统计分析一指标种类与选择

1臨床試驗

Statisticalanalysis(I)

統計分析(一)指標種類與選擇2015-3-18簡國龍老師.edu.tw

【本著作除另有註明外，採取創用CC「姓名標示－非商業性－相同方式分享」台灣3.0版授權釋出】2OutlineRolesandapplicationsofstatisticsinclinicaltrialHypothesistestingandestimationContinuousdataCategoricaldataCensoreddataRepeatedmeasuresInterimanalysisSamplesizedeterminationProblemsnotresolvedbystatistics3TheroleofstatisticinclinicaltrialsSamplesizeestimationRandomizedassignmentoftreatmentAnalyzeresults(hypothesistestingandeffectestimation)Controlforconfounding45UseofstatisticsPowercalculationandefficiencyconsiderations

Samplesizecalculation,Groupsequentialmethods,Cross-overdesign,Factorialdesign,..RandomassignmentoftreatmentgroupsFixedallocation,adaptiveallocationEstimationofclinicaleffects/differenceandHypothesistestingChi-square,t-test,ANOVA,log-ranktest,GEEControlforconfoundingandidentificationofprognosticfactors

StratifiedanalysisandMultivariateanalysis6MethodsofRandomizationFixedrandomizationAllocationratio(i.e.simplerandomization)Allocationstrata(i.e.stratifiedrandomization)Blocksize(randomizedblockdesign,Moses-Oakfordalgorithm)blocksizecanbefixedorvariableAdaptiverandomizationNumberadaptive(e.g.Efron’sbiasedcoinmethod)Baseline(prognosticfactor)adaptive(e.g.Pocock&Simon,Begg&Iglewicz)Oueadaptive(e.g.Zelen’splay-the-winnerdesign)7EfficiencyconsiderationsOptimalallocationofresources:Information/subject,Information/visit,Information/＄Cross-overdesignFactorialdesignEvaluationofthebinationoftwoormoredrugsEvaluationoftwodrugsiftheirmechanismareindependent8HypothesistestingAssumptionsaboutofdatadistributionFormulateHOandHAF(data)=SP=(S∣HOanddistribution)P<α===>rejectP>α===>cannotrejectHO9EffectestimationPointestimate:Howlargeistheclinicaleffect?Confidenceinterval(CI):Whatisthepossiblerangeoftheclinicaleffects?95%CIcorrespondstoα=0.0510Objectivesofaclinicaltrial:estimatethetherapeuticdifference(△)Therapeuticdifference:95%CIof△exclude0Therapeuticequivalence:95%CIof△iswithinapre-specifiedrange11DifferenttypesofdataContinuousdata:Bloodpressure,Cholesterol,Urinaryflow,…Categoricaldata Dichotomous:death,relapse Ordinal:pleteresponse,Partialresponse,Stabledisease,ProgressionTime-to-eventdata/Failuretimedata:Treatment-to-relapse,…Correlateddata:Repeatedmeasures,Correlatedend-points12ContinuousdataEstimationMean,SD,TeststatisticsH0vs.HaStudent’sttest,pairedttest,two-sampletestANOVA:one-way,two-wayANCOVAStratifiedrandomizationNonparametricmethodsWilcoxonsignedranktest,ranksumtest,Kruskal-Wallistest13CategoricaldataOnesamplePre-postparison:changefrombaselineanalysisIndependentsamplesChi-squaretestOrderedcategoricaldatabiningcategoricaldataStratification,Mantel-HaenszeltestModel-basedmethodsLogisticregression14Differentfollow-upmethodsinclinicaltrialsFixedfollow-upperiodVariablefollow-upperiodLongitudinalstudyInterimanalyses15Figure9.2.1censoringpatternincalendartime.o：event;×：censored.16Figure9.2.2censoringpatternindurationoftreatment.o：event;×：censored.17CensoreddataSurvivalfunctionparisonbetweensurvivalfunctionsLogranktestCox’sproportionalhazardmodelCalendartimeandinformationtimeRecruitNinthetimeinterval(0,Tc)Thecontributionbyeachsubjecttothetotalinformationdependsonthenumbersofmeasuresofprimaryendpoints,proportionaltothelengthofdurationstayinginatrial18Survivalanalysis/Analysisoffailure-timedata(e.g.time-torelapse,time-to-death)Censoringinfollow-upofpatientsRightcensoringandLeftcensoringInformativevs.uninformativecensoringEstimationofsurvivalprobabilityS(t)fromcensoreddatae.g.S(5thyear)=five-yearsurvival,S(mediansurvival)=50%Kaplan-MeiercurveandGreenwoodformulaforCI:anon-parametricapproachLife-tablemethod:anapproximateapproachSurvivalfunction<----->Hazardfunction,…19Survivalanalysis/Analysisoffailure-timedata(e.g.time-torelapse,time-to-death)parisonoftwosurvivalcurvesLogranktest:equalweightforalltGeneralizedWilcoxontest:moreweightforearlytMultivariateanalysisDependentvariable:hazardattimetIndependentvariables:Mineffect:TreatmentassignmentCovariates:Age,Sex,Staging,Center,…20Analysisofcorrelateddatae.g.Bloodpressuremeasuredeveryweekforsixweeks painscore,Walkingdistance,JointscoreatsixthweekProblem:multipleparison!SolutionAdjustedP-valuesateachparison(maybetooconservative) e.g.Bonferroniadjustment ScheffeandDuncanprocedureinANOVAMultivariateanalysisofvariance Requiresasymptoticassumptions(sufficientsamplesizeandnormaldistribution)GeneralizedEstimatingEquationmethod(GEE) Robustandflexiblepositeend-points21RepeatedmeasuresAssessmentofoverallerageeffectacrosstimeDetectionoftimeeffectTreatment-by-timeinteractionGEEmethodsContinuousresponsevs.categoricalresponse22Interimanalyses/GroupsequentialmethodsMultiple“peeks”duringthecourseofthetrialContinuoussequentialdesign(pairedsubjects)OpensequentialplanandClosedsequentialplanGroupsequentialdesign(Repeatedsignificanttesting)

