## Study Design 101: Meta-Analysis

- Case Report
- Case Control Study
- Cohort Study
- Randomized Controlled Trial
- Practice Guideline
- Systematic Review

## Meta-Analysis

- Helpful Formulas
- Finding Specific Study Types

A subset of systematic reviews; a method for systematically combining pertinent qualitative and quantitative study data from several selected studies to develop a single conclusion that has greater statistical power. This conclusion is statistically stronger than the analysis of any single study, due to increased numbers of subjects, greater diversity among subjects, or accumulated effects and results.

Meta-analysis would be used for the following purposes:

- To establish statistical significance with studies that have conflicting results
- To develop a more correct estimate of effect magnitude
- To provide a more complex analysis of harms, safety data, and benefits
- To examine subgroups with individual numbers that are not statistically significant

If the individual studies utilized randomized controlled trials (RCT), combining several selected RCT results would be the highest-level of evidence on the evidence hierarchy, followed by systematic reviews, which analyze all available studies on a topic.

- Greater statistical power
- Confirmatory data analysis
- Greater ability to extrapolate to general population affected
- Considered an evidence-based resource

## Disadvantages

- Difficult and time consuming to identify appropriate studies
- Not all studies provide adequate data for inclusion and analysis
- Requires advanced statistical techniques
- Heterogeneity of study populations

## Design pitfalls to look out for

The studies pooled for review should be similar in type (i.e. all randomized controlled trials).

Are the studies being reviewed all the same type of study or are they a mixture of different types?

The analysis should include published and unpublished results to avoid publication bias.

Does the meta-analysis include any appropriate relevant studies that may have had negative outcomes?

## Fictitious Example

Do individuals who wear sunscreen have fewer cases of melanoma than those who do not wear sunscreen? A MEDLINE search was conducted using the terms melanoma, sunscreening agents, and zinc oxide, resulting in 8 randomized controlled studies, each with between 100 and 120 subjects. All of the studies showed a positive effect between wearing sunscreen and reducing the likelihood of melanoma. The subjects from all eight studies (total: 860 subjects) were pooled and statistically analyzed to determine the effect of the relationship between wearing sunscreen and melanoma. This meta-analysis showed a 50% reduction in melanoma diagnosis among sunscreen-wearers.

## Real-life Examples

Goyal, A., Elminawy, M., Kerezoudis, P., Lu, V., Yolcu, Y., Alvi, M., & Bydon, M. (2019). Impact of obesity on outcomes following lumbar spine surgery: A systematic review and meta-analysis. Clinical Neurology and Neurosurgery, 177 , 27-36. https://doi.org/10.1016/j.clineuro.2018.12.012

This meta-analysis was interested in determining whether obesity affects the outcome of spinal surgery. Some previous studies have shown higher perioperative morbidity in patients with obesity while other studies have not shown this effect. This study looked at surgical outcomes including "blood loss, operative time, length of stay, complication and reoperation rates and functional outcomes" between patients with and without obesity. A meta-analysis of 32 studies (23,415 patients) was conducted. There were no significant differences for patients undergoing minimally invasive surgery, but patients with obesity who had open surgery had experienced higher blood loss and longer operative times (not clinically meaningful) as well as higher complication and reoperation rates. Further research is needed to explore this issue in patients with morbid obesity.

Nakamura, A., van Der Waerden, J., Melchior, M., Bolze, C., El-Khoury, F., & Pryor, L. (2019). Physical activity during pregnancy and postpartum depression: Systematic review and meta-analysis. Journal of Affective Disorders, 246 , 29-41. https://doi.org/10.1016/j.jad.2018.12.009

This meta-analysis explored whether physical activity during pregnancy prevents postpartum depression. Seventeen studies were included (93,676 women) and analysis showed a "significant reduction in postpartum depression scores in women who were physically active during their pregnancies when compared with inactive women." Possible limitations or moderators of this effect include intensity and frequency of physical activity, type of physical activity, and timepoint in pregnancy (e.g. trimester).

## Related Terms

A document often written by a panel that provides a comprehensive review of all relevant studies on a particular clinical or health-related topic/question.

Publication Bias

A phenomenon in which studies with positive results have a better chance of being published, are published earlier, and are published in journals with higher impact factors. Therefore, conclusions based exclusively on published studies can be misleading.

## Now test yourself!

1. A Meta-Analysis pools together the sample populations from different studies, such as Randomized Controlled Trials, into one statistical analysis and treats them as one large sample population with one conclusion.

a) True b) False

2. One potential design pitfall of Meta-Analyses that is important to pay attention to is:

a) Whether it is evidence-based. b) If the authors combined studies with conflicting results. c) If the authors appropriately combined studies so they did not compare apples and oranges. d) If the authors used only quantitative data.

## Evidence Pyramid - Navigation

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Open Access

## Ten simple rules for carrying out and writing meta-analyses

* E-mail: [email protected] .

Affiliations Laboratory of NeuroPsychiatric Genetics, Biomedical Sciences Research Group, School of Medicine, Universidad Antonio Nariño, Bogotá, Colombia, PhD Program in Health Sciences, School of Medicine, Universidad Antonio Nariño, Bogotá, Colombia

Affiliation Novartis Pharmaceuticals Corporation, East Hanover, New Jersey, United States of America

Affiliation Departamento de Nutrición y Bioquímica, Facultad de Ciencias, Pontificia Universidad Javeriana, Bogotá., Colombia

Affiliation Department of Computer Science and Biomedical Informatics, University of Thessaly, Lamia, Greece

- Diego A. Forero,
- Sandra Lopez-Leon,
- Yeimy González-Giraldo,
- Pantelis G. Bagos

Published: May 16, 2019

- https://doi.org/10.1371/journal.pcbi.1006922
- Reader Comments

Citation: Forero DA, Lopez-Leon S, González-Giraldo Y, Bagos PG (2019) Ten simple rules for carrying out and writing meta-analyses. PLoS Comput Biol 15(5): e1006922. https://doi.org/10.1371/journal.pcbi.1006922

Editor: Scott Markel, Dassault Systemes BIOVIA, UNITED STATES

Copyright: © 2019 Forero et al. 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.

Funding: YG-G is supported by a PhD fellowship from Centro de Estudios Interdisciplinarios Básicos y Aplicados CEIBA (Rodolfo Llinás Program). DAF is supported by research grants from Colciencias and VCTI. PGB is partially supported by ELIXIR-GR, the Greek Research Infrastructure for data management and analysis in the biosciences. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

## Introduction

In the context of evidence-based medicine, meta-analyses provide novel and useful information [ 1 ], as they are at the top of the pyramid of evidence and consolidate previous evidence published in multiple previous reports [ 2 ]. Meta-analysis is a powerful tool to cumulate and summarize the knowledge in a research field [ 3 ]. Because of the significant increase in the published scientific literature in recent years, there has also been an important growth in the number of meta-analyses for a large number of topics [ 4 ]. It has been found that meta-analyses are among the types of publications that usually receive a larger number of citations in the biomedical sciences [ 5 , 6 ]. The methods and standards for carrying out meta-analyses have evolved in recent years [ 7 – 9 ].

Although there are several published articles describing comprehensive guidelines for specific types of meta-analyses, there is still the need for an abridged article with general and updated recommendations for researchers interested in the development of meta-analyses. We present here ten simple rules for carrying out and writing meta-analyses.

## Rule 1: Specify the topic and type of the meta-analysis

Considering that a systematic review [ 10 ] is fundamental for a meta-analysis, you can use the Population, Intervention, Comparison, Outcome (PICO) model to formulate the research question. It is important to verify that there are no published meta-analyses on the specific topic in order to avoid duplication of efforts [ 11 ]. In some cases, an updated meta-analysis in a topic is needed if additional data become available. It is possible to carry out meta-analyses for multiple types of studies, such as epidemiological variables for case-control, cohort, and randomized clinical trials. As observational studies have a larger possibility of having several biases, meta-analyses of these types of designs should take that into account. In addition, there is the possibility to carry out meta-analyses for genetic association studies, gene expression studies, genome-wide association studies (GWASs), or data from animal experiments. It is advisable to preregister the systematic review protocols at the International Prospective Register of Systematic Reviews (PROSPERO; https://www.crd.york.ac.uk/Prospero ) database [ 12 ]. Keep in mind that an increasing number of journals require registration prior to publication.

## Rule 2: Follow available guidelines for different types of meta-analyses

There are several available general guidelines. The first of such efforts were the Quality of Reports of Meta-analyses of Randomized Controlled Trials (QUORUM) [ 13 ] and the Meta-analysis of Observational Studies in Epidemiology (MOOSE) statements [ 14 ], but currently, the Preferred Reporting Items for Systematic reviews and Meta-analyses (PRISMA) [ 15 ] has been broadly cited and used. In addition, there have been efforts to develop specific guidelines regarding meta-analyses for clinical studies (Cochrane Handbook; https://training.cochrane.org/handbook ), genetic association studies [ 16 ], genome-wide expression studies [ 17 ], GWASs [ 18 ], and animal studies [ 19 ].

## Rule 3: Establish inclusion criteria and define key variables

You should establish in advance the inclusion (such as type of study, language of publication, among others) and exclusion (such as minimal sample size, among others) criteria. Keep in mind that the current consensus advises against strict criteria concerning language or sample size. You should clearly define the variables that will be extracted from each primary article. Broad inclusion criteria increase heterogeneity between studies, and narrow inclusion criteria can make it difficult to find studies; therefore, a compromise should be found. Prospective meta-analyses, which usually are carried out by international consortia, have the advantage of the possibility of including individual-level data [ 20 ].

