Group Sequential and Confirmatory Adaptive Designs in Clinical Trials

310 Pages·2016·9.52 MB·English

by  Gernot Wassmer

Springer Series in Pharmaceutical Statistics
Gernot Wassmer
Werner Brannath
Group Sequential
and Confi rmatory
Adaptive Designs
in Clinical Trials
Springer Series in Pharmaceutical Statistics
Editors
F.Bretz
P.MuRller
T.Permutt
J.Pinheiro
Moreinformationaboutthisseriesathttp://www.springer.com/series/15122
Gernot Wassmer • Werner Brannath
Group Sequential
and Confirmatory Adaptive
Designs in Clinical Trials
123
GernotWassmer WernerBrannath
UniversityofCologne UniversityofBremen
Cologne,Germany Bremen,Germany
ISSN2366-8695 ISSN2366-8709 (electronic)
SpringerSeriesinPharmaceuticalStatistics
ISBN978-3-319-32560-6 ISBN978-3-319-32562-0 (eBook)
DOI10.1007/978-3-319-32562-0
LibraryofCongressControlNumber:2016945375
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Preface
During the last two decades, there was an intensive discussion of a statistical
methodology for clinical trials that generalized the use and conduct of interim
analyses. Using a specific methodology, under control of the Type I error rate,
it was made possible to redesign the trial for the forthcoming stages in relevant
detailsincludingsamplesize,consideredtreatmentarms,subgroupsofpatients,and
others.Theuseofsuchmulti-stageadaptivedesignswasintroducedinanarticleby
PeterBauerentitled“Multi-stagetestingwithadaptivedesigns.”Itappeared1989in
the GermanjournalBiometrie undInformatikin Medizin undBiologie.Especially
thepublicationbyBauerandKöhne1994inBiometricsraisedmanycontroversial
discussions.Inthemeantime,theunderlyingconceptisregardedasarelevantand
importantgeneralizationofthe“classical”groupsequentialdesignmethodology.It
has even found its way into a reflection paper entitled “MethodologicalIssues in
ConfirmatoryClinicalTrialsPlannedWithanAdaptiveDesign”fromtheEuropean
MedicinesAgency(EMA2007),a draftguidanceon“AdaptiveClinicalTrialsfor
DrugandBiologics”fromtheUSFoodandDrugAdministration(FDA2010),and
a draft guidanceon “Adaptive Designs for MedicalDevice Clinical Studies,” also
fromtheUSFoodandDrugAdministration(FDA2015).
This book describes the adaptive design methodology from the standpoint of
confirmatory testing of statistical hypotheses. That is, the problem is to derive
proceduresthatcontrol,atleast approximately,the TypeI errorirrespectiveofthe
data-drivenredesignof the trial. We do notconsiderother veryrelevant“adaptive
topics” such as adaptive dose finding, response adaptive randomization,Bayesian
designmethodology,oradaptiveregressionmodeling.Here,TypeIerrorratecontrol
is not the major issue, and the methodology is often applied in the exploratory
caseonly.Thisissaidwithoutdiminishingitsimportanceandrelevanceforclinical
trials.Wealsoexplicitlyexcludethediscussionofblindedsamplesizereassessment
whichisoneofthesimplestadaptivedesignsandusuallyconsistsoftwostagesin
which the sample size for the second stage is determined based on the first-stage
datainablindedway(forareviewofthesemethods,seeFriedeandKieser2006).
We alsodonotexplicitlydiscusstheregulatoryperspectivesandoperationofdata
monitoringcommittees(forthis,seeDeMetsetal.2006;Ellenbergetal.2003;He
v
vi Preface
et al. 2014; Herson 2009) although we briefly discuss some practical aspects for
adaptivedesignsattheendofthebook.
The most relevant, comprehensive, and modern books on group sequential
methodologyinclinicaltrialsareWhitehead(1997),JennisonandTurnbull(2000),
Moyé (2006), Proschan et al. (2006), and Bartroff et al. (2013); we also refer to
overviewarticlesofWhitehead(2001),Todd(2007),MazumbdarandBang(2008),
andWassmer(2009).BooksandcollectionsonadaptivedesignsareChang(2014),
Chin (2012), Chow and Chang (2006), He et al. (2014), Pong and Chow (2011),
Schmitz(1993),Vandemeulebroecke(2008),andWassmer(2010).Recently,Bauer
et al. (2016) provide a critical overview and perspectives of 25 years of adaptive
designs.
In thismonograph,we giveanoverviewanda basic introductionintoboth,the
group sequential and the adaptive design methodology.Wassmer (1999c) already
gaveanearlyattempt(inGerman)tosummarizetheapproaches;thecurrentbookis
partlydevelopedfromthetranslationandtheextensionofthissmallbook.Itisalso
Proschan et al. (2006), who already explicitly considered the adaptive extension
within a unified approach; in our book there will be the focus on the adaptive
designs.
The monograph consists of three parts. The first part provides the group
sequential methods that are necessary for the understanding and the application
of the generalization to the adaptive methodology supplied in Parts II and III of
the book. We try to provide the necessary details as well as an insight into the
complexityandrichnessofthesedesignsincludingtheestimationproblemandmore
flexible designs when using this “classical” approach. It is by no means intended
to givea completesurveyofgroupsequentialdesigns(orevensequentialtheory).
Especially the books of Jennison and Turnbull (2000) and Proschan et al. (2006)
provide a much deeper insight into this methodology, but we hope to provide an
elementaryintroductioninthisarea.
PartIIisthecoreofthemonograph.Itderivestheadaptivedesignmethodology
asitwasintroducedinthemid-1990softhelastcentury.Thetwobasicapproaches
of Bauer and Köhne (1994) and Proschan and Hunsberger (1995), which are
the combination testing principle and the conditional error function approach,
respectively, are presented in Chap.6 in a unified framework, together with some
relevant generalizations of the principles. Chapter 7 describes decision tools that
can be used for adaptive decision making where here we only consider the case
of sample size reassessment based on conditional power and related tools. In
Chap.8, we describesolutionsfor the estimation problemin adaptivedesignsand
also discuss some open issues. Adaptive designs with survival data involve some
difficultieswhicharediscussedinChap.9.
Primarily,thefocusofflexibledesignswasonsamplesizereassessmentalthough
fromtheverybeginningitwasalreadyemphasizedthattheprincipleallowsmuch
more general design adaptations including a data-driven selection of hypotheses
withinasetofhypotheses.ThisisthetopicofPartIIIwherewedescribetheclosed
testingprincipleanditsuseinadaptivemulti-stagedesignswithmultiplehypothe-
ses. It is the nowadays highlighted topic. The most prominent applications are
Preface vii
adaptive multi-arm trials or adaptive population enrichment designs. We describe
theseinChap.11togetherwithsomeclinicaltrialexamples.Thereisstillongoing
researchinthisarea,andwehopetogiveanup-to-datereviewoftheapproachesthat
were proposedin the literature. We admit that we were notable to include all the
differentaspectsintheconsiderationsoftheseoreventhemoreelementaryadaptive
designs.Particularly,thereferencescannotconsiderallpapersthatwerepublished
in this excitingarea of the statistical methodology.Prophylactically,we apologize
thatwemissedtocitesomeimportantwork.Weweresimplynotabletociteallthe
numerousarticlesthathavebeenpublishedinthelasttwodecades.
Wethankthemanycolleaguesthatwentalongwithusinthelast20years.1995
and1998weretheyearswhenwe(GWandWB,respectively)startedresearchinthe
adaptivedesignmethodology.Itistoomuchtoexplicitlynameallofthecolleagues
who contributed and discussed the topics with us; to name all of them is easier
andlessproblematicwithrespecttoforgettingsomeone.WeespeciallythankFrank
BretzandSilkeJörgensforprovidinginputonrelevanttopicsforthebook.Wealso
thankthepublisherforhissupportonthemanuscript.Lastbutnotleast,wewantto
thankourwives,AnneandStela,andourchildrenforacceptingandsupportingour
work.
Cologne,Germany GernotWassmer
Bremen,Germany WernerBrannath
October2015