Adjustp-valueateach“peek”tomaintainnominalsignificancelevels.Expectednumberofenrolledsubjectsorexpectedtotalfollow-upperson-timeStoppingrulesandDataMonitoringmitteeshouldbepre-specifiedintheprotocol.23ProtocoldeviationsBeforerandomization:EnrollsubjectswhoarelikelytoplywiththeprotocolDoctor-patientrelationship,Run-inphase,Financialreward,..Afterrandomization:Oncerandomized,alwaysanalyzeIntent-to-treatanalysis/Intention-to-treatanalysisvs.per-protocolanalysis24Protocoldeviationsmonreasonsforprotocoldeviationsincorrectdiagnosis,incorrectselectioncriteria,departurefromtreatmentschedule,lossoffollow-up,administrativeerror,…Conditionsforprotocoldeviations,ifnotspecifiedintheprotocol,areusuallydeterminedbytheDatamonitoringBoard.25Intention-to-treatanalysisvs.per-protocolanalysisparethetreatmentsthatareintendedtobegiventothepatients,notwhatthepatientsactuallyreceived.Preservationoftheparabilityofpopulationsisofutmostimportance.Othermethods,suchastheper-protocolmethod(i.e.excludenonpliantpatients)arenotstatisticallyvalid.26Confoundingparability-basedcriteriaThefactorisunevenlydistributedinthetreatmentgroups.Thefactorsisanindependentriskfactorforthedisease.Thefactorisnotanintermediatevariableinthetherapeuticmechanism.Collapsibility-basedcriteria.Adjustedeffectdoesnotequaltoapparenteffect.Thefactorisnotanintermediatevariableinthetherapeuticmechanism.27Effectmodification(interaction)EffectingroupA≠EffectingroupBAconfounderisanindependentrisk/prognosticfactor.Itissomethingthatwewanttocontrol/oid.Aneffectmodifiermodifiesthetreatmenteffect,itmayormaynotbeanindependentprognosticfactor.Effectmodificationisabiologicalphenomenonthatwewanttoexplore.28Figure11.4.1Adjustmentforcovariateinestimationoftreatmenteffect.CaseI:monslope.29Figure11.4.2Adjustmentforcovariateinestimationoftreatmenteffect.CaseI:Differentslope,samedirectionbutdifferentmagnitude.30Figure11.4.3Adjustmentforcovariateinestimationoftreatmenteffect.CaseIII:Differentslopes,differentdirectionwithdifferentmagnitude.31Figure11.5.1Differenceintreatmentmeansand95%confidenceintervals.Meantestdrugchangefromthebaselineminusthemeanplacebochangefromthebaseline.(Source:U.S.FDAGuidelinefortheFormatandContentoftheClinicalandstatisticalSectionsofanApplication,1988).32MultiplelinearregressionanalysesTheprimarygoalistoestimatethedifferencebetweenthetwo(ormore)treatmentgroupsortotestthenullhypothesisofnodifference.Givengoodstudydesign,sufficientsamplesize,andrandomization,multivariateanalysesisusuallynotnecessary.If,unfortunately,confoundingexists,multivariateanalysiscanhelp.Resultsfortreatmenteffectifvalidbutresultsforconfounderscanonlybeusedtogeneratefurtherhypothesis.Resultsofpost-hocstratification(post-stratificationanalysis)canonlyservetogeneratefurtherhypothesis.33IdentificationofprognosticfactorsinclinicaltrialsEffectonprimaryend-pointispositive,andtheeffectismorepronouncedincertainsubgroups==>prognosticfactorisidentifiedEffectonprimaryend-pointisnegative,buttheeffectsisstatisticallysignificantinonesubgroup===>requiresfurtherinvestigations頁碼作品版權圖示來源/作者1-35本作品轉載自MicrosoftOffice2010

PowerPoint設計主題範本-Pixel，依據Microsoft服務合約及著作權法第46、52、65條合理使用。4

《Responsibilitiesofthestatisticalunitinaclinicaltrialgroup》中研院統計科學研究所，陳珍信。本作品依據著作權法第46、52、65條合理使用。15

《Designandanalysisofclinicaltrials:conceptsandmethodologies》，w,SC,Liu,JP，出版社:Wiley(thirdedition)，p.391。本作品依據著作權法第46、52、65條合理使用。16《Designandanalysisofclinicaltrials:conceptsandmethodologies》，w,SC,Liu,JP，出版社:Wiley(thirdedition)，p.392。本作品依據著作權法第46、52、65條合理使用。21

Assessmentofoverallerageeffect