## Rule 4: Carry out a systematic search in different databases and extract key data

You can carry out your systematic search in several bibliographic databases, such as PubMed, Embase, The Cochrane Central Register of Controlled Trials, Scopus, Web of Science, and Google Scholar [ 21 ]. Usually, searching in several databases helps to minimize the possibility of failing to identify all published studies [ 22 ]. In some specific areas, searching in specialized databases is also worth doing (such as BIOSIS, Cumulative index to Nursing and Allied Health Literature (CINAHL), PsycINFO, Sociological Abstracts, and EconLit, among others). Moreover, in other cases, direct search for the data is also advisable (i.e., Gene Expression Omnibus [GEO] database for gene expression studies) [ 23 ]. Usually, the bibliography of review articles might help to identify additional articles and data from other types of documents (such as theses or conference proceedings) that might be included in your meta-analysis. The Web of Science database can be used to identify publications that have cited key articles. Adequate extraction and recording of key data from primary articles are fundamental for carrying out a meta-analysis. Quality assessment of the included studies is also an important issue; it can be used for determining inclusion criteria, sensitivity analysis, or differential weighting of the studies. For example the Jadad scale [ 24 ] is frequently used for randomized clinical trials, the Newcastle–Ottawa scale [ 25 ] for nonrandomized studies, and QUADAS-2 for the Quality Assessment of Diagnostic Accuracy Studies [ 26 ]. It is recommended that these steps be carried out by two researchers in parallel and that discrepancies be resolved by consensus. Nevertheless, the reader must be aware that quality assessment has been criticized, especially when it reduces the studies to a single “quality” score [ 27 , 28 ]. In any case, it is important to avoid the confusion of using guidelines for the reporting of primary studies as scales for the assessment of the quality of included articles [ 29 , 30 ].

## Rule 5: Contact authors of primary articles to ask for missing data

It is common that key data are not available in the main text or supplementary files of primary articles [ 31 ], leading to the need to contact the authors to ask for missing data. However, the rate of response from authors is lower than expected. There are multiple standards that promote the availability of primary data in published articles, such as the minimum information about a microarray experiment (MIAME) [ 32 ] and the STrengthening the REporting of Genetic Association Studies (STREGA) [ 33 ]. In some areas, such as genetics, in which it was shown that it is possible to identify an individual using the aggregated statistics from a particular study [ 34 ], strict criteria are imposed for data sharing, and specialized permissions might be needed.

## Rule 6: Select the best statistical models for your question

For cases in which there is enough primary data of adequate quality for a quantitative summary, there is the option to carry out a meta-analysis. The potential analyst must be warned that in many cases the data are reported in noncompatible forms, so one must be ready to perform various types of transformations. Thankfully, there are methods available for extracting and transforming data regarding continuous variables [ 35 – 37 ], 2 × 2 tables [ 38 , 39 ], or survival data [ 40 ]. Frequently, meta-analyses are based on fixed-effects or random-effects statistical models [ 20 ]. In addition, models based on combining ranks or p -values are also available and can be used in specific cases [ 41 – 44 ]. For more complex data, multivariate methods for meta-analysis have been proposed [ 45 , 46 ]. Additional statistical examinations involve sensitivity analyses, metaregressions, subgroup analyses, and calculation of heterogeneity metrics, such as Q or I 2 [ 20 ]. It is fundamental to assess and, if present, explain the possible sources of heterogeneity. Although random-effects models are suitable for cases of between-studies heterogeneity, the sources of between-studies variation should be identified, and their impact on effect size should be quantified using statistical tests, such as subgroup analyses or metaregression. Publication bias is an important aspect to consider [ 47 ], since in many cases negative findings have less probability of being published. Other types of bias, such as the so-called “Proteus phenomenon” [ 48 ] or “winner’s curse” [ 49 ], are common in some scientific fields, such as genetics, and the approach of cumulative meta-analysis is suggested in order to identify them.

## Rule 7: Use available software to carry metastatistics

There are several very user-friendly and freely available programs for carrying out meta-analyses [ 43 , 44 ], either within the framework of a statistical package such as Stata or R or as stand-alone applications. Stata and R [ 50 – 52 ] have dozens of routines, mostly user written, that can handle most meta-analysis tasks, even complex analyses such as network meta-analysis and meta-analyses of GWASs and gene expression studies ( https://cran.r-project.org/web/views/MetaAnalysis.html ; https://www.stata.com/support/faqs/statistics/meta-analysis ). There are also stand-alone packages that can be useful for general applications or for specific areas, such as OpenMetaAnalyst [ 53 ], NetworkAnalyst [ 54 ], JASP [ 55 ], MetaGenyo [ 56 ], Cochrane RevMan ( https://community.cochrane.org/help/tools-and-software/revman-5 ), EpiSheet (krothman.org/episheet.xls), GWAR [ 57 ], GWAMA [ 58 ], and METAL [ 59 ]. Some of these programs are web services or stand-alone software. In some cases, certain programs can present issues when they are run because of their dependency on other packages.

## Rule 8: The records and study report must be complete and transparent

Following published guidelines for meta-analyses guarantees that the manuscript will describe the different steps and methods used, facilitating their transparency and replicability [ 15 ]. Data such as search and inclusion criteria, numbers of abstracts screened, and included studies are quite useful, in addition to details of meta-analytical strategies used. An assessment of quality of included studies is also useful [ 60 ]. A spreadsheet can be constructed in which every step in the selection criteria is recorded; this will be helpful to construct flow charts. In this context, a flow diagram describing the progression between the different steps is quite useful and might enhance the quality of the meta-analysis [ 61 ]. Records will be also useful if, in the future, the meta-analysis needs to be updated. Stating the limitations of the analysis is also important [ 62 ].

## Rule 9: Provide enough data in your manuscript

A table with complete information about included studies (such as author, year, details of included subjects, DOIs, or PubMed IDs, among others) is quite useful in an article reporting a meta-analysis; it can be included in the main text of the manuscript or as a supplementary file. Software used for carrying out meta-analyses and to generate key graphs, such as forest plots, should be referenced. Summary effect measures, such as a pooled odds ratios or the counts used to generate them, should be always reported, including confidence intervals. It is also possible to generate figures with information from multiple forest plots [ 63 ]. In the case of positive findings, plots from sensitivity analyses are quite informative. In more-complex analyses, it is advisable to include in the supplementary files the scripts used to generate the results [ 64 ].

## Rule 10: Provide context for your findings and suggest future directions

The Discussion section is an important scientific component in a manuscript describing a meta-analysis, as the authors should discuss their current findings in the context of the available scientific literature and existing knowledge [ 65 ]. Authors can discuss possible reasons for the positive or negative results of their meta-analysis, provide an interpretation of findings based on available biological or epidemiological evidence, and comment on particular features of individual studies or experimental designs used [ 66 ]. As meta-analyses are usually synthesizing the existing evidence from multiple primary studies, which commonly took years and large amounts of funding, authors can recommend key suggestions for conducting and/or reporting future primary studies [ 67 ].

As open science is becoming more important around the globe [ 68 , 69 ], adherence to published standards, in addition to the evolution of methods for different meta-analytical applications, will be even more important to carry out meta-analyses of high quality and impact.

- View Article
- PubMed/NCBI
- Google Scholar
- 47. Rothstein HR, Sutton AJ, Borenstein M (2006) Publication bias in meta-analysis: Prevention, assessment and adjustments. Hoboken, NJ: John Wiley & Sons.
- 50. Sterne JA, Bradburn MJ, Egger M (2001) Meta‒Analysis in Stata™. In: Egger M, Smith GD, Altman DG, editors. Systematic reviews in health care: meta‐analysis in context. Hoboken, NJ: Wiley. pp. 347–369.

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## Introduction to Systematic Review and Meta-Analysis

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## There are 6 modules in this course

We will introduce methods to perform systematic reviews and meta-analysis of clinical trials. We will cover how to formulate an answerable research question, define inclusion and exclusion criteria, search for the evidence, extract data, assess the risk of bias in clinical trials, and perform a meta-analysis.

Upon successfully completing this course, participants will be able to: - Describe the steps in conducting a systematic review - Develop an answerable question using the “Participants Interventions Comparisons Outcomes” (PICO) framework - Describe the process used to collect and extract data from reports of clinical trials - Describe methods to critically assess the risk of bias of clinical trials - Describe and interpret the results of meta-analyses

## Introduction

To get the ball rolling, we'll take a broad overview of what to expect in this course and then introduce you to the high-level concepts of systematic review and meta-analysis and take a look at who produces and uses systematic reviews.

## What's included

5 videos 3 readings

## 5 videos • Total 40 minutes

- Welcome to Systematic Reviews and Meta-Analysis • 2 minutes • Preview module
- Lecture 1A : Introduction to Systematic Reviews • 15 minutes
- Lecture 1B: Introduction to Meta-Analysis • 12 minutes
- Lecture 1C: Producers and Users of Systematic Reviews • 8 minutes
- Hannah Rothstein, PhD • 1 minute

## 3 readings • Total 30 minutes

- Syllabus • 10 minutes
- Pre Course Survey • 10 minutes
- From the Field Videos • 10 minutes

## Framing the Question

In this module, we will discuss how to frame a question, as well as scope, elements, and refining the question.

7 videos 1 reading 1 quiz 1 peer review

## 7 videos • Total 72 minutes

- Lecture 2A: Resources for How to Frame Your Question • 7 minutes • Preview module
- Lecture 2B: Deciding the Type and Scope of Your Question • 17 minutes
- Lecture 2C: Elements of the Question • 16 minutes
- Lecture 2D: Refining the Question • 10 minutes
- Lecture 2E: Some Examples • 8 minutes
- Lecture 2F: Analytic Frameworks • 10 minutes
- Betsy Becker, PhD • 2 minutes

## 1 reading • Total 10 minutes

- Welcome to the first Peer Assignment! • 10 minutes

## 1 quiz • Total 30 minutes

- Module 2 • 30 minutes

## 1 peer review • Total 60 minutes

- Peer Assessment 1 • 60 minutes

## Searching Principles and Bias Assessment

In this module we will look at finding the evidence, as well as key sources, search strategy, and assessing the risk of bias.

