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HST190:IntroductiontoBiostatistics
Lecture4:Clinicaltrials
Simplelinearregression
1 HST190:IntrotoBiostatistics
Clinicaltrials
• Throughoutthecontinuumofhealthcare,patientsandprovidershavetomakedecisions§ e.g.betweenonetreatmentchoiceoranother
• Asresearchers,weseektoestablishevidencetohelpthatdecision
• Thearemanywaysthatwecouldchoosetoachievethis
• Randomizedclinicaltrialsareviewedasgeneratingthestrongest,mostcompellingevidence§ atleastforindividualstudies
§ metaanalyses/systematicreviews
HST190:IntrotoBiostatistics2
HST190:IntrotoBiostatistics3
• Clinicaltrialscanandhavebeenusedtoinvestigateawidevarietyofpotentialdecisions:1) prevention
§ Mediterranean-styledietoncardiovascularoutcomes§ Estruch etal(AnnalsofInternalMedicine,2006)
2) screening/earlydetection§ breastcancerscreening§ Tabar etal(TheLancet,1985)
3) diagnostictesting§ ventilator-associatedpneumonia§ CanadianCriticalCareTrialsGroup(NEJM,2006)
4) therapeutics/treatment§ chemotherapy&radiationvs.radiationaloneforesophagealcancer§ Cooperetal(JAMA,1999)
5) qualityoflife§ family-supportinterventioninICUs§ Whiteetal(NEJM,2018)
HST190:IntrotoBiostatistics4
• Fortherapeutics,thereareusuallyfourphases:
• Randomizedtrialsarerequiredtoberegistered§ atwww.ClinicalTrials.gov intheUS
§ otherentitiessuchaswww.clinicaltrialsregister.eu inEurope
§ submitadetailedprotocolbefore thestudybegins
Components
• FundamentalsofClinicalTrials.Friedman,Furberg,DeMets.2010
• Scientificcomponents:§ studypopulation§ interventionsandhypotheses§ primary(andpossiblysecondary)endpoints
• Studyfeatures:§ typeofrandomization§ extentofblinding
• Analyses:§ choiceofstatisticalframework§ samplesize/powercalculations§ interimmonitoring
HST190:IntrotoBiostatistics5
Specifyingthestudypopulation
HST190:IntrotoBiostatistics6
• Basisfortheinterpretationofthestudyresults
• BreastcancerscreeningfromLecture1:§ generalpopulation
§ women<40yearsofage
§ womenwhohadundergonebreastaugmentation
§ womenwhoare“medicallyvulnerable”
• Key:thereisnosingle“correct”answer
• Choiceshouldbe:§ clinicallymeaningfulandrelevant
§ onefromwhichitwillbefeasibletorecruitandfollowparticipants
HST190:IntrotoBiostatistics7
• Choicemaybedetermined,inpart,by§ previouswork/studiesinthesamearea
§ likelihoodofadverseeventsorcompetingrisks
• Importanttorecognizethatinterventionslikelyhaveheterogeneouseffects
• Thebroaderthechoiceofstudypopulation,theresultswillbe:§ moreinclusivebutlessspecific
§ moreamenabletouseinpolicydecisionsbutlesssotopersonalizeddecisions
Hypotheses
HST190:IntrotoBiostatistics8
• InLecture3wewereintroducedtohypothesistesting:§ nullhypothesisisthe“statusquo”§ gatherandquantifyevidenceinfavorofsomealternativehypothesis
• Inthissense,thealternativetypicallyrepresentstheprimarygoalsofthestudy
• Usuallyframedinoneoftwoways:1. Superiority
§ treatmentAbetter thanB
2. Non-inferiority§ treatmentAnotworse thanB§ treatmentAmaybebetterthanBintermsof,say,cost orsafety§ requiresspecificationofanacceptablemargin
HST190:IntrotoBiostatistics9
• TheARISTOTLEstudy§ Grangeretal(NEJM,2011)
• Primaryobjective:non-inferiority§ upper95%confidencelimitofthehazardratio<1.38
• Secondaryobjective:superiority§ upper95%confidencelimitofthehazardratio<1.00
n engl j med 365;11 nejm.org september 15, 2011 981
The new england journal of medicineestablished in 1812 september 15, 2011 vol. 365 no. 11
Apixaban versus Warfarin in Patients with Atrial Fibrillation
