Doing Meta-Analysis with R: A Hands-On Guide

501 Pages·2021·50.969 MB·English

by  Mathias Harrer, Pim Cuijpers, Toshi Furukawa, David Ebert

Doing Meta-Analysis
with R

Doing Meta-Analysis
with R
A Hands-On Guide
Mathias Harrer
Pim Cuijpers
Toshi A. Furukawa
David D. Ebert
First edition published 2022
by CRC Press
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© 2022 Mathias Harrer, Pim Cuijpers, Toshi A. Furukawa, David D. Ebert

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Library of Congress Cataloging-in-Publication Data
Names: Harrer, Mathias, author.
Title: Doing meta-analysis with R : a hands-on guide / Mathias Harrer [and
three others].
Description: First edition. | Boca Raton : CRC Press, 2022. | Includes
bibliographical references and index.
Identifiers: LCCN 2021017096 (print) | LCCN 2021017097 (ebook) | ISBN
9780367610074 (hardback) | ISBN 9780367619770 (paperback) | ISBN
9780367619770 (ebook)
Subjects: LCSH: Meta-analysis. | R (Computer program language)
Classification: LCC R853.M48 H37 2022 (print) | LCC R853.M48 (ebook) |
DDC 610.727--dc23
LC record available at https://lccn.loc.gov/2021017096
LC ebook record available at https://lccn.loc.gov/2021017097
ISBN: 9780367610074 (hbk)
ISBN: 9780367619770 (pbk)
ISBN: 9781003107347 (ebk)
DOI: 10.1201/9781003107347
Typeset in Alegreya
by KnowledgeWorks Global Ltd.
Theproblemsaresolved,notbygivingnewinformation,
butbyarrangingwhatwehaveknownsincelong.
–LudwigWittgenstein,PhilosophicalInvestigations