11 videos 2 quizzes

## 11 videos • Total 118 minutes

- Searching Principles and Assessing Bias • 2 minutes • Preview module
- Lecture 3A: Finding the Evidence: Searching Principles • 5 minutes
- Lecture 3B: Identifying Key Sources and Techniques for Searching • 17 minutes
- Lecture 3C: Building a High-Quality Search Strategy • 17 minutes
- Lecture 3D: Documenting Your Search and Conclusions • 8 minutes
- Lecture 4A: Why Bias in the Individual Study is Important to a Systematic Review and Meta-Analysis • 7 minutes
- Lecture 4B: Selection Bias • 18 minutes
- Lecture 4C: Information Bias • 8 minutes
- Lecture 4D: Bias in the Analysis • 15 minutes
- Lecture 4E: Displaying Study "Quality" in Your Systematic Review • 16 minutes
- Byron Wallace, Phd • 2 minutes

## 2 quizzes • Total 60 minutes

- Module 3 • 30 minutes
- Module 4 • 30 minutes

## Minimizing Metabias, Qualitative Synthesis, and Interpreting Results

In this module, we will cover minimizing metabias, selection bias, information bias, how to report transparently, qualitative synthesis, and interpreting results.

9 videos 2 quizzes

## 9 videos • Total 87 minutes

- Lecture 5A: Standards for Systematic Reviews • 6 minutes • Preview module
- Lecture 5B: Selection Bias • 22 minutes
- Lecture 5C: Information Bias • 12 minutes
- Lecture 5D: Bias in the Analysis • 15 minutes
- Lecture 5E: Reporting Transparently • 6 minutes
- Lecture 6A: Qualitative Synthesis and Interpreting Results Section A • 7 minutes
- Lecture 6B: What is Qualitative Synthesis • 10 minutes
- Lecture 6C: Some Examples • 5 minutes
- Christopher Schmid, PhD • 1 minute
- Module 5 • 30 minutes
- Module 6 • 30 minutes

## Planning the Meta-Analysis and Statistical Methods

This module will cover the planning of your meat-analysis and the statistical methods for meta-analysis.

## 9 videos • Total 109 minutes

- Planning Meta-Analysis and Statistical Methods • 1 minute • Preview module
- Lecture 7A: Planning Your Meta-Analysis Section A • 7 minutes
- Lecture 7B: Introduction to Meta-Analysis • 15 minutes
- Lecture 7C: Why Do a Meta-Analysis? • 10 minutes
- Lecture 7D: Types of Data and Effect Measures • 19 minutes
- Lecture 8A: Fixed Effect Model • 20 minutes
- Lecture 8B: Random Effects Model • 14 minutes
- Lecture 8C: Random Effects Model • 17 minutes
- Michael Borenstein, PhD • 2 minutes
- Module 7 • 30 minutes
- Module 8 • 30 minutes

## Wrap Up and Final Peer Review Assignment

In this final module, we'll wrap up with a look back at the key concepts covered over the past few weeks. Afterwards, you will submit your final Peer Review Assignment and evaluate some of your classmates' submissions.

2 videos 1 reading 1 peer review

## 2 videos • Total 12 minutes

- Lecture 9A: Wrap Up • 11 minutes • Preview module
- Closing Remarks • 1 minute
- Welcome to Your Final Peer Review Assignment • 10 minutes
- Peer Review Assignment 2 • 60 minutes

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This course helps to learn basics about systematic review and meta-analysis. I recommend this course to the beginners, who wants to do systematic review in future.

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This course has added valuable insights to my existing understanding of systematic reviews. After completing this course, I feel more confident in my pursuit of conducting a systematic review.

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The course is a good introduction to the topic, however, it is a pity that there is no follow up to the course. At the end of the course you will not be able to perform a SLR + meta-analysis.

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## A Guide to Conducting a Meta-Analysis

- Published: 21 May 2016
- Volume 26 , pages 121–128, ( 2016 )
- Mike W.-L. Cheung 1 &
- Ranjith Vijayakumar 1

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Meta-analysis is widely accepted as the preferred method to synthesize research findings in various disciplines. This paper provides an introduction to when and how to conduct a meta-analysis. Several practical questions, such as advantages of meta-analysis over conventional narrative review and the number of studies required for a meta-analysis, are addressed. Common meta-analytic models are then introduced. An artificial dataset is used to illustrate how a meta-analysis is conducted in several software packages. The paper concludes with some common pitfalls of meta-analysis and their solutions. The primary goal of this paper is to provide a summary background to readers who would like to conduct their first meta-analytic study.

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## Acknowledgments

Mike W.-L. Cheung was supported by the Academic Research Fund Tier 1 (FY2013-FRC5-002) from the Ministry of Education, Singapore. We would like to thank Maggie Chan for providing comments on an earlier version of this manuscript.

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Cheung, M.WL., Vijayakumar, R. A Guide to Conducting a Meta-Analysis. Neuropsychol Rev 26 , 121–128 (2016). https://doi.org/10.1007/s11065-016-9319-z

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Published : 21 May 2016

Issue Date : June 2016

DOI : https://doi.org/10.1007/s11065-016-9319-z

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## Conducting a meta-analysis: basics and good practices

Affiliation.

- 1 Department of Psychology, Faculty of Arts and Social Sciences, National University of Singapore, Singapore. [email protected]
- PMID: 22462415
- DOI: 10.1111/j.1756-185X.2012.01712.x

Meta-analysis is a statistical method to compare and combine effect sizes from a pool of relevant empirical studies. It is now a standard approach to synthesize research findings in many disciplines, including medical and healthcare research. This paper is the third paper of a mini-series introducing systematic review and meta-analysis. First, common effect sizes used in meta-analysis are presented. Fixed-, random- and mixed-effects models are then introduced. Next, a real data set from a published meta-analysis will be used to illustrate the procedures and interpretations. Last, software packages that may be used to conduct meta-analyses will be highlighted.

© 2012 The Authors International Journal of Rheumatic Diseases © 2012 Asia Pacific League of Associations for Rheumatology and Blackwell Publishing Asia Pty Ltd.

## Publication types

- Research Support, Non-U.S. Gov't
- Biomedical Research / methods*
- Biomedical Research / statistics & numerical data
- Meta-Analysis as Topic*
- Models, Statistical
- Research Design*

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## Cochrane Training

Chapter 10: analysing data and undertaking meta-analyses.

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

## Key Points:

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

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

## 10.1 Do not start here!

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

## 10.2 Introduction to meta-analysis

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

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

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

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

## 10.2.1 Principles of meta-analysis

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

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

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

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

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

## 10.3 A generic inverse-variance approach to meta-analysis

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

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

## 10.3.1 Fixed-effect method for meta-analysis

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

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

## 10.3.2 Random-effects methods for meta-analysis

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

## 10.3.3 Performing inverse-variance meta-analyses

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

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

## 10.4 Meta-analysis of dichotomous outcomes

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

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

## 10.4.1 Mantel-Haenszel methods

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

## 10.4.2 Peto odds ratio method

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

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

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

## 10.4.3 Which effect measure for dichotomous outcomes?

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

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

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

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

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

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

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

## 10.4.4 Meta-analysis of rare events

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

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

## 10.4.4.1 Studies with no events in one or more arms

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

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

## 10.4.4.2 Studies with no events in either arm

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

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

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

## 10.4.4.3 Validity of methods of meta-analysis for rare events

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

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

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

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

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

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

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

## 10.5 Meta-analysis of continuous outcomes

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

## 10.5.1 Which effect measure for continuous outcomes?

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

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

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

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

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

## 10.5.2 Meta-analysis of change scores

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

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

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

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

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

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

## 10.5.3 Meta-analysis of skewed data

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

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

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

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

## 10.6 Combining dichotomous and continuous outcomes

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

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

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

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

## 10.7 Meta-analysis of ordinal outcomes and measurement scale s

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

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

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

## 10.8 Meta-analysis of counts and rates

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

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

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

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

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

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

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

## 10.9 Meta-analysis of time-to-event outcomes

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

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

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

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

## 10.10 Heterogeneity

10.10.1 what is heterogeneity.

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

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

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

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

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

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

## 10.10.2 Identifying and measuring heterogeneity

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

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

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

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

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

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

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

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

## 10.10.3 Strategies for addressing heterogeneity

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

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

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

## 10.10.4 Incorporating heterogeneity into random-effects models

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

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

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

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

## 10.10.4.1 Fixed or random effects?

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

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

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

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

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

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

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

## 10.10.4.2 Interpretation of random-effects meta-analyses

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

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

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

## 10.10.4.3 Prediction intervals from a random-effects meta-analysis

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

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

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

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

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

## 10.10.4.4 Implementing random-effects meta-analyses

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

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

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

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

## 10.11 Investigating heterogeneity

10.11.1 interaction and effect modification.

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

## 10.11.2 What are subgroup analyses?

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

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

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

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

## 10.11.3 Undertaking subgroup analyses

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

## 10.11.3.1 Is the effect different in different subgroups?

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

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

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

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

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

## 10.11.4 Meta-regression

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

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

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

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

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

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

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

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

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

## 10.11.5.2 Specify characteristics in advance

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

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

## 10.11.5.3 Select a small number of characteristics

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

## 10.11.5.4 Ensure there is scientific rationale for investigating each characteristic

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

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

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

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

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

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

## 10.11.6 Interpretation of subgroup analyses and meta-regressions

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

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

## 10.11.7 Investigating the effect of underlying risk

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

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

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

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

## 10.11.8 Dose-response analyses

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

## 10.12 Missing data

10.12.1 types of missing data.

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

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

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

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

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

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

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

## 10.12.2 General principles for dealing with missing data

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

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

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

The principal options for dealing with missing data are:

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

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

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

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

## 10.12.3 Dealing with missing outcome data from individual participants

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

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

## 10.13 Bayesian approaches to meta-analysis

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

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

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

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

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

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

## 10.14 Sensitivity analyses

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

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

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

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

Searching for studies:

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

Eligibility criteria:

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

What data should be analysed?

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

Analysis methods:

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

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

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

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

## 10.15 Chapter information

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

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

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

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

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

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

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

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

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

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

## Introduction

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

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

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

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

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

## Methods and results

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

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

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

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

## Research question and objectives

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

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

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

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

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

## Preliminary research and idea validation

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

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

## Inclusion and exclusion criteria

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

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

PRISMA flow diagram of studies’ screening and selection

## Search strategy

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

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

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

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

With all of the words: ebola virus

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

Where my words occur: in the title of the article

With all of the words: EVD

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

## Protocol writing and registration

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

## Title and abstract screening

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

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

## Full text downloading and screening

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

## Manual search

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

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

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

## Data extraction and quality assessment

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

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

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

## Data checking

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

## Statistical analysis

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

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

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

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

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

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

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

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

Publication bias funnel plot for comparison of vaccine A versus placebo

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

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

## Double data checking

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

## Manuscript writing, revision, and submission to a journal

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

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

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

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

## Conclusions

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

## Availability of data and materials

Not applicable.

