain biology in autistic and non-autistic individuals.

Our work will inform a more personalized medicine approach to autism. Not everyone in our study will respond the same way to psilocybin. Whilst our study design may reveal differences in the response to psilocybin at the group-level, crucially, our prior studies have shown that its constituents are also sensitive to the potential variability at the individual-level. For example, we have been able to plot individual ‘shifts’ in GABA and glutamate spectroscopy, task-dependent and resting-state fMRI measures in response to several drug challenges [ 6 , 36 , 37 , 38 , 74 ], and calculated an individual ‘sensitivity index’ across the different sensory modalities examined in response to a GABA challenge [ 21 , 46 ]. Thus, by investigating individual biology in both autistic and non-autistic people, this experimental medicine approach may help identify autistic individuals whose serotonin system functions no differently from non-autistic people, and who might therefore not be expected to show a clinical response in a clinical trial. And vice versa; those who respond biologically to psilocybin challenge might ultimately benefit clinically. To date, all clinical trials for the core features of autism have failed to reach their primary endpoint. This is in large part because they have included participants based on diagnosis alone and measured outcomes, often without evaluating mechanisms in the same cohort. Existing pharmacological options available for autistic people that target the serotonin system are mainly selective serotonin reuptake inhibitors (reviewed in Howes et al., 2017 [ 79 ]). These show limited efficacy in core domains. For example, there is some evidence for their utility in addressing repetitive behaviours in adults, as assessed using obsessive compulsive symptom outcome measures [ 80 ]. They have also been used to manage co-occurring mental health conditions such as anxiety and depression. Unfortunately, these medications can be poorly tolerated [ 81 ], highlighting the need for novel options, and the importance of identifying serotonergic mechanisms to target in the autistic brain specifically prior to clinical trials. Therefore, in depth pharmacological ‘profiling’ adopting some of the methods described here may help avoid the unnecessary expense and likely failure of clinical trials and facilitate the discovery of novel pharmacological support options for those who would like that choice.

Availability of data and materials

No datasets were generated or analysed during the current study.

Abbreviations

5-Dimensional altered states of consciousness

5-Hydroxytryptamine

Default mode network

Electroencephalography

Excitation/Inhibition

Event-related potential

Gamma-aminobutyric acid

Hadamard Encoding and Reconstruction of MEGA-Edited Spectroscopy

Magnetic resonance imaging

Magnetic Resonance Spectroscopy

Reading the mind in the eyes test

Selective-serotonin reuptake inhibitor

Steady-state evoked potential

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The PSILAUT study is an Independent Investigator Study (G.M.M.) funded in part by Compass Pathfinder Ltd. The authors also receive support from EU-AIMS (European Autism Interventions)/EU AIMS-2-TRIALS, an Innovative Medicines Initiative Joint Undertaking under Grant Agreement No. 777394. In addition, this paper represents independent research part funded by the infrastructure of the National Institute for Health Research (NIHR) Mental Health Biomedical Research Centre (BRC) at South London and Maudsley NHS Foundation Trust and King’s College London, and the Medical Research Council Centre for Neurodevelopmental Disorders. The views expressed are those of the author(s) and not necessarily those of the NHS, the NIHR or the Department of Health and Social Care.

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Nicolaas A. Puts, Declan G. M. Murphy & Grainne M. McAlonan

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T.P.W. contributed to study design, supported community engagement, prepared Figs. 1 and 2 and drafted the manuscript. E.D. contributed to study design and helped draft the manuscript; N.A.P. contributed to study design and helped draft the manuscript; P.S., C.A. and S.B-C. led community engagement and helped draft the manuscript; E.M. contributed to study design, supported community engagement and helped draft the manuscript; D.G.M.M. contributed to study design and helped draft the manuscript. G.M.M. conceived the idea for the study; contributed to study design and drafted the manuscript. All authors reviewed and approved the final manuscript.

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Correspondence to Grainne M. McAlonan .

