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9781119558354

Introduction to Meta-Analysis

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  • ISBN13:

    9781119558354

  • ISBN10:

    1119558352

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2021-04-19
  • Publisher: Wiley
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Summary

A clear and thorough introduction to meta-analysis, the process of synthesizing data from a series of separate studies

The first edition of this text was widely acclaimed for the clarity of the presentation, and quickly established itself as the definitive text in this field. The fully updated second edition includes new and expanded content on avoiding common mistakes in meta-analysis, understanding heterogeneity in effects, publication bias, and more. Several brand-new chapters provide a systematic "how to" approach to performing and reporting a meta-analysis from start to finish.

Written by four of the world's foremost authorities on all aspects of meta-analysis, the new edition:

  • Outlines the role of meta-analysis in the research process
  • Shows how to compute effects sizes and treatment effects
  • Explains the fixed-effect and random-effects models for synthesizing data
  • Demonstrates how to assess and interpret variation in effect size across studies
  • Explains how to avoid common mistakes in meta-analysis
  • Discusses controversies in meta-analysis
  • Includes access to a companion website containing videos, spreadsheets, data files, free software for prediction intervals, and step-by-step instructions for performing analyses using Comprehensive Meta-Analysis (CMA)

Download videos, class materials, and worked examples at www.Introduction-to-Meta-Analysis.com

"This book offers the reader a unified framework for thinking about meta-analysis, and then discusses all elements of the analysis within that framework. The authors address a series of common mistakes and explain how to avoid them. As the editor-in-chief of the American Psychologist and former editor of Psychological Bulletin, I can say without hesitation that the quality of manuscript submissions reporting meta-analyses would be vastly better if researchers read this book."
Harris Cooper, Hugo L. Blomquist Distinguished Professor Emeritus of Psychology and Neuroscience, Editor-in-chief of the American Psychologist, former editor of Psychological Bulletin

"A superb combination of lucid prose and informative graphics, the authors provide a refreshing departure from cookbook approaches with their clear explanations of the what and why of meta-analysis. The book is ideal as a course textbook or for self-study. My students raved about the clarity of the explanations and examples."
David Rindskopf, Distinguished Professor of Educational Psychology, City University of New York, Graduate School and University Center, & Editor of the Journal of Educational and Behavioral Statistics

"The approach taken by Introduction to Meta-analysis is intended to be primarily conceptual, and it is amazingly successful at achieving that goal. The reader can comfortably skip the formulas and still understand their application and underlying motivation. For the more statistically sophisticated reader, the relevant formulas and worked examples provide a superb practical guide to performing a meta-analysis. The book provides an eclectic mix of examples from education, social science, biomedical studies, and even ecology. For anyone considering leading a course in meta-analysis, or pursuing self-directed study, Introduction to Meta-analysis would be a clear first choice."
Jesse A. Berlin, ScD

Author Biography

Michael Borenstein is the Director of Biostat, a leading developer of statistical software. He is the primary developer of Comprehensive Meta-Analysis (CMA), the world's most widely used program for meta-analysis.  He is the recipient of numerous grants from the NIH to develop methods, software, and educational materials for meta-analysis. He has lectured widely on meta-analysis, including at the NIH, CDC, and FDA. 

Larry V. Hedges is Board of Trustees Professor of Statistics and Education and Social Policy, Professor of Psychology, Professor of Medical Social Sciences, and IPR Fellow, Northwestern University, USA. He is a national leader in the fields of educational statistics and evaluation and is an elected member of many leading associations. 

Julian P.T. Higgins is Professor of Evidence Synthesis at the University of Bristol, UK, and a National Institute for Health Research (NIHR) Senior Investigator. He has had numerous core roles in the Cochrane Collaboration, including editing its methodological Handbook since 2003. His many contributions to meta-analysis include the foundation of network meta-analysis, methods for describing and explaining heterogeneity and a general framework for individual participant data meta-analysis. He is a Highly Cited Researcher with over a quarter of a million citations to his work and has been a recipient of the Ingram Olkin Award for distinguished lifetime achievement in research synthesis methodology. 

