urvival Analysis.ppt

IntroductiontoSurvivalAnalysisOctober19,2004,BrianF.Gage,MD,MScwiththankstoBingHo,MD,MPHDivisionofGeneralMedicalSciences,Presentationgoals,Survivalanalysiscomparedw/otherregressiontechniquesWhatissurvivalanalysisWhentousesurvivalanalysisUnivariatemethod:Kaplan-MeiercurvesMultivariatemethods:Cox-proportionalhazardsmodelParametricmodelsAssessmentofadequacyofanalysisExamples,Regressionvs.SurvivalAnalysis,Regressionvs.SurvivalAnalysis,Whatissurvivalanalysis?,ModeltimetofailureortimetoeventUnlikelinearregression,survivalanalysishasadichotomous(binary)outcomeUnlikelogisticregression,survivalanalysisanalyzesthetimetoaneventWhyisthatimportant?AbletoaccountforcensoringCancomparesurvivalbetween2+groupsAssessrelationshipbetweencovariatesandsurvivaltime,Importanceofcensoreddata,Whyiscensoreddataimportant?Whatisthekeyassumptionofcensoring?,Typesofcensoring,SubjectdoesnotexperienceeventofinterestIncompletefollow-upLosttofollow-upWithdrawsfromstudyDies(ifnotbeingstudied)Leftorrightcensored,Whentousesurvivalanalysis,ExamplesTimetodeathorclinicalendpointTimeinremissionaftertreatmentofdiseaseRecidivismrateafteraddictiontreatmentWhenonebelievesthat1+explanatoryvariable(s)explainsthedifferencesintimetoaneventEspeciallywhenfollow-upisincompleteorvariable,Relationshipbetweensurvivorfunctionandhazardfunction,Survivorfunction,S(t)definestheprobabilityofsurvivinglongerthantimetthisiswhattheKaplan-Meiercurvesshow.Hazardfunctionisthederivativeofthesurvivorfunctionovertimeh(t)=dS(t)/dtinstantaneousriskofeventattimet(conditionalfailurerate)Survivorandhazardfunctionscanbeconvertedintoeachother,Approachtosurvivalanalysis,Likeotherstatisticswehavestudiedwecandoanyofthefollowingw/survivalanalysis:DescriptivestatisticsUnivariatestatisticsMultivariatestatistics,Descriptivestatistics,AveragesurvivalWhencanthisbecalculated?Whattestwouldyouusetocompareaveragesurvivalbetween2cohorts?AveragehazardrateTotal#offailuresdividedbyobservedsurvivaltime(unitsaretherefore1/tor1/pt-yrs)Anincidencerate,withahighervaluesindicatingmoreeventspertime,Univariatemethod:Kaplan-Meiersurvivalcurves,Alsoknownasproduct-limitformulaAccountsforcensoringGeneratesthecharacteristic“stairstep”survivalcurvesDoesnotaccountforconfoundingoreffectmodificationbyothercovariatesWhenisthataproblem?WhenisthatOK?,TimetoCardiovascularAdverseEventinVIGORTrial,ComparingKaplan-Meiercurves,Log-ranktestcanbeusedtocomparesurvivalcurvesLess-commonlyusedtest:Wilcoxon,whichplacesgreaterweightsoneventsneartime0.Hypothesistest(testofsignificance)H0:thecurvesarestatisticallythesameH1:thecurvesarestatisticallydifferentComparesobservedtoexpectedcellcountsTeststatisticwhichiscomparedto2distribution,ComparingmultipleKaplan-Meiercurves,Multiplepair-wisecomparisonsproducecumulativeTypeIerrormultiplecomparisonproblemInstead,compareallcurvesatonceanalogoustousingANOVAtocompare2cohortsThenusejudiciouspair-wisetesting,LimitofKaplan-Meiercurves,Whathappenswhenyouhaveseveralcovariatesthatyoubelievecontributetosurvival?ExampleSmoking,hyperlipidemia,diabetes,hypertension,contributetotimetomyocardialinfarctCanusestratifiedK-Mcurvesfor2ormaybe3covariatesNeedanotherapproachmultivariateCoxproportionalhazardsmodelismostcommon-formanycovariates(thinkmultivariateregressionorlogisticregressionratherthanaStudentst-testortheoddsratiofroma2x2table),Multivariatemethod:Coxproportionalhazards,NeededtoassesseffectofmultiplecovariatesonsurvivalCox-proportionalhazardsisthemostcommonlyusedmultivariatesurvivalmethodEasytoimplementinSPSS,Stata,orSASParametricapproachesareanalternative,buttheyrequirestrongerassumptionsabouth(t).,Coxproportionalhazardmodel,WorkswithhazardmodelConvenientlyseparatesbaselinehazardfunctionfromcovariatesBaselinehazardfunctionovertimeh(t)=ho(t)exp(B1X+Bo)CovariatesaretimeindependentB1isusedtocalculatethehazardratio,whichissimilartotherelativeriskNonparametricQuasi-likelihoodfunction,Coxproportionalhazardsmodel,continued,Canhandlebothcontinuousandcategoricalpredictorvariables(think:logistic,linearregression)Withoutknowingbaselinehazardho(t),canstillcalculatecoefficientsforeachcovariate,andthereforehazardratioAssumesmultiplicativeriskthisistheproportionalhazardassumptionCanbecompensatedinpartwithinteractionterms,LimitationsofCoxPHmodel,DoesnotaccommodatevariablesthatchangeovertimeLuckilymostvariables(e.g.gender,ethnicity,orcongenitalcondition)areconstantIfnecessary,onecanprogramtime-dependentvariablesWhenmightyouwantthis?Baselinehazardfunction,ho(t),isneverspecifiedYoucanestimateho(t)accuratelyifyouneedtoestimateS(t).,Hazardratio,Whatisthehazardratioandhowtoyoucalculateitfromyourparameters,Howdoweestimatetherelativeriskfromthehazardratio(HR)?Howdoyoudeterminesignificanceofthehazardratios(HRs).ConfidenceintervalsChisquaretest,Assessingmodeladequacy,MultiplicativeassumptionProportionalassumption:covariatesareindependentwithrespecttotimeandtheirhazardsareconstantovertimeThreegeneralwaystoexaminemodeladequacyGraphicallyMathematicallyComputationally:Time-dependentvariables(extendedmodel),Modeladequacy:graphicalapproaches,SeveralgraphicalapproachesDothesurvivalcurvesintersect?Log-minus-logplotsObservedvs.expectedplots,Testingmodeladequacymathematicallywithagoodness-of-fittest,Usesatestofsignificance(hypothesistest)One-degreeoffreedomchi-squaredistributionpvalueforeachcoefficientDoesnotdiscriminatehowacoefficientmightdeviatefromthePHassumption,Example:TumorExtent,3000patientsderivedfromSEERcancerregistryandMedicarebillinginformationExploringtherelationshipbetweentumorextentandsurvivalHypothesisisthatmoreextensivetumorinvolvementisrelatedtopoorersurvival,Log-Rank2=269.0973pChiSqRatioConfidenceLimitsLabelage210.156900.050799.54300.00201.1701.0591.2927080race210.160880.079534.09210.04311.1751.0051.373blackrace310.050600.095900.27840.59771.0520.8721.269othercomorb110.270870.0567822.7549.00011.3111.1731.465comorb210.322710.0634125.9046.00011.3811.2191.564comorb310.617520.0676883.2558.00011.8541.6242.117DISTANT10.862130.07300139.487