Christopher B. Granger, M.D., John H. Alexander, M.D., M.H.S., John J.V. McMurray, M.D., Renato D. Lopes, M.D., Ph.D., Elaine M. Hylek, M.D., M.P.H., Michael Hanna, M.D., Hussein R. Al-Khalidi, Ph.D., Jack Ansell, M.D., Dan Atar, M.D.,
Alvaro Avezum, M.D., Ph.D., M. Cecilia Bahit, M.D., Rafael Diaz, M.D., J. Donald Easton, M.D., Justin A. Ezekowitz, M.B., B.Ch., Greg Flaker, M.D., David Garcia, M.D., Margarida Geraldes, Ph.D.,
Bernard J. Gersh, M.D., Sergey Golitsyn, M.D., Ph.D., Shinya Goto, M.D., Antonio G. Hermosillo, M.D., Stefan H. Hohnloser, M.D., John Horowitz, M.D., Puneet Mohan, M.D., Ph.D., Petr Jansky, M.D., Basil S. Lewis, M.D.,
Jose Luis Lopez-Sendon, M.D., Prem Pais, M.D., Alexander Parkhomenko, M.D., Freek W.A. Verheugt, M.D., Ph.D., Jun Zhu, M.D., and Lars Wallentin, M.D., Ph.D., for the ARISTOTLE Committees and Investigators*
A bs tr ac t
The authors’ affiliations are listed in the Appendix. Address reprint requests to Dr. Granger at the Duke Clinical Research Institute, Duke University Medical Cen-ter, DUMC Box 3850, Durham, NC 27715, or at [email protected].
*The members of the steering commit-tee, as well as other committee members and investi gators in the Apixaban for Reduction in Stroke and Other Throm-boembolic Events in Atrial Fibrillation (ARISTOTLE) study, are listed in the Supplementary Appendix, available at NEJM.org.
This article (10.1056/NEJMoa1107039) was published on August 28, 2011, and up-dated on August 30, 2011, at NEJM.org.
N Engl J Med 2011;365:981-92.Copyright © 2011 Massachusetts Medical Society.
BackgroundVitamin K antagonists are highly effective in preventing stroke in patients with atrial fibrillation but have several limitations. Apixaban is a novel oral direct factor Xa inhibitor that has been shown to reduce the risk of stroke in a similar population in comparison with aspirin.MethodsIn this randomized, double-blind trial, we compared apixaban (at a dose of 5 mg twice daily) with warfarin (target international normalized ratio, 2.0 to 3.0) in 18,201 patients with atrial fibrillation and at least one additional risk factor for stroke. The primary outcome was ischemic or hemorrhagic stroke or systemic em-bolism. The trial was designed to test for noninferiority, with key secondary objec-tives of testing for superiority with respect to the primary outcome and to the rates of major bleeding and death from any cause.ResultsThe median duration of follow-up was 1.8 years. The rate of the primary outcome was 1.27% per year in the apixaban group, as compared with 1.60% per year in the war-farin group (hazard ratio with apixaban, 0.79; 95% confidence interval [CI], 0.66 to 0.95; P
Choiceofcontrolgroup
HST190:IntrotoBiostatistics10
• Suppose“TreatmentA”isthekeyinterventionthatweareinterestedin§ e.g.onedevelopedbyyourresearchgroup
• Howdowechoosethecomparisonorcontrolintervention,“TreatmentB”?§ choicehasimplicationsforboththeinterpretationandnumericalvalueoftheeffectthatisultimatelyestimated
• Ideally,thechoiceshouldreflectthechoicethatpatientsactuallyhave§ premiseisthatweareconductingthetrialtogatherevidencethatwillinformsomesuchdecision
HST190:IntrotoBiostatistics11
• Ifthereisnoestablishedstandardofcare,thenonemaysetthecontroltobeaplacebo§ i.e.interventionwithoutany(biological)therapeuticeffect
• Ifthereisanestablishedstandardofcarethenoneshould,arguably,useit§ unethicaltotreatpatientsinawaythathasthepotentialtobelesseffectivethanaknowncourseoftreatment
§ wouldnotgiveaplacebotoapatientwithmalaria!