## Abbreviations

Network meta-analysis

Principal investigator

Population, Intervention, Comparison, Outcome

Preferred Reporting Items for Systematic Review and Meta-analysis statement

Quality assessment

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

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## Acknowledgements

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

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## Additional files

Additional file 1:.

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

## Additional file 2:

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

## Additional file 3:

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

## Additional file 4:

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

## Additional file 5:

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

## Additional file 6:

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

## Additional file 7:

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

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## Systematic review and meta-analysis of depression, anxiety, and suicidal ideation among Ph.D. students

- Emily N. Satinsky 1 ,
- Tomoki Kimura 2 ,
- Mathew V. Kiang 3 , 4 ,
- Rediet Abebe 5 , 6 ,
- Scott Cunningham 7 ,
- Hedwig Lee 8 ,
- Xiaofei Lin 9 ,
- Cindy H. Liu 10 , 11 ,
- Igor Rudan 12 ,
- Srijan Sen 13 ,
- Mark Tomlinson 14 , 15 ,
- Miranda Yaver 16 &
- Alexander C. Tsai 1 , 11 , 17

Scientific Reports volume 11 , Article number: 14370 ( 2021 ) Cite this article

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- Epidemiology
- Health policy
- Quality of life

University administrators and mental health clinicians have raised concerns about depression and anxiety among Ph.D. students, yet no study has systematically synthesized the available evidence in this area. After searching the literature for studies reporting on depression, anxiety, and/or suicidal ideation among Ph.D. students, we included 32 articles. Among 16 studies reporting the prevalence of clinically significant symptoms of depression across 23,469 Ph.D. students, the pooled estimate of the proportion of students with depression was 0.24 (95% confidence interval [CI], 0.18–0.31; I 2 = 98.75%). In a meta-analysis of the nine studies reporting the prevalence of clinically significant symptoms of anxiety across 15,626 students, the estimated proportion of students with anxiety was 0.17 (95% CI, 0.12–0.23; I 2 = 98.05%). We conclude that depression and anxiety are highly prevalent among Ph.D. students. Data limitations precluded our ability to obtain a pooled estimate of suicidal ideation prevalence. Programs that systematically monitor and promote the mental health of Ph.D. students are urgently needed.

## Introduction

Mental health problems among graduate students in doctoral degree programs have received increasing attention 1 , 2 , 3 , 4 . Ph.D. students (and students completing equivalent degrees, such as the Sc.D.) face training periods of unpredictable duration, financial insecurity and food insecurity, competitive markets for tenure-track positions, and unsparing publishing and funding models 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 —all of which may have greater adverse impacts on students from marginalized and underrepresented populations 13 , 14 , 15 . Ph.D. students’ mental health problems may negatively affect their physical health 16 , interpersonal relationships 17 , academic output, and work performance 18 , 19 , and may also contribute to program attrition 20 , 21 , 22 . As many as 30 to 50% of Ph.D. students drop out of their programs, depending on the country and discipline 23 , 24 , 25 , 26 , 27 . Further, while mental health problems among Ph.D. students raise concerns for the wellbeing of the individuals themselves and their personal networks, they also have broader repercussions for their institutions and academia as a whole 22 .

Despite the potential public health significance of this problem, most evidence syntheses on student mental health have focused on undergraduate students 28 , 29 or graduate students in professional degree programs (e.g., medical students) 30 . In non-systematic summaries, estimates of the prevalence of clinically significant depressive symptoms among Ph.D. students vary considerably 31 , 32 , 33 . Reliable estimates of depression and other mental health problems among Ph.D. students are needed to inform preventive, screening, or treatment efforts. To address this gap in the literature, we conducted a systematic review and meta-analysis to explore patterns of depression, anxiety, and suicidal ideation among Ph.D. students.

Flowchart of included articles.

The evidence search yielded 886 articles, of which 286 were excluded as duplicates (Fig. 1 ). An additional nine articles were identified through reference lists or grey literature reports published on university websites. Following a title/abstract review and subsequent full-text review, 520 additional articles were excluded.

Of the 89 remaining articles, 74 were unclear about their definition of graduate students or grouped Ph.D. and non-Ph.D. students without disaggregating the estimates by degree level. We obtained contact information for the authors of most of these articles (69 [93%]), requesting additional data. Three authors clarified that their study samples only included Ph.D. students 34 , 35 , 36 . Fourteen authors confirmed that their study samples included both Ph.D. and non-Ph.D. students but provided us with data on the subsample of Ph.D. students 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 . Where authors clarified that the sample was limited to graduate students in non-doctoral degree programs, did not provide additional data on the subsample of Ph.D. students, or did not reply to our information requests, we excluded the studies due to insufficient information (Supplementary Table S1 ).

Ultimately, 32 articles describing the findings of 29 unique studies were identified and included in the review 16 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 (Table 1 ). Overall, 26 studies measured depression, 19 studies measured anxiety, and six studies measured suicidal ideation. Three pairs of articles reported data on the same sample of Ph.D. students 33 , 38 , 45 , 51 , 53 , 56 and were therefore grouped in Table 1 and reported as three studies. Publication dates ranged from 1979 to 2019, but most articles (22/32 [69%]) were published after 2015. Most studies were conducted in the United States (20/29 [69%]), with additional studies conducted in Australia, Belgium, China, Iran, Mexico, and South Korea. Two studies were conducted in cross-national settings representing 48 additional countries. None were conducted in sub-Saharan Africa or South America. Most studies included students completing their degrees in a mix of disciplines (17/29 [59%]), while 12 studies were limited to students in a specific field (e.g., biomedicine, education). The median sample size was 172 students (interquartile range [IQR], 68–654; range, 6–6405). Seven studies focused on mental health outcomes in demographic subgroups, including ethnic or racialized minority students 37 , 41 , 43 , international students 47 , 50 , and sexual and gender minority students 42 , 54 .

In all, 16 studies reported the prevalence of depression among a total of 23,469 Ph.D. students (Fig. 2 ; range, 10–47%). Of these, the most widely used depression scales were the PHQ-9 (9 studies) and variants of the Center for Epidemiologic Studies-Depression scale (CES-D, 4 studies) 63 , and all studies assessed clinically significant symptoms of depression over the past one to two weeks. Three of these studies reported findings based on data from different survey years of the same parent study (the Healthy Minds Study) 40 , 42 , 43 , but due to overlap in the survey years reported across articles, these data were pooled. Most of these studies were based on data collected through online surveys (13/16 [81%]). Ten studies (63%) used random or systematic sampling, four studies (25%) used convenience sampling, and two studies (13%) used multiple sampling techniques.

Pooled estimate of the proportion of Ph.D. students with clinically significant symptoms of depression.

The estimated proportion of Ph.D. students assessed as having clinically significant symptoms of depression was 0.24 (95% confidence interval [CI], 0.18–0.31; 95% predictive interval [PI], 0.04–0.54), with significant evidence of between-study heterogeneity (I 2 = 98.75%). A subgroup analysis restricted to the twelve studies conducted in the United States yielded similar findings (pooled estimate [ES] = 0.23; 95% CI, 0.15–0.32; 95% PI, 0.01–0.60), with no appreciable difference in heterogeneity (I 2 = 98.91%). A subgroup analysis restricted to the studies that used the PHQ-9 to assess depression yielded a slightly lower prevalence estimate and a slight reduction in heterogeneity (ES = 0.18; 95% CI, 0.14–0.22; 95% PI, 0.07–0.34; I 2 = 90.59%).

Nine studies reported the prevalence of clinically significant symptoms of anxiety among a total of 15,626 Ph.D. students (Fig. 3 ; range 4–49%). Of these, the most widely used anxiety scale was the 7-item Generalized Anxiety Disorder scale (GAD-7, 5 studies) 64 . Data from three of the Healthy Minds Study articles were pooled into two estimates, because the scale used to measure anxiety changed midway through the parent study (i.e., the Patient Health Questionnaire-Generalized Anxiety Disorder [PHQ-GAD] scale was used from 2007 to 2012 and then switched to the GAD-7 in 2013 40 ). Most studies (8/9 [89%]) assessed clinically significant symptoms of anxiety over the past two to four weeks, with the one remaining study measuring anxiety over the past year. Again, most of these studies were based on data collected through online surveys (7/9 [78%]). Five studies (56%) used random or systematic sampling, two studies (22%) used convenience sampling, and two studies (22%) used multiple sampling techniques.

Pooled estimate of the proportion of Ph.D. students with clinically significant symptoms of anxiety.

The estimated proportion of Ph.D. students assessed as having anxiety was 0.17 (95% CI, 0.12–0.23; 95% PI, 0.02–0.41), with significant evidence of between-study heterogeneity (I 2 = 98.05%). The subgroup analysis restricted to the five studies conducted in the United States yielded a slightly lower proportion of students assessed as having anxiety (ES = 0.14; 95% CI, 0.08–0.20; 95% PI, 0.00–0.43), with no appreciable difference in heterogeneity (I 2 = 98.54%).

Six studies reported the prevalence of suicidal ideation (range, 2–12%), but the recall windows varied greatly (e.g., ideation within the past 2 weeks vs. past year), precluding pooled estimation.

Additional stratified pooled estimates could not be obtained. One study of Ph.D. students across 54 countries found that phase of study was a significant moderator of mental health, with students in the comprehensive examination and dissertation phases more likely to experience distress compared with students primarily engaged in coursework 59 . Other studies identified a higher prevalence of mental ill-health among women 54 ; lesbian, gay, bisexual, transgender, and queer (LGBTQ) students 42 , 54 , 60 ; and students with multiple intersecting identities 54 .

Several studies identified correlates of mental health problems including: project- and supervisor-related issues, stress about productivity, and self-doubt 53 , 62 ; uncertain career prospects, poor living conditions, financial stressors, lack of sleep, feeling devalued, social isolation, and advisor relationships 61 ; financial challenges 38 ; difficulties with work-life balance 58 ; and feelings of isolation and loneliness 52 . Despite these challenges, help-seeking appeared to be limited, with only about one-quarter of Ph.D. students reporting mental health problems also reporting that they were receiving treatment 40 , 52 .

