Statistics for Biology and Health Shahjahan Khan Meta-Analysis Methods for Health and Experimental Studies Statistics for Biology and Health Series Editors Mitchell Gail, Division of Cancer Epidemiology and Genetics, National Cancer Institute, Rockville, MD, USA Jonathan M. Samet, Department of Epidemiology, School of Public Health, Johns Hopkins University, Baltimore, MD, USA Statistics for Biology and Health (SBH) includes monographs and advanced textbooks on statistical topics relating to biostatistics, epidemiology, biology, and ecology. More information about this series at http://www.springer.com/series/2848 Shahjahan Khan Meta-Analysis Methods for Health and Experimental Studies 123 Shahjahan Khan University of SouthernQueensland Toowoomba, QLD,Australia ISSN 1431-8776 ISSN 2197-5671 (electronic) Statistics for Biology andHealth ISBN978-981-15-5031-7 ISBN978-981-15-5032-4 (eBook) https://doi.org/10.1007/978-981-15-5032-4 ©SpringerNatureSingaporePteLtd.2020 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained hereinorforanyerrorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregard tojurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSingaporePteLtd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore This book is dedicated to my late parents Alhajj Moksudul Haque Khan and Zayeda Khatum. May their souls rest in heaven. Shahjahan Khan Preface Themainpurposeofthisbookistomakemeta-analysiseasyforallresearchersand users, especially for the students, health scientists, public health workers and nontechnical scholars who wish to perform meta-analysis and interpret the results for the first time. It simplifies all concepts, methods, computations and models related to meta-analysis through heuristic examples and illustrations using real-life data. It takes a step-by-step approach to performing meta-analyses using different statistical models for various effect size measures. Evidence-based approach has been adopted in many areas of modern decision-making.Itismorefrequentlyusedinallbranchesofthehealthsciencesas well as in education, psychology and social sciences. The evidence-based decision-making primarily relies on the systematic reviews which often includes meta-analysis. Meta-analysisisaveryimportantcomponentofmanysystematicreviewsandis the best way to provide systematic review of quantitative data. It enables researchers to pool summary statistics/data of individual independent studies to synthesise the results for all the studies under investigation. The idea of writing this book evolved from my efforts in preparing notes and making presentations in a series of workshops on statistical meta-analysis with applications in health sciences in Malaysia, Brunei, Japan and Bangladesh. Effect Size Meta-analyses are conducted on the summary data on various effect size measures thatnumericallyevaluatetheeffectivenessofanyinterventionortreatment.Inmost studies, meta-analytic methods are used to estimate the unknown common popu- lation effect size. The effect size is the common name to a family of indices that vii viii Preface measurethemagnitudeofatreatmentorinterventioneffect.Dependingonthetype ofstudyandtheunderlyingoutcomevariables,therearevariousmeasuresthatcan be used to determine the effect size for the intervention of interest. If the underlying outcome variable is binary (or categorical with two arms), the effectsizeismeasuredbyRelativeRiskorRiskRatio(RR)orOddsRatio(OR)or simple proportion or difference of two proportions. If the outcome variable is continuous,theeffectsizeismeasuredbyStandardisedMeanDifference(SMD)or Weighted Mean Difference (WMD). If the outcome of interest is the linear rela- tionship between two quantitative variables, the correlation coefficient is the effect size measure. Statistical Model Every meta-analysis uses statistical models regardless of the effect size measure involved in the investigation. The oldest statistical model is the Fixed Effect (FE) model. This is applicable when effect size of interest is homogeneous across all studies, that is, there is no heterogeneity in the data, and variation among the observedeffectsizeisonlyduetowithinstudiesrandomfluctuation attributable to chancecauses.Italsoassumesthattherandomerror(inthedata)followsanormal distribution.Toaddresstheissueofheterogeneity,theRandomEffects(REs)model isused.Underthismodel,thestudiesincludedinanyinvestigationsareconsidered to be a random sample from the population of all studies, and there is significant between-studyvariationalongwiththewithin-studyvariation.Itassumesthatboth random error and treatment effect follow normal distribution. A more recent approach to tackle heterogeneity is the Inverse Variance Heterogeneity (IVhet) model that does not require any of the unrealistic assumptions of REs. Meta-analysisisaboutestimatingthecommonpopulationeffectsizeofallstudies based on the observed data available from the selected primary studies. Normally point estimates (andstandard deviations) ofthe common effect size observed from the individual studies are used to obtain the confidence intervals. The results pro- duced by any meta-analysis are usually presented in a forest plot which is a scat- terplotof95%confidenceintervalsoftheeffectsizeofeveryindividualstudies,and that of thecommon effect size using the pooled/synthesisedestimate. In any specific investigation involving meta-analysis, the researcher requires to identify the type of outcome variable involved, decide appropriate effect size measure,selectcorrectstatisticalmodelandthenproceedtoperformmeta-analysis using preferred statistical software (e.g. MetaXL), and finally interpret the results produced by the meta-analytic methods. Preface ix Simplified Approach This book simplifies meta-analytical methods by dedicating a chapter for each of the commonly used effect size measures such as RR, OR, SMD, WMD, etc. Whenanyresearcheridentifiestheeffectsizemeasureofinterest,itiseasytogoto the relevant chapter of the book to find all related concepts, methods and step-by-step guidance to perform meta-analysis. The book uses a very easy to use free software as an add-on to MS Excel to demonstrate meta-analytical methods with real datasets. The MetaXL package is availableforfreedownloadfromInternetandcomeswithanInstructionManualto guidetheuserstoperformmeta-analysis.Forthebenefitoftheusers,thebookalso provides Stata codes to perform meta-analysis on each of the popularly known effect size measures. The Contents Covered Chapter 1 introduces the systematic review as a general premise of synthesising independentstudieswithintheframeworkofevidence-baseddecision-making.The second chapter discusses elementary concepts related to meta-analysis along with introducing some issues and statistical fundamentals. These two chapters form Part I of the book. Part II of the book consists of three chapters on general introduction to the relevantconcepts,definitions,illustrationsandinterpretationofeffectsizemeasures for binary outcomes of two arms studies. Chapter 3 introduces the relative risk or riskratioandoddsratio.Chapter4coversmeta-analysisofRelativeRisk(RR)with illustrative examples including construction of forest plot using MetaXl under different statistical models and interpretation of results. Similar contents on odds ratio(OR)areprovidedinChap.5.Subgroupanalysisanddetectionofpublications bias (details in Chapter 2) using funnel plot and Doi plot are briefly introduced in these chapters. The one proportion problem is covered in Chap. 6, and the risk difference in Chap. 7. The meta-analytic methods for continuous outcome variables are covered in PartIIIwhichincludesStandardisedMeanDifference(SMD)inChap.8,Weighted Mean Difference (WMD) in Chap. 9 and correlation coefficient in Chap. 10. Part IV includes special topics in meta-analysis, namely, Meta-regression in Chap. 11, Publication bias in Chap. 12, and Dose-response meta-analysis in Chap. 13. x Preface Words of Thanks I am grateful to the School of Sciences; Faculty of Health, Engineering and Sciences; University of Southern Queensland, Australia for allowing me leave to prepare and finalise the manuscript of the book. Finally,Imustthankmylateparentswhocaredandsacrificedsomuchtoensure my high quality education; dedicated wife Anarkali L Nahar for her patience and continuing support; and proud sons Imran, Adnun and Albab; daughters-in-law, Naafiya,Farhana andAnika,and lovelygrandchildrenZara, Zayena,Aydin,Aarib and Esme for their inspiration. Toowoomba, Australia Shahjahan Khan