Introduction to Meta-Analysis PDF
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Introduction to Meta-Analysis Introduction to Meta-Analysis. Michael Borens t ein, L. V. Hedges, J. P. T. Higgins and H. R. Rothstein © 2009 John Wiley & Sons, Ltd. ISBN: 978-0-470-05724-7 Introduction to Meta-Analysis Michael Borenstein Biostat,Inc,NewJersey,USA. Larry V. Hedges NorthwesternUniversity,Evanston,USA. JulianP.T. Higgins MRC,Cambridge,UK. HannahR. Rothstein BaruchCollege,NewYork,USA. A John Wiley and Sons, Ltd., Publication Thiseditionfirstpublished2009 (cid:2)2009JohnWiley&Sons,Ltd Registeredoffice JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UnitedKingdom Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyfor permissiontoreusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com. Therightoftheauthortobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewiththe Copyright,DesignsandPatentsAct1988. Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted, inanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptas permittedbytheUKCopyright,DesignsandPatentsAct1988,withoutthepriorpermissionofthepublisher. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmaynotbe availableinelectronicbooks. Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks.Allbrand namesandproductnamesusedinthisbookaretradenames,servicemarks,trademarksorregistered trademarksoftheirrespectiveowners.Thepublisherisnotassociatedwithanyproductorvendormentioned inthisbook.Thispublicationisdesignedtoprovideaccurateandauthoritativeinformationinregardtothe subjectmattercovered.Itissoldontheunderstandingthatthepublisherisnotengagedinrendering professionalservices.Ifprofessionaladviceorotherexpertassistanceisrequired,theservicesofacompetent professionalshouldbesought. LibraryofCongressCataloguing-in-PublicationData Introductiontometa-analysis/MichaelBorenstein...[etal.]. p. ; cm. Includesbibliographicalreferencesandindex. ISBN978-0-470-05724-7(cloth) 1. Meta-analysis. I. Borenstein,Michael. [DNLM:1. Meta-AnalysisasTopic. WA950I6142009]. R853.M48I582009 610.72—dc22 2008043732 AcataloguerecordforthisbookisavailablefromtheBritishLibrary. ISBN:978-0-470-05724-7 Setin10.5/13ptTimesbyIntegraSoftwareServicesPvt.Ltd,Pondicherry,India PrintedintheUKbyTJInternational,Padstow,Cornwall Contents ListofTables xiii ListofFigures xv Acknowledgements xix Preface xxi Website xxix PART1:INTRODUCTION 1 HOWAMETA-ANALYSISWORKS 3 Introduction 3 Individualstudies 3 Thesummaryeffect 5 Heterogeneityofeffectsizes 6 Summarypoints 7 2 WHYPERFORMAMETA-ANALYSIS 9 Introduction 9 Thestreptokinasemeta-analysis 10 Statisticalsignificance 11 Clinicalimportanceoftheeffect 12 Consistencyofeffects 12 Summarypoints 14 PART2:EFFECTSIZEANDPRECISION 3 OVERVIEW 17 Treatmenteffectsandeffectsizes 17 Parametersandestimates 18 Outlineofeffectsizecomputations 19 4 EFFECTSIZESBASEDONMEANS 21 Introduction 21 Raw(unstandardized)meandifferenceD 21 Standardizedmeandifference,dandg 25 Responseratios 30 Summarypoints 32 vi Contents 5 EFFECTSIZESBASEDONBINARYDATA(2(cid:2)2TABLES) 33 Introduction 33 Riskratio 34 Oddsratio 36 Riskdifference 37 Choosinganeffectsizeindex 38 Summarypoints 39 6 EFFECTSIZESBASEDONCORRELATIONS 41 Introduction 41 Computingr 41 Otherapproaches 43 Summarypoints 43 7 CONVERTINGAMONGEFFECTSIZES 45 Introduction 45 Convertingfromthelogoddsratiotod 47 Convertingfromdtothelogoddsratio 47 Convertingfromrtod 48 Convertingfromdtor 48 Summarypoints 49 8 FACTORSTHATAFFECTPRECISION 51 Introduction 51 Factorsthataffectprecision 52 Samplesize 52 Studydesign 53 Summarypoints 55 9 CONCLUDINGREMARKS 57 PART3:FIXED-EFFECTVERSUSRANDOM-EFFECTSMODELS 10 OVERVIEW 61 Introduction 61 Nomenclature 62 11 FIXED-EFFECTMODEL 63 Introduction 63 Thetrueeffectsize 63 Impactofsamplingerror 63 Contents vii Performingafixed-effectmeta-analysis 65 Summarypoints 67 12 RANDOM-EFFECTSMODEL 69 Introduction 69 Thetrueeffectsizes 69 Impactofsamplingerror 70 Performingarandom-effectsmeta-analysis 72 Summarypoints 74 13 FIXED-EFFECTVERSUSRANDOM-EFFECTSMODELS 77 Introduction 77 Definitionofasummaryeffect 77 Estimatingthesummaryeffect 78 Extremeeffectsizeinalargestudyorasmallstudy 79 Confidenceinterval 80 Thenullhypothesis 83 Whichmodelshouldweuse? 