## Risk of bias

Twenty-one of 32 articles were assessed as having low risk of bias (Supplementary Table S2 ). Five articles received one point for all five categories on the risk of bias assessment (lowest risk of bias), and one article received no points (highest risk). The mean risk of bias score was 3.22 (standard deviation, 1.34; median, 4; IQR, 2–4). Restricting the estimation sample to 12 studies assessed as having low risk of bias, the estimated proportion of Ph.D. students with depression was 0.25 (95% CI, 0.18–0.33; 95% PI, 0.04–0.57; I 2 = 99.11%), nearly identical to the primary estimate, with no reduction in heterogeneity. The estimated proportion of Ph.D. students with anxiety, among the 7 studies assessed as having low risk of bias, was 0.12 (95% CI, 0.07–0.17; 95% PI, 0.01–0.34; I 2 = 98.17%), again with no appreciable reduction in heterogeneity.

In our meta-analysis of 16 studies representing 23,469 Ph.D. students, we estimated that the pooled prevalence of clinically significant symptoms of depression was 24%. This estimate is consistent with estimated prevalence rates in other high-stress biomedical trainee populations, including medical students (27%) 30 , resident physicians (29%) 65 , and postdoctoral research fellows (29%) 66 . In the sample of nine studies representing 15,626 Ph.D. students, we estimated that the pooled prevalence of clinically significant symptoms of anxiety was 17%. While validated screening instruments tend to over-identify cases of depression (relative to structured clinical interviews) by approximately a factor of two 67 , 68 , our findings nonetheless point to a major public health problem among Ph.D. students. Available data suggest that the prevalence of depressive and anxiety disorders in the general population ranges from 5 to 7% worldwide 69 , 70 . In contrast, prevalence estimates of major depressive disorder among young adults have ranged from 13% (for young adults between the ages of 18 and 29 years in the 2012–2013 National Epidemiologic Survey on Alcohol and Related Conditions III 71 ) to 15% (for young adults between the ages of 18 and 25 in the 2019 U.S. National Survey on Drug Use and Health 72 ). Likewise, the prevalence of generalized anxiety disorder was estimated at 4% among young adults between the ages of 18 and 29 in the 2001–03 U.S. National Comorbidity Survey Replication 73 . Thus, even accounting for potential upward bias inherent in these studies’ use of screening instruments, our estimates suggest that the rates of recent clinically significant symptoms of depression and anxiety are greater among Ph.D. students compared with young adults in the general population.

Further underscoring the importance of this public health issue, Ph.D. students face unique stressors and uncertainties that may put them at increased risk for mental health and substance use problems. Students grapple with competing responsibilities, including coursework, teaching, and research, while also managing interpersonal relationships, social isolation, caregiving, and financial insecurity 3 , 10 . Increasing enrollment in doctoral degree programs has not been matched with a commensurate increase in tenure-track academic job opportunities, intensifying competition and pressure to find employment post-graduation 5 . Advisor-student power relations rarely offer options for recourse if and when such relationships become strained, particularly in the setting of sexual harassment, unwanted sexual attention, sexual coercion, and rape 74 , 75 , 76 , 77 , 78 . All of these stressors may be magnified—and compounded by stressors unrelated to graduate school—for subgroups of students who are underrepresented in doctoral degree programs and among whom mental health problems are either more prevalent and/or undertreated compared with the general population, including Black, indigenous, and other people of color 13 , 79 , 80 ; women 81 , 82 ; first-generation students 14 , 15 ; people who identify as LGBTQ 83 , 84 , 85 ; people with disabilities; and people with multiple intersecting identities.

Structural- and individual-level interventions will be needed to reduce the burden of mental ill-health among Ph.D. students worldwide 31 , 86 . Despite the high prevalence of mental health and substance use problems 87 , Ph.D. students demonstrate low rates of help-seeking 40 , 52 , 88 . Common barriers to help-seeking include fears of harming one’s academic career, financial insecurity, lack of time, and lack of awareness 89 , 90 , 91 , as well as health care systems-related barriers, including insufficient numbers of culturally competent counseling staff, limited access to psychological services beyond time-limited psychotherapies, and lack of programs that address the specific needs either of Ph.D. students in general 92 or of Ph.D. students belonging to marginalized groups 93 , 94 . Structural interventions focused solely on enhancing student resilience might include programs aimed at reducing stigma, fostering social cohesion, and reducing social isolation, while changing norms around help-seeking behavior 95 , 96 . However, structural interventions focused on changing stressogenic aspects of the graduate student environment itself are also needed 97 , beyond any enhancements to Ph.D. student resilience, including: undercutting power differentials between graduate students and individual faculty advisors, e.g., by diffusing power among multiple faculty advisors; eliminating racist, sexist, and other discriminatory behaviors by faculty advisors 74 , 75 , 98 ; valuing mentorship and other aspects of “invisible work” that are often disproportionately borne by women faculty and faculty of color 99 , 100 ; and training faculty members to emphasize the dignity of, and adequately prepare Ph.D. students for, non-academic careers 101 , 102 .

Our findings should be interpreted with several limitations in mind. First, the pooled estimates are characterized by a high degree of heterogeneity, similar to meta-analyses of depression prevalence in other populations 30 , 65 , 103 , 104 , 105 . Second, we were only able to aggregate depression prevalence across 16 studies and anxiety prevalence across nine studies (the majority of which were conducted in the U.S.) – far fewer than the 183 studies included in a meta-analysis of depression prevalence among medical students 30 and the 54 studies included in a meta-analysis of resident physicians 65 . These differences underscore the need for more rigorous study in this critical area. Many articles were either excluded from the review or from the meta-analyses for not meeting inclusion criteria or not reporting relevant statistics. Future research in this area should ensure the systematic collection of high-quality, clinically relevant data from a comprehensive set of institutions, across disciplines and countries, and disaggregated by graduate student type. As part of conducting research and addressing student mental health and wellbeing, university deans, provosts, and chancellors should partner with national survey and program institutions (e.g., Graduate Student Experience in the Research University [gradSERU] 106 , the American College Health Association National College Health Assessment [ACHA-NCHA], and HealthyMinds). Furthermore, federal agencies that oversee health and higher education should provide resources for these efforts, and accreditation agencies should require monitoring of mental health and programmatic responses to stressors among Ph.D. students.

Third, heterogeneity in reporting precluded a meta-analysis of the suicidality outcomes among the few studies that reported such data. While reducing the burden of mental health problems among graduate students is an important public health aim in itself, more research into understanding non-suicidal self-injurious behavior, suicide attempts, and completed suicide among Ph.D. students is warranted. Fourth, it is possible that the grey literature reports included in our meta-analysis are more likely to be undertaken at research-intensive institutions 52 , 60 , 61 . However, the direction of bias is unpredictable: mental health problems among Ph.D. students in research-intensive environments may be more prevalent due to detection bias, but such institutions may also have more resources devoted to preventive, screening, or treatment efforts 92 . Fifth, inclusion in this meta-analysis and systematic review was limited to those based on community samples. Inclusion of clinic-based samples, or of studies conducted before or after specific milestones (e.g., the qualifying examination or dissertation prospectus defense), likely would have yielded even higher pooled prevalence estimates of mental health problems. And finally, few studies provided disaggregated data according to sociodemographic factors, stage of training (e.g., first year, pre-prospectus defense, all-but-dissertation), or discipline of study. These factors might be investigated further for differences in mental health outcomes.

Clinically significant symptoms of depression and anxiety are pervasive among graduate students in doctoral degree programs, but these are understudied relative to other trainee populations. Structural and clinical interventions to systematically monitor and promote the mental health and wellbeing of Ph.D. students are urgently needed.

This systematic review and meta-analysis follows the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) approach (Supplementary Table S3 ) 107 . This study was based on data collected from publicly available bibliometric databases and did not require ethical approval from our institutional review boards.

## Eligibility criteria

Studies were included if they provided data on either: (a) the number or proportion of Ph.D. students with clinically significant symptoms of depression or anxiety, ascertained using a validated scale; or (b) the mean depression or anxiety symptom severity score and its standard deviation among Ph.D. students. Suicidal ideation was examined as a secondary outcome.

We excluded studies that focused on graduate students in non-doctoral degree programs (e.g., Master of Public Health) or professional degree programs (e.g., Doctor of Medicine, Juris Doctor) because more is known about mental health problems in these populations 30 , 108 , 109 , 110 and because Ph.D. students face unique uncertainties. To minimize the potential for upward bias in our pooled prevalence estimates, we excluded studies that recruited students from campus counseling centers or other clinic-based settings. Studies that measured affective states, or state anxiety, before or after specific events (e.g., terrorist attacks, qualifying examinations) were also excluded.

If articles described the study sample in general terms (i.e., without clarifying the degree level of the participants), we contacted the authors by email for clarification. Similarly, if articles pooled results across graduate students in doctoral and non-doctoral degree programs (e.g., reporting a single estimate for a mixed sample of graduate students), we contacted the authors by email to request disaggregated data on the subsample of Ph.D. students. If authors did not reply after two contact attempts spaced over 2 months, or were unable to provide these data, we excluded these studies from further consideration.

## Search strategy and data extraction

PubMed, Embase, PsycINFO, ERIC, and Business Source Complete were searched from inception of each database to November 5, 2019. The search strategy included terms related to mental health symptoms (e.g., depression, anxiety, suicide), the study population (e.g., graduate, doctoral), and measurement category (e.g., depression, Columbia-Suicide Severity Rating Scale) (Supplementary Table S4 ). In addition, we searched the reference lists and the grey literature.

After duplicates were removed, we screened the remaining titles and abstracts, followed by a full-text review. We excluded articles following the eligibility criteria listed above (i.e., those that were not focused on Ph.D. students; those that did not assess depression and/or anxiety using a validated screening tool; those that did not report relevant statistics of depression and/or anxiety; and those that recruited students from clinic-based settings). Reasons for exclusion were tracked at each stage. Following selection of included articles, two members of the research team extracted data and conducted risk of bias assessments. Discrepancies were discussed with a third member of the research team. Key extraction variables included: study design, geographic region, sample size, response rate, demographic characteristics of the sample, screening instrument(s) used for assessment, mean depression or anxiety symptom severity score (and its standard deviation), and the number (or proportion) of students experiencing clinically significant symptoms of depression or anxiety.

