CHAPTER14InternalPilotStudies:SampleSizeRe-estimation14.1TheRoleofanInternalPilotPhaseInsettingthesamplesizeforastudy,onemayfindthepowercalculationrequiresknowledgeofanunknownparameter,suchasaresponsevarianceoraneventrate,whichcanonlybeestimatedfromthedatatobecollectedinthestudy.Onesolutiontothisproblemistocarryoutapreliminarypilotstudybeforecommencingthemaintrial.Theremaybeotherusesforsuchapilotstudy:checkingwhetheratreatmentprocessisfeasible,refiningthedefinitionofatreatment,learninghowtoidentifysuitableparticipants,orensuringthatrandomizationanddatacollectionrunsmoothly.However,iforganizersareconfidentthattheirtreatmentsandexperimentalproceduresarealreadywelldefined,theymaywishtolaunchintothemainstudywithoutdelay.Wittes&Brittain(1990)quoteW.G.Cochran’swarningthatover-interpretationofresultsfromasmallpilotstudy,eitherpositiveornegative,mayunderminesupportforthemajorinvestigation.Theirsolutionistoforegoan“external”pilotstudybuttreatthefirstpartofthemainstudyasan“internalpilot”andre-calculatetheoverallsamplesizeusingestimatesoftherelevantparametersobtainedfromtheinternalpilotdata.Wittes&Brittainemphasizetheneedtoestimateparametersgoverningsamplesizefromtheactualstudypopulation,andtheyciteexamplesofclinicaltrialswhereinitialestimatesofresponsevariance,recruitmentrateormortalityratewerewildlyinaccurate.Theynotetheefficiencygainedbyusingdataobtainedduringaninternalpilotphaseintheendofstudyanalysis,whereasdatafromanexternalpilotstudywouldnormallybediscardedfromthemainanalysis.Re-estimationofsamplesizefrominternalpilotdataissimplestwhenthestudywillhaveasingleanalysisofthemajoroutcomemeasureoncesamplingiscomplete.Thus,theexperimentaldesignissequentialonlyinthatinterimdataareusedtomodifyafixedsampledesign.Inthiscase,themathematicaldetailsarequitestraightforward.SupposehypothesesandTypeIandIIerrorrateshavebeenspecifiedandthesamplesizeneededforafixedsamplestudycanbeexpressedasafunctionn(φ)oftheunknownparameterφ.Basedonapre-studyestimateˆφ0,thestudycommenceswithta...