Contents
Preface xiii
AbouttheAuthors xxiii
ListofSymbols xxv
I GettingStarted 1
1 Introduction 3
1.1 WhatAreMeta-Analyses? . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 “ExercisesinMega-Silliness”:AHistoricalAnecdote . . . . . . . . . 6
1.3 ApplesandOranges:AQuickTourofMeta-AnalysisPitfalls . . . . 8
1.4 ProblemSpecification,StudySearch&Coding . . . . . . . . . . . 11
1.4.1 DefiningtheResearchQuestion . . . . . . . . . . . . . . . 12
1.4.2 AnalysisPlan&Preregistration . . . . . . . . . . . . . . . . 16
1.4.3 StudySearch . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4.4 StudySelection . . . . . . . . . . . . . . . . . . . . . . . . 21
1.4.5 DataExtraction&Coding . . . . . . . . . . . . . . . . . . . 24
1.5 Questions&Answers . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2 DiscoveringR 29
2.1 InstallingR&RStudio . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 Packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3 The{dmetar}Package . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.4 DataPreparation&Import . . . . . . . . . . . . . . . . . . . . . . 36
2.5 DataManipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.5.1 ClassConversion . . . . . . . . . . . . . . . . . . . . . . . 39
2.5.2 DataSlicing . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.5.3 DataTransformation . . . . . . . . . . . . . . . . . . . . . 44
2.5.4 SavingData . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.6 Questions&Answers . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
vii
viii Contents
II Meta-AnalysisinR 51
3 EffectSizes 53
3.1 WhatIsanEffectSize? . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2 Measures&EffectSizesinSingleGroupDesigns . . . . . . . . . . 59
3.2.1 Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2.2 Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.2.3 Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.3 EffectSizesinControlGroupDesigns . . . . . . . . . . . . . . . . 64
3.3.1 (Standardized)MeanDifferences. . . . . . . . . . . . . . . 64
3.3.2 Risk&OddsRatios . . . . . . . . . . . . . . . . . . . . . . 70
3.3.3 IncidenceRateRatios . . . . . . . . . . . . . . . . . . . . . 76
3.4 EffectSizeCorrection . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.4.1 SmallSampleBias . . . . . . . . . . . . . . . . . . . . . . . 80
3.4.2 Unreliability . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.4.3 RangeRestriction . . . . . . . . . . . . . . . . . . . . . . . 84
3.5 CommonProblems . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.5.1 DifferentEffectSizeDataFormats . . . . . . . . . . . . . . 87
3.5.2 TheUnit-of-AnalysisProblem . . . . . . . . . . . . . . . . . 88
3.6 Questions&Answers . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4 PoolingEffectSizes 93
4.1 TheFixed-Effect&Random-EffectsModel . . . . . . . . . . . . . . 94
4.1.1 TheFixed-EffectModel . . . . . . . . . . . . . . . . . . . . 95
4.1.2 TheRandom-EffectsModel . . . . . . . . . . . . . . . . . . 99
4.2 EffectSizePoolinginR . . . . . . . . . . . . . . . . . . . . . . . . 105
4.2.1 Pre-CalculatedEffectSizeData . . . . . . . . . . . . . . . . 108
4.2.2 (Standardized)MeanDifferences. . . . . . . . . . . . . . . 112
4.2.3 BinaryOutcomes . . . . . . . . . . . . . . . . . . . . . . . 115
4.2.4 Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . 127
4.2.5 Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.2.6 Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.3 Questions&Answers . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
5 Between-StudyHeterogeneity 139
5.1 MeasuresofHeterogeneity . . . . . . . . . . . . . . . . . . . . . . 140
5.1.1 Cochran’s𝑄 . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.1.2 Higgins&Thompson’s𝐼2Statistic . . . . . . . . . . . . . . 145
5.1.3 The𝐻2Statistic . . . . . . . . . . . . . . . . . . . . . . . . 147
5.1.4 HeterogeneityVariance𝜏2&StandardDeviation𝜏 . . . . . 147
5.2 WhichMeasureShouldIUse? . . . . . . . . . . . . . . . . . . . . . 149
5.3 AssessingHeterogeneityinR . . . . . . . . . . . . . . . . . . . . . 150
5.4 Outliers&InfluentialCases . . . . . . . . . . . . . . . . . . . . . . 153
Contents ix
5.4.1 BasicOutlierRemoval . . . . . . . . . . . . . . . . . . . . . 153
5.4.2 InfluenceAnalysis . . . . . . . . . . . . . . . . . . . . . . . 156
5.4.3 GOSHPlotAnalysis . . . . . . . . . . . . . . . . . . . . . . 163
5.5 Questions&Answers . . . . . . . . . . . . . . . . . . . . . . . . . 170
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
6 ForestPlots 173
6.1 WhatIsaForestPlot? . . . . . . . . . . . . . . . . . . . . . . . . . 173
6.2 ForestPlotsinR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
6.2.1 LayoutTypes . . . . . . . . . . . . . . . . . . . . . . . . . . 177
6.2.2 SavingtheForestPlots . . . . . . . . . . . . . . . . . . . . 178
6.3 DraperyPlots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
6.4 Questions&Answers . . . . . . . . . . . . . . . . . . . . . . . . . 182
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
7 SubgroupAnalyses 183
7.1 TheFixed-Effects(Plural)Model . . . . . . . . . . . . . . . . . . . 184
7.1.1 PoolingtheEffectinSubgroups . . . . . . . . . . . . . . . 184
7.1.2 ComparingtheSubgroupEffects . . . . . . . . . . . . . . . 185
7.2 Limitations&PitfallsofSubgroupAnalyses . . . . . . . . . . . . . 187
7.3 SubgroupAnalysisinR . . . . . . . . . . . . . . . . . . . . . . . . 190
7.4 Questions&Answers . . . . . . . . . . . . . . . . . . . . . . . . . 194
7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
8 Meta-Regression 197
8.1 TheMeta-RegressionModel . . . . . . . . . . . . . . . . . . . . . . 198
8.1.1 Meta-RegressionwithaCategoricalPredictor . . . . . . . . 198
8.1.2 Meta-RegressionwithaContinuousPredictor . . . . . . . . 200
8.1.3 AssessingtheModelFit . . . . . . . . . . . . . . . . . . . . 201
8.2 Meta-RegressioninR . . . . . . . . . . . . . . . . . . . . . . . . . 203
8.3 MultipleMeta-Regression . . . . . . . . . . . . . . . . . . . . . . . 206
8.3.1 Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . 207
8.3.2 CommonPitfallsinMultipleMeta-Regression . . . . . . . . 209
8.3.3 MultipleMeta-RegressioninR . . . . . . . . . . . . . . . . 212
8.4 Questions&Answers . . . . . . . . . . . . . . . . . . . . . . . . . 224
8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
9 PublicationBias 227
9.1 WhatIsPublicationBias? . . . . . . . . . . . . . . . . . . . . . . . 228
9.2 AddressingPublicationBiasinMeta-Analyses . . . . . . . . . . . . 230
9.2.1 Small-StudyEffectMethods. . . . . . . . . . . . . . . . . . 231
9.2.2 P-Curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
9.2.3 SelectionModels . . . . . . . . . . . . . . . . . . . . . . . . 272
9.3 WhichMethodShouldIUse? . . . . . . . . . . . . . . . . . . . . . 281
9.4 Questions&Answers . . . . . . . . . . . . . . . . . . . . . . . . . 283
9.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283