## Risk of bias assessment

Following prior work 30 , 65 , the Newcastle–Ottawa Scale 111 was adapted and used to assess risk of bias in the included studies. Each study was assessed across 5 categories: sample representativeness, sample size, non-respondents, ascertainment of outcomes, and quality of descriptive statistics reporting (Supplementary Information S5 ). Studies were judged as having either low risk of bias (≥ 3 points) or high risk of bias (< 3 points).

## Analysis and synthesis

Before pooling the estimated prevalence rates across studies, we first transformed the proportions using a variance-stabilizing double arcsine transformation 112 . We then computed pooled estimates of prevalence using a random effects model 113 . Study specific confidence intervals were estimated using the score method 114 , 115 . We estimated between-study heterogeneity using the I 2 statistic 116 . In an attempt to reduce the extent of heterogeneity, we re-estimated pooled prevalence restricting the analysis to studies conducted in the United States and to studies in which depression assessment was based on the 9-item Patient Health Questionnaire (PHQ-9) 117 . All analyses were conducted using Stata (version 16; StataCorp LP, College Station, Tex.). Where heterogeneity limited our ability to summarize the findings using meta-analysis, we synthesized the data using narrative review.

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## Acknowledgements

We thank the following investigators for generously sharing their time and/or data: Gordon J. G. Asmundson, Ph.D., Amy J. L. Baker, Ph.D., Hillel W. Cohen, Dr.P.H., Alcir L. Dafre, Ph.D., Deborah Danoff, M.D., Daniel Eisenberg, Ph.D., Lou Farrer, Ph.D., Christy B. Fraenza, Ph.D., Patricia A. Frazier, Ph.D., Nadia Corral-Frías, Ph.D., Hanga Galfalvy, Ph.D., Edward E. Goldenberg, Ph.D., Robert K. Hindman, Ph.D., Jürgen Hoyer, Ph.D., Ayako Isato, Ph.D., Azharul Islam, Ph.D., Shanna E. Smith Jaggars, Ph.D., Bumseok Jeong, M.D., Ph.D., Ju R. Joeng, Nadine J. Kaslow, Ph.D., Rukhsana Kausar, Ph.D., Flavius R. W. Lilly, Ph.D., Sarah K. Lipson, Ph.D., Frances Meeten, D.Phil., D.Clin.Psy., Dhara T. Meghani, Ph.D., Sterett H. Mercer, Ph.D., Masaki Mori, Ph.D., Arif Musa, M.D., Shizar Nahidi, M.D., Ph.D., Arthur M. Nezu, Ph.D., D.H.L., Angelo Picardi, M.D., Nicole E. Rossi, Ph.D., Denise M. Saint Arnault, Ph.D., Sagar Sharma, Ph.D., Bryony Sheaves, D.Clin.Psy., Kennon M. Sheldon, Ph.D., Daniel Shepherd, Ph.D., Keisuke Takano, Ph.D., Sara Tement, Ph.D., Sherri Turner, Ph.D., Shawn O. Utsey, Ph.D., Ron Valle, Ph.D., Caleb Wang, B.S., Pengju Wang, Katsuyuki Yamasaki, Ph.D.

A.C.T. acknowledges funding from the Sullivan Family Foundation. This paper does not reflect an official statement or opinion from the County of San Mateo.

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## Contributions

A.C.T. conceptualized the study and provided supervision. T.K. conducted the search. E.N.S. contacted authors for additional information not reported in published articles. E.N.S. and T.K. extracted data and performed the quality assessment appraisal. E.N.S. and A.C.T. conducted the statistical analysis and drafted the manuscript. T.K., M.V.K., R.A., S.C., H.L., X.L., C.H.L., I.R., S.S., M.T. and M.Y. contributed to the interpretation of the results. All authors provided critical feedback on drafts and approved the final manuscript.

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Satinsky, E.N., Kimura, T., Kiang, M.V. et al. Systematic review and meta-analysis of depression, anxiety, and suicidal ideation among Ph.D. students. Sci Rep 11 , 14370 (2021). https://doi.org/10.1038/s41598-021-93687-7

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## Systematic review and meta-analysis of depression, anxiety, and suicidal ideation among Ph.D. students

Emily n. satinsky.

1 Center for Global Health, Massachusetts General Hospital, Boston, MA USA

## Tomoki Kimura

2 San Mateo County Behavioral Health and Recovery Services, San Mateo, CA USA

## Mathew V. Kiang

3 Department of Epidemiology and Population Health, Stanford University, Palo Alto, CA USA

4 Center for Population Health Sciences, Stanford University School of Medicine, Palo Alto, CA USA

## Rediet Abebe

5 Harvard Society of Fellows, Harvard University, Cambridge, MA USA

6 Department of Electrical Engineering and Computer Science, University of California Berkeley, Berkeley, CA USA

## Scott Cunningham

7 Department of Economics, Hankamer School of Business, Baylor University, Waco, TX USA

8 Department of Sociology, Washington University in St. Louis, St. Louis, MO USA

## Xiaofei Lin

9 Department of Microbiology, Immunology, and Molecular Genetics, Institute for Quantitative and Computational Biosciences, University of California Los Angeles, Los Angeles, CA USA

## Cindy H. Liu

10 Departments of Newborn Medicine and Psychiatry, Brigham and Women’s Hospital, Boston, MA USA

11 Harvard Medical School, Boston, MA USA

12 Centre for Global Health, Edinburgh Medical School, Usher Institute, University of Edinburgh, Edinburgh, Scotland, UK

13 Department of Psychiatry, University of Michigan, Ann Arbor, MI USA

## Mark Tomlinson

14 Department of Global Health, Institute for Life Course Health Research, Stellenbosch University, Cape Town, South Africa

15 School of Nursing and Midwifery, Queens University, Belfast, UK

## Miranda Yaver

16 Fielding School of Public Health, Los Angeles Area Health Services Research Training Program, University of California Los Angeles, Los Angeles, CA USA

## Alexander C. Tsai

17 Mongan Institute, Massachusetts General Hospital, Boston, MA USA

## Associated Data

University administrators and mental health clinicians have raised concerns about depression and anxiety among Ph.D. students, yet no study has systematically synthesized the available evidence in this area. After searching the literature for studies reporting on depression, anxiety, and/or suicidal ideation among Ph.D. students, we included 32 articles. Among 16 studies reporting the prevalence of clinically significant symptoms of depression across 23,469 Ph.D. students, the pooled estimate of the proportion of students with depression was 0.24 (95% confidence interval [CI], 0.18–0.31; I 2 = 98.75%). In a meta-analysis of the nine studies reporting the prevalence of clinically significant symptoms of anxiety across 15,626 students, the estimated proportion of students with anxiety was 0.17 (95% CI, 0.12–0.23; I 2 = 98.05%). We conclude that depression and anxiety are highly prevalent among Ph.D. students. Data limitations precluded our ability to obtain a pooled estimate of suicidal ideation prevalence. Programs that systematically monitor and promote the mental health of Ph.D. students are urgently needed.

## Introduction

Mental health problems among graduate students in doctoral degree programs have received increasing attention 1 – 4 . Ph.D. students (and students completing equivalent degrees, such as the Sc.D.) face training periods of unpredictable duration, financial insecurity and food insecurity, competitive markets for tenure-track positions, and unsparing publishing and funding models 5 – 12 —all of which may have greater adverse impacts on students from marginalized and underrepresented populations 13 – 15 . Ph.D. students’ mental health problems may negatively affect their physical health 16 , interpersonal relationships 17 , academic output, and work performance 18 , 19 , and may also contribute to program attrition 20 – 22 . As many as 30 to 50% of Ph.D. students drop out of their programs, depending on the country and discipline 23 – 27 . Further, while mental health problems among Ph.D. students raise concerns for the wellbeing of the individuals themselves and their personal networks, they also have broader repercussions for their institutions and academia as a whole 22 .

Despite the potential public health significance of this problem, most evidence syntheses on student mental health have focused on undergraduate students 28 , 29 or graduate students in professional degree programs (e.g., medical students) 30 . In non-systematic summaries, estimates of the prevalence of clinically significant depressive symptoms among Ph.D. students vary considerably 31 – 33 . Reliable estimates of depression and other mental health problems among Ph.D. students are needed to inform preventive, screening, or treatment efforts. To address this gap in the literature, we conducted a systematic review and meta-analysis to explore patterns of depression, anxiety, and suicidal ideation among Ph.D. students.

The evidence search yielded 886 articles, of which 286 were excluded as duplicates (Fig. 1 ). An additional nine articles were identified through reference lists or grey literature reports published on university websites. Following a title/abstract review and subsequent full-text review, 520 additional articles were excluded.

Flowchart of included articles.

Of the 89 remaining articles, 74 were unclear about their definition of graduate students or grouped Ph.D. and non-Ph.D. students without disaggregating the estimates by degree level. We obtained contact information for the authors of most of these articles (69 [93%]), requesting additional data. Three authors clarified that their study samples only included Ph.D. students 34 – 36 . Fourteen authors confirmed that their study samples included both Ph.D. and non-Ph.D. students but provided us with data on the subsample of Ph.D. students 37 – 50 . Where authors clarified that the sample was limited to graduate students in non-doctoral degree programs, did not provide additional data on the subsample of Ph.D. students, or did not reply to our information requests, we excluded the studies due to insufficient information (Supplementary Table S1 ).