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T.P.W. is an employee of COMPASS Pathfinder Ltd., T.P.W. and E.M. hold shares in the company. P.S. and C.A. have no conflicts to declare, S-B.C. is co-editor-in-chief of Molecular Autism. N.A.P. has consulted for Deerfield Discovery and Research. D.G.M.M. has consulted for Jaguar Gene Therapy LLC. G.M.M. has received funding for investigator-initiated studies from GW Pharmaceuticals and COMPASS Pathfinder Ltd.. G.M.M. has consulted for Greenwich Biosciences, Inc.

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Whelan, T.P., Daly, E., Puts, N.A. et al. The ‘PSILAUT’ protocol: an experimental medicine study of autistic differences in the function of brain serotonin targets of psilocybin. BMC Psychiatry 24 , 319 (2024). https://doi.org/10.1186/s12888-024-05768-2

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Published : 25 April 2024

DOI : https://doi.org/10.1186/s12888-024-05768-2

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Moderna partners with OpenAI to deploy ChatGPT Enterprise to thousands of employees across the company. Now every function is empowered with AI, creating novel use cases and GPTs that accelerate and expand the impact of every team.

Moderna has been at the intersection of science, technology, and health for more than 10 years. Moderna’s mission is to deliver the greatest possible impact to people through mRNA medicines—with the COVID-19 vaccine being their most well-known breakthrough. 

The company has partnered with OpenAI since early 2023. Now, ChatGPT Enterprise is evolving how Moderna operates across each function.

Moderna is using its platform for developing mRNA medicines to bring up to 15 new products to market in the next 5 years—from a vaccine against RSV to individualized cancer treatments. In order to achieve its ambitions, Moderna has adopted a people-centric, technology-forward approach, constantly testing new technology and innovation that can increase human capacity and clinical performance.

We believe very profoundly at Moderna that ChatGPT and what OpenAI is doing is going to change the world. We’re looking at every business process—from legal, to research, to manufacturing, to commercial—and thinking about how to redesign them with AI.

Moderna brings AI to everyone

Moderna adopted generative AI the same way Moderna adopts other technology: with the mindset of using the power of digital to maximize its positive impact on patients. To allow AI to flourish, they knew they needed to start with the user and invest in laying a strong foundation for change.

Moderna’s objective was to achieve 100% adoption and proficiency of generative AI by all its people with access to digital solutions in six months. “We believe in collective intelligence when it comes to paradigm changes,” said Miller, “it’s everyone together, everyone with a voice and nobody left behind.” For this, Moderna assigned a team of dedicated experts to drive a bespoke transformation program. Their approach combined individual, collective and structural change management initiatives.   

Individual change management initiatives included in-depth research and listening programs, as well as trainings hosted in person, online and with dedicated AI learning companions. “Using AI to teach AI was key to our success”, Miller points out. Collective change management initiatives included an AI prompt contest to identify the top 100 AI power users who were then structured as a cohort of internal Generative AI Champions. Moderna’s culture of learning led to local office hours in every business line and geography, and scaled through an internal forum on AI, which now has 2,000 active weekly participants. Lastly, structural change management initiatives included engaging Moderna’s CEO and executive committee members to foster AI culture through leadership meetings and town halls as well as incentive programs and sponsored events with internal and external experts.  

 This work led to an early win with the launch of an internal AI chatbot tool, mChat, at the beginning of 2023. Built on OpenAI’s API, mChat was a success, adopted by more than 80% of employees across the company, building a solid foundation for the adoption of ChatGPT Enterprise.  

90% of companies want to do GenAI, but only 10% of them are successful, and the reason they fail is because they haven’t built the mechanisms of actually transforming the workforce to adopt new technology and new capabilities.

Building momentum with ChatGPT Enterprise

With the launch of ChatGPT Enterprise, Moderna had a decision to make: continue developing mChat as an all-purpose AI tool, or give employees access to ChatGPT Enterprise?

“As a science-based company, we research everything,” said Brice Challamel, Head of AI Products and Platforms at Moderna. Challamel’s team did extensive user testing comparing mChat, Copilot, and ChatGPT Enterprise. “We found out that the net promoter score of ChatGPT Enterprise was through the roof. This was by far the company-favorite solution, and the one we decided to double down on,” Challamel said.  

