CHAPTER8AnalysisFollowingaSequentialTest8.1IntroductionSofarwehaveconcentratedonhypothesistests,establishingaframeworkfordesigningagroupsequentialstudy,i.e.,forperforminga“pre-data”calculation.However,oncedatahavebeencollected,thehypothesistestingparadigmmaynolongerbethemostusefuloneforstatisticalanalysis;see,forexample,thediscussioninCutleretal.(1966).Whereasinindustrialacceptancesamplingitmaywellbethatdecisionsaremadeandactionstakenassoonasastudyisterminated,inmedicalstudiesamorecompleteanalysisisusuallyrequiredthanthesimple“accept”or“reject”decisionofahypothesistest.Inthischapterwediscusstheconstructionofpointestimates,P-valuesandconfidenceintervals.Inparticular,anintervalestimateforthetreatmenteffectθwillallowconsiderationofthemagnitudeofthetreatmentdifferenceandindicateitspracticalimportance,irrespectiveofwhetherahypothesistestdeclaresstatisticalsignificance(seeSimon,1993andBraitman,1993).Therearetwosituationsinwhichintervalestimatesmightberequiredinagroupsequentialstudy.Thefirstisuponconclusionofthetrialaftertheteststatistichascrossedastoppingboundary,asdescribedinpreviouschapters.Thisisthecaseweshallconsiderinthischapter.Alternatively,onemaywishtogiveanintervalestimateofthetreatmenteffectataninterimstageofthestudy,regardlessofwhetherthedesigncallsforterminationornot;thissituationcallsfora“repeatedconfidenceinterval”sequence,thesubjectofChapter9.Inneithersituationisitappropriatetocomputea“naive”confidenceinterval,treatingthedataasiftheyhadbeenobtainedinafixedsamplesizeexperiment.Tsiatis,Rosner&Mehta(1984)investigatenaive90%confidenceintervalscalculatedonterminationofafive-stagePococktestwithTypeIerrorprobability0.05andfindtheircoverageprobabilitiestovarybetween0.846and0.929,dependingonthetrueparametervalue.Notethatinthischapterweshallbeconcernedwithfrequentistpropertiesofintervalestimates.ThetopicofcredibleintervalsintheBayesianparadigmwillbediscussedlaterinChapter18.8.2DistributionTheoryWesawinSection3.1thatmanycommonproblemsproduceasequenceofte...