Ultimately, 32 articles describing the findings of 29 unique studies were identified and included in the review 16 , 32 – 48 , 50 – 62 (Table (Table1). 1 ). Overall, 26 studies measured depression, 19 studies measured anxiety, and six studies measured suicidal ideation. Three pairs of articles reported data on the same sample of Ph.D. students 33 , 38 , 45 , 51 , 53 , 56 and were therefore grouped in Table Table1 1 and reported as three studies. Publication dates ranged from 1979 to 2019, but most articles (22/32 [69%]) were published after 2015. Most studies were conducted in the United States (20/29 [69%]), with additional studies conducted in Australia, Belgium, China, Iran, Mexico, and South Korea. Two studies were conducted in cross-national settings representing 48 additional countries. None were conducted in sub-Saharan Africa or South America. Most studies included students completing their degrees in a mix of disciplines (17/29 [59%]), while 12 studies were limited to students in a specific field (e.g., biomedicine, education). The median sample size was 172 students (interquartile range [IQR], 68–654; range, 6–6405). Seven studies focused on mental health outcomes in demographic subgroups, including ethnic or racialized minority students 37 , 41 , 43 , international students 47 , 50 , and sexual and gender minority students 42 , 54 .

Summary of included articles.

Beck Depression Inventory (BDI), Brief Symptom Inventory (BSI), Center for Epidemiologic Studies–Depression (CES-D), Center for Epidemiologic Studies–Depression–Revised (CES-D-R), Depression Anxiety and Stress Subscales (DASS), Diagnostic and Statistical Manual (DSM), Generalized Anxiety Disorder (GAD), General Health Questionnaire (GHQ), Inventory of Depression and Anxiety Symptoms–Second Version (IDAS-II), Mood and Anxiety Symptom Questionnaire–Short Form (MASQ-SF), National Comorbidity Survey Replication, (NCS-R), Patient Health Questionnaire (PHQ), Suicide Behaviors Questionnaire-Revised (SBQR), State-Trait Anxiety Inventory (STAI), standard deviation (SD), Structured Clinical Interview for DSM-5 Axis I Disorders Research Version (SCID-5-RV).

*Author provided clarification—entire sample consisted of doctoral degree students.

**Author provided additional data—doctoral students reflect a subsample of the total number reported in the published article.

In all, 16 studies reported the prevalence of depression among a total of 23,469 Ph.D. students (Fig. 2 ; range, 10–47%). Of these, the most widely used depression scales were the PHQ-9 (9 studies) and variants of the Center for Epidemiologic Studies-Depression scale (CES-D, 4 studies) 63 , and all studies assessed clinically significant symptoms of depression over the past one to two weeks. Three of these studies reported findings based on data from different survey years of the same parent study (the Healthy Minds Study) 40 , 42 , 43 , but due to overlap in the survey years reported across articles, these data were pooled. Most of these studies were based on data collected through online surveys (13/16 [81%]). Ten studies (63%) used random or systematic sampling, four studies (25%) used convenience sampling, and two studies (13%) used multiple sampling techniques.

Pooled estimate of the proportion of Ph.D. students with clinically significant symptoms of depression.

The estimated proportion of Ph.D. students assessed as having clinically significant symptoms of depression was 0.24 (95% confidence interval [CI], 0.18–0.31; 95% predictive interval [PI], 0.04–0.54), with significant evidence of between-study heterogeneity (I 2 = 98.75%). A subgroup analysis restricted to the twelve studies conducted in the United States yielded similar findings (pooled estimate [ES] = 0.23; 95% CI, 0.15–0.32; 95% PI, 0.01–0.60), with no appreciable difference in heterogeneity (I 2 = 98.91%). A subgroup analysis restricted to the studies that used the PHQ-9 to assess depression yielded a slightly lower prevalence estimate and a slight reduction in heterogeneity (ES = 0.18; 95% CI, 0.14–0.22; 95% PI, 0.07–0.34; I 2 = 90.59%).

Nine studies reported the prevalence of clinically significant symptoms of anxiety among a total of 15,626 Ph.D. students (Fig. 3 ; range 4–49%). Of these, the most widely used anxiety scale was the 7-item Generalized Anxiety Disorder scale (GAD-7, 5 studies) 64 . Data from three of the Healthy Minds Study articles were pooled into two estimates, because the scale used to measure anxiety changed midway through the parent study (i.e., the Patient Health Questionnaire-Generalized Anxiety Disorder [PHQ-GAD] scale was used from 2007 to 2012 and then switched to the GAD-7 in 2013 40 ). Most studies (8/9 [89%]) assessed clinically significant symptoms of anxiety over the past two to four weeks, with the one remaining study measuring anxiety over the past year. Again, most of these studies were based on data collected through online surveys (7/9 [78%]). Five studies (56%) used random or systematic sampling, two studies (22%) used convenience sampling, and two studies (22%) used multiple sampling techniques.

Pooled estimate of the proportion of Ph.D. students with clinically significant symptoms of anxiety.

The estimated proportion of Ph.D. students assessed as having anxiety was 0.17 (95% CI, 0.12–0.23; 95% PI, 0.02–0.41), with significant evidence of between-study heterogeneity (I 2 = 98.05%). The subgroup analysis restricted to the five studies conducted in the United States yielded a slightly lower proportion of students assessed as having anxiety (ES = 0.14; 95% CI, 0.08–0.20; 95% PI, 0.00–0.43), with no appreciable difference in heterogeneity (I 2 = 98.54%).

Six studies reported the prevalence of suicidal ideation (range, 2–12%), but the recall windows varied greatly (e.g., ideation within the past 2 weeks vs. past year), precluding pooled estimation.

Additional stratified pooled estimates could not be obtained. One study of Ph.D. students across 54 countries found that phase of study was a significant moderator of mental health, with students in the comprehensive examination and dissertation phases more likely to experience distress compared with students primarily engaged in coursework 59 . Other studies identified a higher prevalence of mental ill-health among women 54 ; lesbian, gay, bisexual, transgender, and queer (LGBTQ) students 42 , 54 , 60 ; and students with multiple intersecting identities 54 .

Several studies identified correlates of mental health problems including: project- and supervisor-related issues, stress about productivity, and self-doubt 53 , 62 ; uncertain career prospects, poor living conditions, financial stressors, lack of sleep, feeling devalued, social isolation, and advisor relationships 61 ; financial challenges 38 ; difficulties with work-life balance 58 ; and feelings of isolation and loneliness 52 . Despite these challenges, help-seeking appeared to be limited, with only about one-quarter of Ph.D. students reporting mental health problems also reporting that they were receiving treatment 40 , 52 .

## Risk of bias

Twenty-one of 32 articles were assessed as having low risk of bias (Supplementary Table S2 ). Five articles received one point for all five categories on the risk of bias assessment (lowest risk of bias), and one article received no points (highest risk). The mean risk of bias score was 3.22 (standard deviation, 1.34; median, 4; IQR, 2–4). Restricting the estimation sample to 12 studies assessed as having low risk of bias, the estimated proportion of Ph.D. students with depression was 0.25 (95% CI, 0.18–0.33; 95% PI, 0.04–0.57; I 2 = 99.11%), nearly identical to the primary estimate, with no reduction in heterogeneity. The estimated proportion of Ph.D. students with anxiety, among the 7 studies assessed as having low risk of bias, was 0.12 (95% CI, 0.07–0.17; 95% PI, 0.01–0.34; I 2 = 98.17%), again with no appreciable reduction in heterogeneity.

In our meta-analysis of 16 studies representing 23,469 Ph.D. students, we estimated that the pooled prevalence of clinically significant symptoms of depression was 24%. This estimate is consistent with estimated prevalence rates in other high-stress biomedical trainee populations, including medical students (27%) 30 , resident physicians (29%) 65 , and postdoctoral research fellows (29%) 66 . In the sample of nine studies representing 15,626 Ph.D. students, we estimated that the pooled prevalence of clinically significant symptoms of anxiety was 17%. While validated screening instruments tend to over-identify cases of depression (relative to structured clinical interviews) by approximately a factor of two 67 , 68 , our findings nonetheless point to a major public health problem among Ph.D. students. Available data suggest that the prevalence of depressive and anxiety disorders in the general population ranges from 5 to 7% worldwide 69 , 70 . In contrast, prevalence estimates of major depressive disorder among young adults have ranged from 13% (for young adults between the ages of 18 and 29 years in the 2012–2013 National Epidemiologic Survey on Alcohol and Related Conditions III 71 ) to 15% (for young adults between the ages of 18 and 25 in the 2019 U.S. National Survey on Drug Use and Health 72 ). Likewise, the prevalence of generalized anxiety disorder was estimated at 4% among young adults between the ages of 18 and 29 in the 2001–03 U.S. National Comorbidity Survey Replication 73 . Thus, even accounting for potential upward bias inherent in these studies’ use of screening instruments, our estimates suggest that the rates of recent clinically significant symptoms of depression and anxiety are greater among Ph.D. students compared with young adults in the general population.

Further underscoring the importance of this public health issue, Ph.D. students face unique stressors and uncertainties that may put them at increased risk for mental health and substance use problems. Students grapple with competing responsibilities, including coursework, teaching, and research, while also managing interpersonal relationships, social isolation, caregiving, and financial insecurity 3 , 10 . Increasing enrollment in doctoral degree programs has not been matched with a commensurate increase in tenure-track academic job opportunities, intensifying competition and pressure to find employment post-graduation 5 . Advisor-student power relations rarely offer options for recourse if and when such relationships become strained, particularly in the setting of sexual harassment, unwanted sexual attention, sexual coercion, and rape 74 – 78 . All of these stressors may be magnified—and compounded by stressors unrelated to graduate school—for subgroups of students who are underrepresented in doctoral degree programs and among whom mental health problems are either more prevalent and/or undertreated compared with the general population, including Black, indigenous, and other people of color 13 , 79 , 80 ; women 81 , 82 ; first-generation students 14 , 15 ; people who identify as LGBTQ 83 – 85 ; people with disabilities; and people with multiple intersecting identities.