Choiceofendpoints
HST190:IntrotoBiostatistics12
• IntheARISTOLEtrial,theprimaryendpoint wasincidenceofischemicorhemorrhagicstrokeorsystemicembolism§ duringupto30monthsoffollow-up
• Theyalsoreportontwosecondaryendpoints§ bleedingandmortality
• Usualparadigmrequirespre-specificationofprimaryendpoint:§ basisforpower/samplesize
§ dependingonthedisease,FDAmaymandatespecificendpoints
§ typicallyrequiredtoreporttheresultsfortheprimaryoutcome,regardlessofwhetherthehypothesesareconfirmed
HST190:IntrotoBiostatistics13
• Mayuseco-primaryendpoints,suchasfunctionalandcognitiveendpointsforAlzheimer’sdisease,oracompositeendpoint,suchasdisease-freesurvival
• Secondaryendpointsalsotypicallypre-specified§ typicallylessstringencywithregardtoerrorrates
§ consideraccommodatingpowerforsecondaryendpoints
Iteration
HST190:IntrotoBiostatistics14
• Studyisconceivedthroughdiscussionaboutquestionsofinterest§ arepopulationsavailabletoaddressquestions?
§ areendpointsavailableandmeasurabletoaddressquestions?
§ isthisallfeasible(time,money,ethics,patientsupport,cliniciansupport)?
• Questionsmayneedtoberevisedaccordingly§ givenreality,whatrelatedquestionscanactuallybeaddressed?
§ arethesequestionsasimpactfulasthoseoriginallyposed?
• Endpointsmayalsoberevised§ givenreality,whatcanactuallybemeasured?
§ willtheseendpointsservetoaddressthequestionsofinterest?
HST190:IntrotoBiostatistics15
• Asanexample,considerpatientswhoarehospitalizedafterhavingexperiencedanacutestroke
• Question:§ Dopatientsonoxygenexhibitbetterfunctionaloutcomesat24hoursthanpatientsonroomair?
• Plantoconductarandomized,double-blind,clinicaltrialofoxygenvsair§ primaryoutcome:NationalInstitutesofHealthStrokeScale(NIHSS)
§ measureNIHSSat0hoursand24hours
• Problem:§ somepatientsdiewithin24hours
§ NIHSSat24hoursisnotwell-definedfortheseindividuals
HST190:IntrotoBiostatistics16
• Possiblewaysforward:1) changequestion:amongpatientswhosurviveto24hours,are
patientsonoxygenbetterwithrespecttoNIHSSthanpatientswithoutoxygen?
2) somehowconstructacompositeendpointthatfoldsindeathwithin24hours
3) changeeligibilitycriteriatofocusonpatientswhoareveryunlikelytodiewithin24hours
Randomization
HST190:IntrotoBiostatistics17
• Centraltothestrengthofevidencethatclinicaltrialsprovide§ intuitively,ruleoutallotherexplanationsfordifferencesbetweenthetwogroups
§ onaverageatleast(!)
• Supposetherandomizedtrialhastwoarms§ asintheARISTOTLEtrial
• Onewayofallocatingpatientstoagiveninterventionistoflipa(digital)coinforeachpatientastheyarerecruited§ simpleandeasytoimplement
§ drawbackisthatyoumightget“unlucky”andendupwithunevennumbersinthetwogroupsand/oroverrepresentationofimportantsubgroupsinonearmortheother
HST190:IntrotoBiostatistics18
• Blocking:§ aspatientsarerecruited,createblocksofsize2,4or6etc
§ randomlyallocatehalftoonearmandhalftotheother
§ guaranteesbalance(orveryclosetoit)inthesamplesizeswithineacharm
• Stratification:§ toachievebalanceintreatmentassignmentwithinimportantfactors
§ itwouldbedisappointingif,bychance,allofthetreatmentAwasallocatedtoasinglestudysite
§ otherfactorsmightinclude:gender,baselinediseaseseverity,pastexposure
• Adaptivedesigns§ basedonbaselineprognosticfactors
§ basedonresponses
Blinding
HST190:IntrotoBiostatistics19
• Thereisapotentialforbiastoariseifeitherpatientsorstudystaffknowwhichtreatmentisbeingadministered§ perhapsespeciallysoinplacebo-controlledtrials