Contents
PartI GroupSequentialDesigns
1 RepeatedSignificanceTests ............................................... 3
1.1 Introduction........................................................... 3
1.2 Basics................................................................. 7
1.3 PowerandAverageSampleSize .................................... 15
1.4 TheRecursiveIntegrationFormula.................................. 20
2 ProcedureswithEquallySizedStages ................................... 25
2.1 ClassicalDesigns..................................................... 26
2.1.1 Definition ................................................... 26
2.1.2 PowerandAverageSampleSize........................... 30
2.1.3 WangandTsiatisPowerFamily ........................... 36
2.1.4 OtherDesigns............................................... 42
2.2 SymmetricDesigns................................................... 43
2.3 One-SidedDesigns................................................... 50
2.4 ANoteonTwo-SidedDesigns ...................................... 62
3 ProcedureswithUnequallySizedStages................................. 63
3.1 EffectofUsingBoundariesforEquallySizedStages.............. 64
3.2 SampleSizesFixedinAdvance..................................... 69
3.3 The˛-SpendingFunctionApproach................................ 74
4 ConfidenceIntervals,p-Values,andPointEstimation ................. 83
4.1 ConfidenceIntervalsandp-Values .................................. 84
4.1.1 SampleSpaceOrderings ................................... 84
4.1.2 MonitoringaTrial.......................................... 91
4.2 PointEstimation...................................................... 95
ix