CHAPTER13SurvivalData13.1IntroductionInmanyfollow-uptrials,theprimaryresponsevariableisasubject’ssurvivaltimeorthetimetooccurrenceofaparticulareventsuchasrelapseorremissionofsymptoms.Theseareelapsedtimesmeasuredfromanoriginpertinenttoeachsubject,oftenthedateofentryintothestudy.Althoughtimeistypicallymeasuredonachronologicalscaleofdays,weeksormonths,thisneednotalwaysbeso.Insomeepidemiologicalstudiescumulativeexposureplaystheroleofsurvivaltime,inaveterinarystudyofdairycattletheequivalentmeasuremightbecumulativemilkproduction,orinareliabilitystrengthtestitcouldbethecumulativestressorloadapplied.Weshallphrasethemethodsofthischapterintermsof“survival”or“failure”timemeasuredfromentrytoastudy.However,thesamemethodscanbeappliedquitegenerallyforanytimetoeventresponse.Anindividual’ssurvivaltimemaybecensorediffailurehasnotoccurredwhenthatindividualislastseenorwhenthedataareanalyzed.InSection3.7,weintroducedthebasicconceptsofsurvivalmodels,includingthesurvivalfunctionS(t)andhazardrateh(t)ofaresponsetimedistribution.Wealsodescribedthetwo-sided,groupsequentiallog-ranktestfortestingequalityoftwosurvivaldistributions.Supposetwosetsofsubjects,AandB,haverespectivehazardrateshA(t)andhB(t),thenthelog-ranktestisusedtotestthenullhypothesisH0:hA(t)=hB(t)forallt>0,orequivalentlySA(t)≡SB(t),andisparticularlypowerfulagainst“proportionalhazards”alternativeswherehB(t)≡λhA(t)forsomeconstantλ.InSection3.7wefollowedthesignificancelevelapproachwhichrequiresequalincrementsininformationbetweensuccessiveanalysesiftheTypeIerrorrateαistobeattainedaccurately.Inasurvivalstudy,informationisroughlyproportionaltothetotalnumberofobservedfailuresandincrementsareusuallyunequalandunpredictable.TheerrorspendingapproachofChapter7isthusanattractivealternative,asillustratedintheexampleofSection7.2.3.InSection13.2,weshallreviewthegroupsequentiallog-ranktestdescribedinSection3.7,addingamodificationtoaccommodatetiedsurvivaltimes.ThistestisfurthergeneralizedinSection13.3topermittheinclusionofstrata.InSe...