• Blindingcorrespondstoanefforttohidewhichtreatmentisbeingadministered§ e.g.shape,colorandsizeoftabletisthesame
§ e.g.labellingofstudymaterialsisgeneric
• Canbechallenginginsomesettings§ e.g.surgicalinterventions
§ e.g.mechanicalinterventions
Analyticframework
HST190:IntrotoBiostatistics20
• Determinedby:1. thenatureoftheendpoint
2. thehypothesisbeingassessed
3. thestudydesign
• Natureoftheendpoint:§ continuous(e.g.,cholesterol)
§ binaryorcategorical(e.g.,response)
§ time-to-event(e.g.recurrentormortality)
§ ordinal(e.g.,functionalscale)
§ longitudinal(e.g.weightchangeovertime)
§ multivariate(e.g.,genes,familymembers,voxels)
HST190:IntrotoBiostatistics21
• Translatethehypothesesintoastatisticaltestand/ormodel§ two-sampletest
§ e.g.two-samplet-testorWilcoxontest
§ e.g.two-samplelog-ranktest
§ regressionmodelo e.g.linearregression
o e.g.logisticregression
o e.g.Coxregression
• Additionalanalysisconsiderations§ accommodatingdesignfeaturessuchasblockingand/orstratification
§ interactionterms,suchagroupxtimeinteractions
§ “siteeffects”inmulti-sitestudies
Elementsofdesign
HST190:IntrotoBiostatistics22
• Question:Howbigshouldmysamplesizebe?§ clearlyimportantimplicationsforcostandfeasibility
• Typicalframingistoconsiderstatisticalpower forafixedtypeIerrorrate(i.e.alphalevel)§ Recallslide56inLecture3
§ P(RejectH0|H1 istrue)=1– typeIIerror
• Asoneincreasesthesamplesizeweareincreasinglylikelytorejectthenullhypothesisifitisinfactfalse
• Option#1: Pre-specifypower(e.g.80%or90%)andcalculatetherequiredsamplesize
HST190:IntrotoBiostatistics23
• Insomesettings,theremaybefinancialconstraintsonhowmanypatientscanberecruited§ budgettotalsimposedbythefundingagency
§ costoftreatment
§ costoffollow-up
• Option#2:Pre-specifythesamplesizeanddeterminehowmuchpowerthestudywillhave
• Interplaybetweensamplesizeandpowerwilldependonarangeoffactors(slide65ofLecture3),including:§ effectsize
§ variationintheoutcomeinthepopulation
§ missingdata(e.g.drop-outorcensoring)
Performtheanalysis
HST190:IntrotoBiostatistics24
• Queryandcleanthedata§ resolveissuessuchasimplausiblevalues
• Performatestand/orfitamodel
• Typicallyprescriptive(atleastinitially)§ planshouldhavebeenlaidoutintheprotocol
§ minimizesthepotentialfor“gaming”thedata(oratleasttheperceptionofit)
§ manyjournalswillrequiresubmissionoftheprotocolandholdyoutowhatyousaidyouwoulddo
• Summarizeandinterprettheresults§ frombothastatisticalandscientificperspective
HST190:IntrotoBiostatistics25
• Oftenthecasethatadditionalissuesarise§ difficultiesinrecruitment
§ imbalancebetweenstudyarms
§ non-compliancewiththestudyprotocol(seelater)
§ drop-out
§ lowerthananticipatedeventrate
• Eachofthesewilllikelyrequiresomemodificationtothestatisticalanalysisplan
• Dangerinthatitopensthedoortotheperceptionthattheresultsmaynotbe“objective”§ strongargumenttothinkaboutthesethingsup-front
§ sensitivityanalyseswilllikelybeimportant
Per-protocolvs.intent-to-treatanalyses
HST190:IntrotoBiostatistics26
• Akeycomponentoftheprotocolisadetailedspecificationofwhatthe“intervention”is§ timing(e.g.singlevsatmultipletimepoints)
§ dosage,byarmandovertime
§ modificationsthatmaybeclinicallynecessary,suchascontraindicationsoradverseevents
• Ideally,patientsandstudystafffollowthisprotocol
• Inreality,deviationscanoccur§ non-compliancewithdosingand/orschedule
§ treatmentswitching
§ concomitanttreatment
HST190:IntrotoBiostatistics27
• Impactofdeviationsfromtheprotocol?
