How to Design, Analyse and Report Cluster Randomised Trials in Medicine and Health Related Research STATISTICS IN PRACTICE SeriesAdvisors HumanandBiologicalSciences StephenSenn CRP-Santé,Luxembourg EarthandEnvironmentalSciences MarianScott UniversityofGlasgow,UK Industry,CommerceandFinance WolfgangJank UniversityofMaryland,USA FoundingEditor VicBarnett NottinghamTrentUniversity,UK StatisticsinPracticeisanimportantinternationalseriesoftextswhichprovidedetailedcover- ageofstatisticalconcepts,methodsandworkedcasestudiesinspecificfieldsofinvestigation andstudy. With sound motivation and many worked practical examples, the books show in down-to-earthtermshowtoselectanduseanappropriaterangeofstatisticaltechniquesina particularpracticalfieldwithineachtitle’sspecialtopicarea. Thebooksprovidestatisticalsupportforprofessionalsandresearchworkersacrossarange ofemploymentfieldsandresearchenvironments.Subjectareascoveredincludemedicineand pharmaceutics;industry,financeandcommerce;publicservices;theearthandenvironmental sciences,andsoon. Thebooksalsoprovidesupporttostudentsstudyingstatisticalcoursesappliedtotheabove areas. The demand for graduates to be equipped for the work environment has led to such coursesbecomingincreasinglyprevalentatuniversitiesandcolleges. Itisouraimtopresentjudiciouslychosenandwell-writtenworkbookstomeeteveryday practicalneeds.Feedbackofviewsfromreaderswillbemostvaluabletomonitorthesuccess ofthisaim. Acompletelistoftitlesinthisseriesappearsattheendofthevolume. How to Design, Analyse and Report Cluster Randomised Trials in Medicine and Health Related Research Michael J. Campbell and Stephen J. Walters MedicalStatisticsGroup,SchoolofHealthandRelatedResearch UniversityofSheffield,UK Thiseditionfirstpublished2014 ©2014JohnWiley&Sons,Ltd Registeredoffice JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UnitedKingdom Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyforpermissionto reusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com. TherightoftheauthortobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewiththeCopyright,Designs andPatentsAct1988. Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyform orbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptaspermittedbytheUKCopyright, DesignsandPatentsAct1988,withoutthepriorpermissionofthepublisher. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmaynotbeavailablein electronicbooks. 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Howtodesign,analyseandreportclusterrandomisedtrialsinmedicineandhealthrelatedresearch/MichaelJ.Campbell andStephenJ.Walters. p.;cm. Includesbibliographicalreferencesandindex. ISBN978-1-119-99202-8(hardback) I.Walters,StephenJohn,author.II.Title. [DNLM:1.RandomizedControlledTrialsasTopic.2.DataInterpretation,Statistical.3.HealthServicesResearch– methods.4.ResearchDesign.W84.3] R853.C55 610.72′4–dc23 2013048574 AcataloguerecordforthisbookisavailablefromtheBritishLibrary. ISBN:978-1-119-99202-8 Setin10/12ptTimesLTStdbyLaserwordsPrivateLimited,Chennai,India 1 2014 Contents Preface xiii Acronymsandabbreviations xv 1 Introduction 1 1.1 Randomisedcontrolledtrials 1 1.1.1 A-Allocationatrandom 1 1.1.2 B-Blindness 2 1.1.3 C-Control 2 1.2 Complexinterventions 3 1.3 Historyofclusterrandomisedtrials 4 1.4 Cohortandfieldtrials 4 1.5 Thefield/communitytrial 5 1.5.1 TheREACTtrial 5 1.5.2 TheInformedChoiceleafletstrial 6 1.5.3 TheMwanzatrial 7 1.5.4 Theparamedicspractitionertrial 7 1.6 Thecohorttrial 8 1.6.1 ThePoNDERtrial 8 1.6.2 TheDESMONDtrial 9 1.6.3 TheDiabetesCarefromDiagnosistrial 10 1.6.4 TheREPOSEtrial 11 1.6.5 Otherexamplesofcohortclustertrials 11 1.7 Fieldversuscohortdesigns 11 1.8 Reasonsforclustertrials 12 1.9 Between-andwithin-clustervariation 14 1.10 Random-effectsmodelsforcontinuousoutcomes 15 1.10.1 Themodel 15 1.10.2 Theintraclustercorrelationcoefficient 16 1.10.3 Estimatingtheintraclustercorrelation(ICC)coefficient 16 vi CONTENTS 1.10.4 LinkbetweenthePearsoncorrelationcoefficientandtheintraclass correlationcoefficient 17 1.11 Random-effectsmodelsforbinaryoutcomes 18 1.11.1 Themodel 18 1.11.2 TheICCforbinarydata 19 1.11.3 Thecoefficientofvariation 19 1.11.4 Relationshipbetweencvcand𝜌forbinarydata 20 1.12 Thedesigneffect 20 1.13 Commonlyaskedquestions 21 1.14 Websources 21 Exercise 22 Appendix1.A 22 2 Designissues 27 2.1 Introduction 27 2.2 Issuesforasimpleintervention 28 2.2.1 Phasesofatrial 28 2.2.2 ‘Pragmatic’and‘explanatory’trials 