Hannah R. Rothstein is Professor of Management at Baruch College and the Graduate Center of the City University of New York. She is a Fellow of the American Psychological Association and a past President of the Society for Research Synthesis Methodology. She is former Editor-in-Chief of Research Synthesis Methods and serves on the editorial boards of Psychological Bulletin, Psychological Methods, and Organizational Research Methods. Professor Rothstein is a co-developer of the Comprehensive Meta-Analysis software and has published numerous systematic reviews and meta-analyses. 

Table of Contents

List of Tables xv

List of Figures xix

Acknowledgements xxv

Preface xxvii

Preface to the Second Edition xxxv

Website xxxvii

Part 1: Introduction

1 How a Meta-Analysis Works 3

Introduction 3

Individual studies 3

The summary effect 5

Heterogeneity of effect sizes 6

Summary points 7

2 Why Perform a Meta-Analysis 9

Introduction 9

The streptokinase meta-analysis 10

Statistical significance 11

Clinical importance of the effect 11

Consistency of effects 12

Summary points 13

Part 2: Effect Size and Precision

3 Overview 17

Treatment effects and effect sizes 17

Parameters and estimates 18

Outline of effect size computations 19

4 Effect Sizes Based On Means 21

Introduction 21

Raw (unstandardized) mean difference D 21

Standardized mean difference, d and g 25

Response ratios 30

Summary points 31

5 Effect Sizes Based On Binary Data (2 × 2 Tables) 33

Introduction 33

Risk ratio 33

Odds ratio 35

Risk difference 37

Choosing an effect size index 38

Summary points 38

6 Effect Sizes Based On Correlations 39

Introduction 39

Computing r 39

Other approaches 40

Summary points 41

7 Converting Among Effect Sizes 43

Introduction 43

Converting from the log odds ratio to d 44

Converting from d to the log odds ratio 45

Converting from r to d 45

Converting from d to r 46

Summary points 47

8 Factors That Affect Precision 49

Introduction 49

Factors that affect precision 50

Sample size 50

Study design 51

Summary points 53

9 Concluding Remarks 55

Part 3: Fixed-Effect Versus Random-Effects Models

10 Overview 59

Introduction 59

Nomenclature 60

11 Fixed-Effect Model 61

Introduction 61

The true effect size 61

Impact of sampling error 61

Performing a fixed-effect meta-analysis 63

Summary points 64

12 Random-Effects Model 65

Introduction 65

The true effect sizes 65

Impact of sampling error 66

Performing a random-effects meta-analysis 68

Summary points 70

13 Fixed-Effect Versus Random-Effects Models 71

Introduction 71

Definition of a summary effect 71

Estimating the summary effect 72

Extreme effect size in a large study or a small study 73

Confidence interval 73

The null hypothesis 76

Which model should we use? 76

Model should not be based on the test for heterogeneity 78

Concluding remarks 79

Summary points 79

14 Worked Examples (Part 1) 81

Introduction 81

Worked example for continuous data (Part 1) 81

Worked example for binary data (Part 1) 85

Worked example for correlational data (Part 1) 90

Summary points 94

Part 4: Heterogeneity

15 Overview 97

Introduction 97

Nomenclature 98

Worked examples 98

16 Identifying and Quantifying Heterogeneity 99

Introduction 99

Isolating the variation in true effects 99

Computing Q 101

Estimating 𝜏2 106

The I2 statistic 109

Comparing the measures of heterogeneity 111

Confidence intervals for 𝜏2 114

Confidence intervals (or uncertainty intervals) for I2 115

Summary points 116

17 Prediction Intervals 119

Introduction 119

Prediction intervals in primary studies 119

Prediction intervals in meta-analysis 121

Confidence intervals and prediction intervals 123

Comparing the confidence interval with the prediction interval 123

Summary points 125

18 Worked Examples (Part 2) 127

Introduction 127

Worked example for continuous data (Part 2) 127

Worked example for binary data (Part 2) 131

Worked example for correlational data (Part 2) 134

Summary points 138

19 An Intuitive Look At Heterogeneity 139

Introduction 139

Motivating example 140

The Q-value and the p-value do not tell us howmuch the effect size varies 141