• Supposetherearedeviationsfromtheprotocol
• Onecouldproceedwithananalysisthatattemptstorecoverwhatwewouldhaveseenhadtherebeennodeviations§ per-protocol(PP)analysis
§ onlyincludeonfollow-upduringwhichtheprotocolwasadheredto
§ statisticaladjustmentstoaddresspotentialbiasthatmaybeintroduced
• Analternativewouldbetoignorethefactthatthedeviationsoccur§ intent-to-treat(ITT)analysis
§ maynotreflectthe“biologicaleffect”butis,arguably,betteralignedwitheffectsthatwewouldseeinthe“realworld”
Subgroupanalyses
HST190:IntrotoBiostatistics28
• Theresultsfromclinicaltrialsaretypicallyreportedintheformofasinglecontrast§ acrossallparticipants
§ intentionisthattheresultsbegeneralizabletothestudypopulation
• Itmaybeplausiblethattheeffectofaninterventiondiffersindifferentsub-populations§ treatmenteffectheterogeneity
§ e.g.bydiseaseseverityatpresentation
§ e.g.bysomesocio-demographicfactor,likeageorsex
§ e.g.bysomegenomicmarker
HST190:IntrotoBiostatistics29
• Salloway etal(NEJM,2014)§ Bapineuzumab asatreatmentforAlzheimer’sdisease
§ twodouble-blinded,randomized,placebo-controlledPhaseIIItrialso APOEε4 allele carriers
o APOEε4 allele noncarriers
§ co-primaryendpoints:o Alzheimer'sDiseaseAssessment
Scale(ADAS-cog11)
o DisabilityAssessmentfor
Dementia(DAD)
HST190:IntrotoBiostatistics30
• Subgroupanalysesshouldbepre-specified§ ideally,inthestudyprotocol
• Evenifnotpre-specified,maybeimportantasameanstogeneratepreliminarydataforfuturestudies
• Statisticalassessmentofheterogeneityacrosssubgroupsviaaninteractiontest
• Subgroupanalyses,however,aresusceptibilityto§ falsepositivesbecauseofmultipletestingacrosssubgroups
§ falsenegativesbecauseoflowsamplesizewithinsubgroups
• Myownapproach:§ reportallsubgroupanalyses(i.e.notjustthosethathavep<0.05)
§ donotreportintheAbstract(i.e.justintheResults)
Interimmonitoring
HST190:IntrotoBiostatistics31
• Insomeinstances,itmaybedesirabletostopatrialearly§ efficacy,safetyorfutility
• Toinformsuchadecisionatrialmightpre-specifyinterimanalyses§ performedatasetofpre-specifiedtimesduringthetrial
§ e.g.onthebasisofpatientaccrual
• Decisiontostopistypicallymadebyadatasafetyandmonitoringboard(DSMB)§ independentboardofclinicians,statisticians,patientadvocates,andethicists
§ alsoreviewstudyprogress(e.g.accrualandconduct),andadverseevents
HST190:IntrotoBiostatistics32
• Advantages:§ findeffectivetreatmentquickly
§ minimizeexposuretoanunsafetreatment
§ savemoneyandtimeonineffectivetreatment
• Disadvantages:§ mayloseopportunitytogaininformationonsecondaryendpoints
• Requiresadjustmentstotheanalysistoensuretheoverallalphalevel§ thereisanopportunitytomakea“mistake”ateachinterimanalysis
§ desirabletopreservetheoverallP(rejectH0|H0 istrue)
• Interimmonitoringparameters§ numberofinterimanalyses
§ stoppingrule
Evidencetriangle
HST190:IntrotoBiostatistics33
SimpleLinearRegression
• Sofarwehavefocusedonstudieswherethereareafixednumber(typicallytwo)groupsbeingcompared§ Lecture3:hypothesistesting
§ Lecture4:clinicaltrials
• Framedthroughaninvestigationoftheassociationbetweentreatmentchoiceandsomeclinicalendpoint
• Achievedbycomparingsomepopulationparameter,suchasthemeanormedian,ofY within“levels”of𝑋§ e.g.E Y X = 1 − 𝐸 𝑌 𝑋 = 0 = 𝜇, − 𝜇-
• Note,thiscomparisoncanbeviewedasasummaryofthejointdistributionof(𝑋,Y)
HST190:IntrotoBiostatistics34
HST190:IntrotoBiostatistics35
• Considerthequestion:Whatistheassociationbetweengestationalageandbirthweight?§ dataonbirthstofirst-timemothersinNorthCarolinabetween2003and2004
• “Exposure”iscontinuous,andnotreallyamendabletothe“twogroup”paradigm
• Needtothinkofanalternativewayofsummarizingthejointdistributionofgestationalageandbirthweightsothatwecanlearnabouttheirassociation
Gestational age, weeks
Wei
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