83 Modelshouldnotbebasedonthetestforheterogeneity 84 Concludingremarks 85 Summarypoints 85 14 WORKEDEXAMPLES(PART1) 87 Introduction 87 Workedexampleforcontinuousdata(Part1) 87 Workedexampleforbinarydata(Part1) 92 Workedexampleforcorrelationaldata(Part1) 97 Summarypoints 102 PART4:HETEROGENEITY 15 OVERVIEW 105 Introduction 105 Nomenclature 106 Workedexamples 106 16 IDENTIFYINGANDQUANTIFYINGHETEROGENEITY 107 Introduction 107 Isolatingthevariationintrueeffects 107 ComputingQ 109 Estimating(cid:2)2 114 TheI2statistic 117 viii Contents Comparingthemeasuresofheterogeneity 119 Confidenceintervalsfor(cid:2)2 122 Confidenceintervals(oruncertaintyintervals)forI2 124 Summarypoints 125 17 PREDICTIONINTERVALS 127 Introduction 127 Predictionintervalsinprimarystudies 127 Predictionintervalsinmeta-analysis 129 Confidenceintervalsandpredictionintervals 131 Comparingtheconfidenceintervalwiththepredictioninterval 132 Summarypoints 133 18 WORKEDEXAMPLES(PART2) 135 Introduction 135 Workedexampleforcontinuousdata(Part2) 135 Workedexampleforbinarydata(Part2) 139 Workedexampleforcorrelationaldata(Part2) 143 Summarypoints 147 19 SUBGROUPANALYSES 149 Introduction 149 Fixed-effectmodelwithinsubgroups 151 Computationalmodels 161 Randomeffectswithseparateestimatesof(cid:2)2 164 Randomeffectswithpooledestimateof(cid:2)2 171 Theproportionofvarianceexplained 179 Mixed-effectsmodel 183 Obtaininganoveralleffectinthepresenceofsubgroups 184 Summarypoints 186 20 META-REGRESSION 187 Introduction 187 Fixed-effectmodel 188 Fixedorrandomeffectsforunexplainedheterogeneity 193 Random-effectsmodel 196 Summarypoints 203 21 NOTESONSUBGROUPANALYSESANDMETA-REGRESSION 205 Introduction 205 Computationalmodel 205 Multiplecomparisons 208 Software 209 Analysesofsubgroupsandregressionanalysesareobservational 209 Contents ix Statisticalpowerforsubgroupanalysesandmeta-regression 210 Summarypoints 211 PART5:COMPLEXDATASTRUCTURES 22 OVERVIEW 215 23 INDEPENDENTSUBGROUPSWITHINASTUDY 217 Introduction 217 Combiningacrosssubgroups 218 Comparingsubgroups 222 Summarypoints 223 24 MULTIPLEOUTCOMESORTIME-POINTSWITHINASTUDY 225 Introduction 225 Combiningacrossoutcomesortime-points 226 Comparingoutcomesortime-pointswithinastudy 233 Summarypoints 238 25 MULTIPLECOMPARISONSWITHINASTUDY 239 Introduction 239 Combiningacrossmultiplecomparisonswithinastudy 239 Differencesbetweentreatments 240 Summarypoints 241 26 NOTESONCOMPLEXDATASTRUCTURES 243 Introduction 243 Summaryeffect 243 Differencesineffect 244 PART6:OTHERISSUES 27 OVERVIEW 249 28 VOTECOUNTING–ANEWNAMEFORANOLDPROBLEM 251 Introduction 251 Whyvotecountingiswrong 252 Votecountingisapervasiveproblem 253 Summarypoints 255 29 POWERANALYSISFORMETA-ANALYSIS 257 Introduction 257 Aconceptualapproach 257 Incontext 261 Whentousepoweranalysis 262 x Contents Planningforprecisionratherthanforpower 263 Poweranalysisinprimarystudies 263 Poweranalysisformeta-analysis 267 Poweranalysisforatestofhomogeneity 272 Summarypoints 275 30 PUBLICATIONBIAS 277 Introduction 277 Theproblemofmissingstudies 278 Methodsforaddressingbias 280 Illustrativeexample 281 Themodel 281 Gettingasenseofthedata 281 Isthereevidenceofanybias? 283 Istheentireeffectanartifactofbias? 284 Howmuchofanimpactmightthebiashave? 286 Summaryofthefindingsfortheillustrativeexample 289 Someimportantcaveats 290 Small-studyeffects 291 Concludingremarks 291 Summarypoints 291 PART7:ISSUESRELATEDTOEFFECTSIZE 31 OVERVIEW 295 32 EFFECTSIZESRATHERTHANp-VALUES 297 Introduction 297 Relationshipbetweenp-valuesandeffectsizes 297 Thedistinctionisimportant 299 Thep-valueisoftenmisinterpreted 300 Narrativereviewsvs.meta-analyses 301 Summarypoints 302 33 SIMPSON’SPARADOX 303 Introduction 303 CircumcisionandriskofHIVinfection 303 Anexampleoftheparadox 305 Summarypoints 308 34 GENERALITYOFTHEBASICINVERSE-VARIANCEMETHOD 311 Introduction 311 Othereffectsizes 312 Othermethodsforestimatingeffectsizes 315 Individualparticipantdatameta-analyses 316
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