The confidence interval does not tell us how much the effect size varies 142

The I2 statistic does not tell us how much the effect size varies 142

What I2 tells us 142

The I2 index vs. the prediction interval 145

The prediction interval 145

Prediction interval is clear, concise, and relevant 147

Computing the prediction interval 147

How to use I2 149

How to explain heterogeneity 149

How much does the effect size vary across studies? 150

Caveats 150

Conclusion 150

Further reading 151

Summary points 151

The meaning of I2 in Figure 19.2 151

20 Classifying Heterogeneity As Low, Moderate, Or High 155

Introduction 155

Interest should generally focus on an index of absolute heterogeneity 155

The classifications lead themselves to mistakes of interpretation 158

Classifications focus attention in the wrong direction 158

Summary points 158

Part 5: Explaining Heterogeneity

21 Subgroup Analyses 161

Introduction 161

Fixed-effect model within subgroups 163

Computational models 172

Random effects with separate estimates of 𝜏2 174

Random effects with pooled estimate of 𝜏2 181

The proportion of variance explained 189

Mixed-effects model 192

Obtaining an overall effect in the presence of subgroups 193

Summary points 195

22 Meta-Regression 197

Introduction 197

Fixed-effect model 198

Fixed or random effects for unexplained heterogeneity 203

Random-effects model 206

Summary points 212

23 Notes On Subgroup Analyses and Meta-Regression 213

Introduction 213

Computational model 213

Multiple comparisons 216

Software 216

Analyses of subgroups and regression analyses are observational 217

Statistical power for subgroup analyses and meta-regression 218

Summary points 219

Part 6: Putting It All In Context

24 Looking At the Whole Picture 223

Introduction 223

Methylphenidate for adults with ADHD 226

Impact of GLP-1 mimetics on blood pressure 228

Augmenting clozapine with a second antipsychotic 228

Conclusions 231

Caveats 231

Summary points 232

25 Limitations of the Random-Effects Model 233

Introduction 233

Assumptions of the random-effects model 234

A textbook case 234

When studies are pulled from the literature 235

A useful fiction 237

Transparency 238

A narrowly defined universe 238

Two important caveats 239

In context 239

Extreme cases 240

Summary points 241

26 Knapp–Hartung Adjustment 243

Introduction 243

Adjustment is rarely employed in simple analyses 243

Adjusting the standard error 244

The Knapp–Hartung adjustment for other effect size indices 246

t distribution vs. Z distribution 247

Limitations of the Knapp–Hartung adjustment 248

Summary points 249

Part 7: Complex Data Structures

27 Overview 253

28 Independent Subgroups Within a Study 255

Introduction 255

Combining across subgroups 255

Comparing subgroups 260

Summary points 260

29 Multiple Outcomes or Time-Points Within A Study 263

Introduction 263

Combining across outcomes or time-points 264

Comparing outcomes or time-points within a study 270

Summary points 275

30 Multiple Comparisons Within a Study 277

Introduction 277

Combining across multiple comparisons within a study 277

Differences between treatments 278

Summary points 279

31 Notes On Complex Data Structures 281

Introduction 281

Summary effect 281

Differences in effect 282

Part 8: Other Issues

32 Overview 287

33 Vote Counting – A New Name For An Old Problem 289

Introduction 289

Why vote counting is wrong 290

Vote counting is a pervasive problem 291

Summary points 293

34 Power Analysis For Meta-Analysis 295

Introduction 295

A conceptual approach 295

In context 299

When to use power analysis 300

Planning for precision rather than for power 301

Power analysis in primary studies 301

Power analysis for meta-analysis 304

Power analysis for a test of homogeneity 309

Summary points 312

35 Publication Bias 313

Introduction 313

The problem of missing studies 314

Methods for addressing bias 316

Illustrative example 317

The model 317

Getting a sense of the data 318

Is there evidence of any bias? 320

How much of an impact might the bias have? 320