Structural- and individual-level interventions will be needed to reduce the burden of mental ill-health among Ph.D. students worldwide 31 , 86 . Despite the high prevalence of mental health and substance use problems 87 , Ph.D. students demonstrate low rates of help-seeking 40 , 52 , 88 . Common barriers to help-seeking include fears of harming one’s academic career, financial insecurity, lack of time, and lack of awareness 89 – 91 , as well as health care systems-related barriers, including insufficient numbers of culturally competent counseling staff, limited access to psychological services beyond time-limited psychotherapies, and lack of programs that address the specific needs either of Ph.D. students in general 92 or of Ph.D. students belonging to marginalized groups 93 , 94 . Structural interventions focused solely on enhancing student resilience might include programs aimed at reducing stigma, fostering social cohesion, and reducing social isolation, while changing norms around help-seeking behavior 95 , 96 . However, structural interventions focused on changing stressogenic aspects of the graduate student environment itself are also needed 97 , beyond any enhancements to Ph.D. student resilience, including: undercutting power differentials between graduate students and individual faculty advisors, e.g., by diffusing power among multiple faculty advisors; eliminating racist, sexist, and other discriminatory behaviors by faculty advisors 74 , 75 , 98 ; valuing mentorship and other aspects of “invisible work” that are often disproportionately borne by women faculty and faculty of color 99 , 100 ; and training faculty members to emphasize the dignity of, and adequately prepare Ph.D. students for, non-academic careers 101 , 102 .

Our findings should be interpreted with several limitations in mind. First, the pooled estimates are characterized by a high degree of heterogeneity, similar to meta-analyses of depression prevalence in other populations 30 , 65 , 103 – 105 . Second, we were only able to aggregate depression prevalence across 16 studies and anxiety prevalence across nine studies (the majority of which were conducted in the U.S.) – far fewer than the 183 studies included in a meta-analysis of depression prevalence among medical students 30 and the 54 studies included in a meta-analysis of resident physicians 65 . These differences underscore the need for more rigorous study in this critical area. Many articles were either excluded from the review or from the meta-analyses for not meeting inclusion criteria or not reporting relevant statistics. Future research in this area should ensure the systematic collection of high-quality, clinically relevant data from a comprehensive set of institutions, across disciplines and countries, and disaggregated by graduate student type. As part of conducting research and addressing student mental health and wellbeing, university deans, provosts, and chancellors should partner with national survey and program institutions (e.g., Graduate Student Experience in the Research University [gradSERU] 106 , the American College Health Association National College Health Assessment [ACHA-NCHA], and HealthyMinds). Furthermore, federal agencies that oversee health and higher education should provide resources for these efforts, and accreditation agencies should require monitoring of mental health and programmatic responses to stressors among Ph.D. students.

Third, heterogeneity in reporting precluded a meta-analysis of the suicidality outcomes among the few studies that reported such data. While reducing the burden of mental health problems among graduate students is an important public health aim in itself, more research into understanding non-suicidal self-injurious behavior, suicide attempts, and completed suicide among Ph.D. students is warranted. Fourth, it is possible that the grey literature reports included in our meta-analysis are more likely to be undertaken at research-intensive institutions 52 , 60 , 61 . However, the direction of bias is unpredictable: mental health problems among Ph.D. students in research-intensive environments may be more prevalent due to detection bias, but such institutions may also have more resources devoted to preventive, screening, or treatment efforts 92 . Fifth, inclusion in this meta-analysis and systematic review was limited to those based on community samples. Inclusion of clinic-based samples, or of studies conducted before or after specific milestones (e.g., the qualifying examination or dissertation prospectus defense), likely would have yielded even higher pooled prevalence estimates of mental health problems. And finally, few studies provided disaggregated data according to sociodemographic factors, stage of training (e.g., first year, pre-prospectus defense, all-but-dissertation), or discipline of study. These factors might be investigated further for differences in mental health outcomes.

Clinically significant symptoms of depression and anxiety are pervasive among graduate students in doctoral degree programs, but these are understudied relative to other trainee populations. Structural and clinical interventions to systematically monitor and promote the mental health and wellbeing of Ph.D. students are urgently needed.

This systematic review and meta-analysis follows the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) approach (Supplementary Table S3 ) 107 . This study was based on data collected from publicly available bibliometric databases and did not require ethical approval from our institutional review boards.

## Eligibility criteria

Studies were included if they provided data on either: (a) the number or proportion of Ph.D. students with clinically significant symptoms of depression or anxiety, ascertained using a validated scale; or (b) the mean depression or anxiety symptom severity score and its standard deviation among Ph.D. students. Suicidal ideation was examined as a secondary outcome.

We excluded studies that focused on graduate students in non-doctoral degree programs (e.g., Master of Public Health) or professional degree programs (e.g., Doctor of Medicine, Juris Doctor) because more is known about mental health problems in these populations 30 , 108 – 110 and because Ph.D. students face unique uncertainties. To minimize the potential for upward bias in our pooled prevalence estimates, we excluded studies that recruited students from campus counseling centers or other clinic-based settings. Studies that measured affective states, or state anxiety, before or after specific events (e.g., terrorist attacks, qualifying examinations) were also excluded.

If articles described the study sample in general terms (i.e., without clarifying the degree level of the participants), we contacted the authors by email for clarification. Similarly, if articles pooled results across graduate students in doctoral and non-doctoral degree programs (e.g., reporting a single estimate for a mixed sample of graduate students), we contacted the authors by email to request disaggregated data on the subsample of Ph.D. students. If authors did not reply after two contact attempts spaced over 2 months, or were unable to provide these data, we excluded these studies from further consideration.

## Search strategy and data extraction

PubMed, Embase, PsycINFO, ERIC, and Business Source Complete were searched from inception of each database to November 5, 2019. The search strategy included terms related to mental health symptoms (e.g., depression, anxiety, suicide), the study population (e.g., graduate, doctoral), and measurement category (e.g., depression, Columbia-Suicide Severity Rating Scale) (Supplementary Table S4 ). In addition, we searched the reference lists and the grey literature.

After duplicates were removed, we screened the remaining titles and abstracts, followed by a full-text review. We excluded articles following the eligibility criteria listed above (i.e., those that were not focused on Ph.D. students; those that did not assess depression and/or anxiety using a validated screening tool; those that did not report relevant statistics of depression and/or anxiety; and those that recruited students from clinic-based settings). Reasons for exclusion were tracked at each stage. Following selection of included articles, two members of the research team extracted data and conducted risk of bias assessments. Discrepancies were discussed with a third member of the research team. Key extraction variables included: study design, geographic region, sample size, response rate, demographic characteristics of the sample, screening instrument(s) used for assessment, mean depression or anxiety symptom severity score (and its standard deviation), and the number (or proportion) of students experiencing clinically significant symptoms of depression or anxiety.

## Risk of bias assessment

Following prior work 30 , 65 , the Newcastle–Ottawa Scale 111 was adapted and used to assess risk of bias in the included studies. Each study was assessed across 5 categories: sample representativeness, sample size, non-respondents, ascertainment of outcomes, and quality of descriptive statistics reporting (Supplementary Information S5 ). Studies were judged as having either low risk of bias (≥ 3 points) or high risk of bias (< 3 points).

## Analysis and synthesis

Before pooling the estimated prevalence rates across studies, we first transformed the proportions using a variance-stabilizing double arcsine transformation 112 . We then computed pooled estimates of prevalence using a random effects model 113 . Study specific confidence intervals were estimated using the score method 114 , 115 . We estimated between-study heterogeneity using the I 2 statistic 116 . In an attempt to reduce the extent of heterogeneity, we re-estimated pooled prevalence restricting the analysis to studies conducted in the United States and to studies in which depression assessment was based on the 9-item Patient Health Questionnaire (PHQ-9) 117 . All analyses were conducted using Stata (version 16; StataCorp LP, College Station, Tex.). Where heterogeneity limited our ability to summarize the findings using meta-analysis, we synthesized the data using narrative review.

## Supplementary Information

Acknowledgements.

We thank the following investigators for generously sharing their time and/or data: Gordon J. G. Asmundson, Ph.D., Amy J. L. Baker, Ph.D., Hillel W. Cohen, Dr.P.H., Alcir L. Dafre, Ph.D., Deborah Danoff, M.D., Daniel Eisenberg, Ph.D., Lou Farrer, Ph.D., Christy B. Fraenza, Ph.D., Patricia A. Frazier, Ph.D., Nadia Corral-Frías, Ph.D., Hanga Galfalvy, Ph.D., Edward E. Goldenberg, Ph.D., Robert K. Hindman, Ph.D., Jürgen Hoyer, Ph.D., Ayako Isato, Ph.D., Azharul Islam, Ph.D., Shanna E. Smith Jaggars, Ph.D., Bumseok Jeong, M.D., Ph.D., Ju R. Joeng, Nadine J. Kaslow, Ph.D., Rukhsana Kausar, Ph.D., Flavius R. W. Lilly, Ph.D., Sarah K. Lipson, Ph.D., Frances Meeten, D.Phil., D.Clin.Psy., Dhara T. Meghani, Ph.D., Sterett H. Mercer, Ph.D., Masaki Mori, Ph.D., Arif Musa, M.D., Shizar Nahidi, M.D., Ph.D., Arthur M. Nezu, Ph.D., D.H.L., Angelo Picardi, M.D., Nicole E. Rossi, Ph.D., Denise M. Saint Arnault, Ph.D., Sagar Sharma, Ph.D., Bryony Sheaves, D.Clin.Psy., Kennon M. Sheldon, Ph.D., Daniel Shepherd, Ph.D., Keisuke Takano, Ph.D., Sara Tement, Ph.D., Sherri Turner, Ph.D., Shawn O. Utsey, Ph.D., Ron Valle, Ph.D., Caleb Wang, B.S., Pengju Wang, Katsuyuki Yamasaki, Ph.D.

## Author contributions

A.C.T. conceptualized the study and provided supervision. T.K. conducted the search. E.N.S. contacted authors for additional information not reported in published articles. E.N.S. and T.K. extracted data and performed the quality assessment appraisal. E.N.S. and A.C.T. conducted the statistical analysis and drafted the manuscript. T.K., M.V.K., R.A., S.C., H.L., X.L., C.H.L., I.R., S.S., M.T. and M.Y. contributed to the interpretation of the results. All authors provided critical feedback on drafts and approved the final manuscript.

A.C.T. acknowledges funding from the Sullivan Family Foundation. This paper does not reflect an official statement or opinion from the County of San Mateo.

## Competing interests

The authors declare no competing interests.

Publisher's note

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## Contributor Information

Emily N. Satinsky, Email: ude.csu@yksnitas .

Alexander C. Tsai, Email: gro.srentrap@iastca .

The online version contains supplementary material available at 10.1038/s41598-021-93687-7.

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