Once employees had a way to create their own GPTs easily, the only limit was their imaginations. “We were never here to fill a bucket, but to light a fire,” Challamel said. “We saw the fire spread, with hundreds of use cases creating positive value across teams. We knew we were on to something revolutionary for the company.”

The company’s results are beyond expectations. Within two months of the ChatGPT Enterprise adoption: 

• Moderna had 750 GPTs across the company
• 40% of weekly active users created GPTs 
• Each user has 120 ChatGPT Enterprise conversations per week on average

Augmenting clinical trial development with GPTs

One of the many solutions Moderna has built and is continuing to develop and validate with ChatGPT Enterprise is a GPT pilot called Dose ID. Dose ID has the potential to review and analyze clinical data and is able to integrate and visualize large datasets. Dose ID is intended for use as a data-analysis assistant to the clinical study team, helping to augment the team’s clinical judgment and decision-making.

 “Dose ID has provided supportive rationale for why we have picked a specific dose over other doses. It has allowed us to create customized data visualizations and it has also helped the study team members converse with the GPT to further analyze the data from multiple different angles,” said Meklit Workneh, Director of Clinical Development at Moderna. 

Dose ID uses ChatGPT Enterprise’s advanced data analysis feature to automate the analysis and verify the optimal vaccine dose selected by the clinical study team, by applying standard dose selection criteria and principles. Dose ID provides a rationale, references its sources, and generates informative charts illustrating the key findings. This allows for a detailed review, led by humans and with AI input, prioritizing safety and optimizing the vaccine profile prior to further development in late-stage clinical trials. 

“The Dose ID GPT has the potential to boost the amount of work we’re able to do as a team. We can comprehensively evaluate these extremely large amounts of data, and do it in a very efficient, safe, and accurate way, while helping to ensure security and privacy,” added Workneh.

Improving compliance and telling the company’s story

Moderna’s legal team boasts 100% adoption of ChatGPT Enterprise. “It lets us focus our time and attention on those matters that are truly driving an impact for patients,” said Shannon Klinger, Moderna’s Chief Legal Officer. 

Now, with the Contract Companion GPT, any function can get a clear, readable summary of a contract. The Policy Bot GPT helps employees get quick answers about internal policies without needing to search through hundreds of documents. 

Moderna’s corporate brand team has also found many ways to take advantage of ChatGPT Enterprise. They have a GPT that helps prepare slides for quarterly earnings calls, and another GPT that helps convert biotech terminology into approachable language for investor communications. 

“Sometimes we’re so in our own world, and AI helps the brand think beyond that,” explained Kate Cronin, Chief Brand Officer of Moderna. “What would my mother want to know about Moderna, versus a regulator, versus a doctor? How do we tell our story in an effective way across different audiences? That’s where I think there’s a huge opportunity.”

A team of a few thousand can perform like a team of 100,000

With an ambitious plan to launch multiple products in the next few years, Moderna sees AI as a key component to their success—and their ability to stay lean as a business while setting new benchmarks in innovation. 

“If we had to do it the old biopharmaceutical ways, we might need a hundred thousand people today,” said Bancel. “We really believe we can maximize our impact on patients with a few thousand people, using technology and AI to scale the company.” 

Moderna has been well positioned to leverage generative AI having spent the last decade building a robust tech stack and data platform. The company fosters a culture of learning and curiosity, attracting employees that excel in adopting new technologies and building AI-first solutions.

By making business processes at Moderna more efficient and accurate, the use of AI ultimately translates to better outcomes for patients. “I’m really thankful for the entire OpenAI team, and the time and engagement they have with our team, so that together we can save more lives,” Bancel said. 

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Mathematics > Number Theory

Title: extended genus fields of abelian extensions of rational function fields.

Abstract: In this paper we obtain the extended genus field of a finite abelian extension of a global rational function field. We first study the case of a cyclic extension of prime power degree. Next, we use that the extended genus fields of a composite of two cyclotomic extensions of a global rational function field is equal to the composite of their respective extended genus fields, to obtain our main result. This result is that the extended genus field of a general finite abelian extension of a global rational function field, is given explicitly in terms of the field and of the extended genus field of its "cyclotomic projection".

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