Summary of the findings for the illustrative example 324

Conflating bias with the small-study effect 325

Using logic to disentangle bias from small-study effects 326

These methods do not give us the ‘correct’ effect size 327

Some important caveats 327

Procedures do not apply to studies of prevalence 328

The model for publication bias is simplistic 328

Concluding remarks 329

Putting it all together 330

Summary points 330

Part 9: Issues Related To Effect Size

36 Overview 335

37 Effect Sizes Rather Than P-Values 337

Introduction 337

Relationship between p-values and effect sizes 337

The distinction is important 339

The p-value is often misinterpreted 340

Narrative reviews vs. meta-analyses 341

Summary points 342

38 Simpson’s Paradox 343

Introduction 343

Circumcision and risk of HIV infection 343

An example of the paradox 345

Summary points 348

39 Generality of the Basic Inverse-Variance Method 349

Introduction 349

Other effect sizes 350

Other methods for estimating effect sizes 353

Individual participant data meta-analyses 354

Bayesian approaches 355

Summary points 357

Part 10: Further Methods

40 Overview 361

41 Meta-Analysis Methods Based On Direction and P-Values 363

Introduction 363

Vote counting 363

The sign test 363

Combining p-values 364

Summary points 368

42 Further Methods For Dichotomous Data 369

Introduction 369

Mantel–Haenszel method 369

One-step (Peto) formula for odds ratio 373

Summary points 376

43 Psychometric Meta-Analysis 377

Introduction 377

The attenuating effects of artifacts 378

Meta-analysis methods 380

Example of psychometric meta-analysis 381

Comparison of artifact correction with meta-regression 384

Sources of information about artifact values 384

How heterogeneity is assessed 385

Reporting in psychometric meta-analysis 386

Concluding remarks 386

Summary points 387

Part 11: Meta-Analysis In Context

44 Overview 391

45 When Does It Make Sense To Perform a Meta-Analysis? 393

Introduction 393

Are the studies similar enough to combine? 394

Can I combine studies with different designs? 395

How many studies are enough to carry out a meta-analysis? 399

Summary points 400

46 Reporting The Results of a Meta-Analysis 401

Introduction 401

The computational model 402

Forest plots 402

Sensitivity analysis 404

Summary points 405

47 Cumulative Meta-Analysis 407

Introduction 407

Why perform a cumulative meta-analysis? 409

Summary points 412

48 Criticisms of Meta-Analysis 413

Introduction 413

One number cannot summarize a research field 414

The file drawer problem invalidates meta-analysis 414

Mixing apples and oranges 415

Garbage in, garbage out 416

Important studies are ignored 417

Meta-analysis can disagree with randomized trials 417

Meta-analyses are performed poorly 420

Is a narrative review better? 420

Concluding remarks 422

Summary points 422

49 Comprehensive Meta-Analysis Software 425

Introduction 425

Features in CMA 426

Teaching elements 427

Documentation 427

Availability 427

Acknowledgments 427

Motivating example 428

Data entry 428

Basic analysis 429

What is the average effect size? 430

How much does the effect size vary? 430

Plot showing distribution of effects 431

High-resolution plot 432

Subgroup analysis 433

Meta-regression 435

Publication bias 438

Explaining results 439

50 How To Explain the Results of An Analysis 443

Introduction 443

The overview 444

The mean effect size 444

Variation in effect size 444

Notations 444

Impact of resistance exercise on pain 445

Correlation between letter knowledge and word recognition 450

Statins for prevention of cardiovascular events 455

Bupropion for smoking cessation 460

Mortality following mitral-valve procedures in elderly patients 465

Part 12: Resources

51 Software For Meta-Analysis 471

Comprehensive meta-analysis 471

Metafor 471

Stata 472

Revman 472

52 Web Sites, Societies, Journals, and Books 473

Web sites 473

Professional societies 476

Journals 476

Special issues dedicated to meta-analysis 477

Books on systematic review methods and meta-analysis 477

References 479

Index 491

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