29 2.2.3 Intention-to-treatandper-protocolanalyses 29 2.2.4 Non-inferiorityandequivalencetrials 30 2.3 Complexinterventions 30 2.3.1 Designofcomplexinterventions 30 2.3.2 PhaseImodelling/qualitativedesigns 32 2.3.3 Pilotorfeasibilitystudies 33 2.3.4 Exampleofpilot/feasibilitystudiesinclustertrials 33 2.4 Recruitmentbias 34 2.5 Matched-pairtrials 34 2.5.1 Designofmatched-pairstudies 34 2.5.2 Limitationsofmatched-pairsdesigns 36 2.5.3 Exampleofmatched-pairdesign:TheFamilyHeartStudy 36 2.6 Othertypesofdesigns 37 2.6.1 Clusterfactorialdesigns 37 2.6.2 Exampleclusterfactorialtrial 38 2.6.3 Clustercrossovertrials 38 2.6.4 Exampleofaclustercrossovertrial 39 2.6.5 Steppedwedge 39 2.6.6 Pseudorandomisedtrials 40 2.7 Otherdesignissues 41 2.8 Strategiesforimprovingprecision 41 2.9 Randomisation 42 2.9.1 Reasonsforrandomisation 42 2.9.2 Simplerandomisation 43 2.9.3 Stratifiedrandomisation 43 2.9.4 Restrictedrandomisation 43 2.9.5 Minimisation 44 Exercise 45 Appendix2.A 48 CONTENTS vii 3 Samplesize:Howmanysubjects/clustersdoIneedformyclusterrandomised controlledtrial? 50 3.1 Introduction 51 3.1.1 Justificationoftherequirementforasamplesize 51 3.1.2 Significancetests,P-valuesandpower 51 3.1.3 Samplesizeandclustertrials 53 3.2 Samplesizeforcontinuousdata–comparingtwomeans 53 3.2.1 Basicformulae 53 3.2.2 Thedesigneffect(DE)inclusterRCTs 54 3.2.3 Examplefromgeneralpractice 55 3.3 Samplesizeforbinarydata–comparingtwoproportions 56 3.3.1 Samplesizeformula 56 3.3.2 Examplecalculations 57 3.3.3 Example:TheInformedChoiceleafletsstudy 58 3.4 Samplesizefororderedcategorical(ordinal)data 59 3.4.1 Samplesizeformula 59 3.4.2 Examplecalculations 60 3.5 Samplesizeforrates 62 3.5.1 Formulae 62 3.5.2 Examplecomparingrates 63 3.6 Samplesizeforsurvival 63 3.6.1 Formulae 63 3.6.2 Exampleofsamplesizeforsurvival 64 3.7 Equivalence/non-inferioritystudies 64 3.7.1 Equivalence/non-inferiorityversussuperiority 64 3.7.2 Continuousdata–comparingtheequivalenceoftwomeans 65 3.7.3 Examplecalculationsforcontinuousdata 65 3.7.4 Binarydata–comparingtheequivalenceoftwoproportions 66 3.8 Unknownstandarddeviationandeffectsize 66 3.9 Practicalproblems 67 3.9.1 TipsongettingtheSD 67 3.9.2 Non-response 67 3.9.3 Unequalgroups 67 3.10 Numberofclustersfixed 68 3.10.1 Numberofclustersandnumberofsubjectspercluster 68 3.10.2 Examplewithnumberofclustersfixed 69 3.10.3 Increasingthenumberofclustersornumberofpatientspercluster? 69 3.11 ValuesoftheICC 69 3.12 AllowingforimprecisionintheICC 70 3.13 Allowingforvaryingclustersizes 70 3.13.1 Formulae 70 3.13.2 Exampleofeffectofvariableclustersize 71 3.14 Samplesizere-estimation 71 3.14.1 Adjustingforcovariates 72 3.15 Matched-pairstudies 72 3.15.1 Samplesizesformatcheddesigns 72 3.15.2 Exampleofasamplesizecalculationforamatchedstudy 72 viii CONTENTS 3.16 Multipleoutcomes/endpoints 73 3.17 Threeormoregroups 74 3.18 Crossovertrials 74 3.18.1 Formulae 75 3.18.2 Exampleofasamplesizeformulainacrossovertrial 75 3.19 Posthocsamplesizecalculations 75 3.20 Conclusion:Usefulnessofsamplesizecalculations 76 3.21 Commonlyaskedquestions 76 Exercise 77 Appendix3.A 78 4 SimpleanalysisofcRCToutcomesusingaggregatecluster-levelsummaries 83 4.1 Introduction 83 4.1.1 Methodsofanalysingclusterrandomisedtrials 83 4.1.2 Choosingthestatisticalmethod 84 4.2 Aggregatecluster-levelanalysis–carriedoutattheclusterlevel,using aggregatesummarydata 84 4.3 Statisticalmethodsforcontinuousoutcomes 86 4.3.1 Twoindependent-samplest-test 86 4.3.2 Example 88 4.4 Mann–WhitneyUtest 91 4.5 Statisticalmethodsforbinaryoutcomes 94 4.6 Analysisofamatcheddesign 95 4.7 Discussion 98 4.8 Commonlyaskedquestion 98 Exercise 99 Appendix4.A 99 5 Regressionmethodsofanalysisforcontinuousoutcomesusingindividual person-leveldata 102 5.1 Introduction 102 5.2 Incorrectmodels 104 5.2.1 Thesimple(independence)model 104 5.2.2 Fixedeffects 104 5.3 Linearregressionwithrobuststandarderrors 105 5.3.1 Robuststandarderrors 105 5.3.2 Exampleofuseofrobuststandarderrors 107 5.3.3 Cluster-specificversuspopulation-averagedmodels 107 5.4 Random-effectsgenerallinearmodelsinacohortstudy 108 5.4.1 Generalmodels 108 5.4.2 Fittingarandom-effectsmodel 109 5.4.3 Exampleofarandom-effectsmodelfromthePoNDERstudy 110 5.4.4 Checkingtheassumptions 110 5.5 Marginal general linear model with coefficients estimated by generalised estimatingequations(GEE) 112 5.5.1 Generalisedestimatingequations 112 5.5.2 ExampleofamarginalmodelfromthePoNDERstudy 113