Planning and Analyzing Clinical Trials with Composite Endpoints

254 Pages·2017·2.286 MB·English

by  Geraldine Rauch, Svenja Schüler, Meinhard Kieser

Springer Series in Pharmaceutical Statistics
Geraldine Rauch
Svenja Schüler
Meinhard Kieser
Planning and
Analyzing
Clinical Trials
with Composite
Endpoints
Springer Series in Pharmaceutical Statistics
Editors
F.Bretz
P.Müller
T.Permutt
J.Pinheiro
Moreinformationaboutthisseriesathttp://www.springer.com/series/15122
Geraldine Rauch (cid:129) Svenja SchuRler (cid:129)
Meinhard Kieser
Planning and Analyzing
Clinical Trials
with Composite Endpoints
123
GeraldineRauch SvenjaSchuRler
InstituteofBiometryandClinical InstituteofMedicalBiometryand
Epidemiology Informatics
Charité-UniversitaRtsmedizinBerlin UniversityofHeidelberg
Berlin,Germany Heidelberg,Germany
MeinhardKieser
InstituteofMedicalBiometryand
Informatics
UniversityofHeidelberg
Heidelberg,Germany
ISSN2366-8695 ISSN2366-8709 (electronic)
SpringerSeriesinPharmaceuticalStatistics
ISBN978-3-319-73769-0 ISBN978-3-319-73770-6 (eBook)
https://doi.org/10.1007/978-3-319-73770-6
LibraryofCongressControlNumber:2017964233
MathematicsSubjectClassification(2010):62L05,62P10
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Wewouldliketothankourcolleaguesfrom
theInstituteofMedical Biometryand
Informatics,UniversityofHeidelberg, for
manydiscussionson thetopicofcomposite
endpointsandfor reviewingpartsof thetext,
especiallyEva Dölger,Ann-KathrinOzga,
andStellaPreussler.In addition,weare
gratefultoSpringerPublishersforthe
decisiontopublishthisbook. A special
thanksgoesto oureditorDr.Eva Hiripifor
hercontinuousencouragementand support
forthisproject.
Preface
Compositeendpointsareoftenusedasprimaryefficacyvariablesforclinicaltrials,
particularly in the field of oncology and cardiology. These endpoints combine
severalvariablesofinterestwithinasinglecompositemeasure.Bythis,allvariables
which are of major clinical relevance can be considered in the primary analysis
without the need to adjust for multiplicity. Moreover,it is intended to enlarge the
number of expected events and thereby to increase the power of the clinical trial.
For the latter reason, composite endpoints are often employed if the variables of
interestcorrespondto rather rareevents.This conceptcan be illustrated bymeans
of a fairytale. Each of the following animals—donkey,dog, cat, and cock—taken
onitsownhasarelativelysmallheight.Puttingtheseanimalsontopofeachother,
theyformthe“BremerTownMusicians”(BremerStadtmusikanten)whicharenow
verylargeandimpressive.
Coming back to real clinical trial applications in oncology and cardiology,the
most relevant endpoint often corresponds to “death”. However, if the survival
prognosis of the patient population of interest is not too bad, then it might not
be feasible to wait until an effect in the death rates can be observed. To resolve
this problem, the outcome “death” might be combined with other disease-related
events which occur more frequently. There exist some major challenges when
using such a composite endpoint as primary efficacy variable. On the one hand,
a serious difficulty in the planning stage is that the sample size calculation is
based on more parameter assumptions as compared to a clinical trial with a
single-variable primary endpoint. Thus, the target sample size is often subject
to a high level of uncertainty. This is due to the fact that the assumed effect
for the composite endpoint which is used for sample size calculation depends
both on the effects in the single components and on the correlation between
them. On the other hand, the interpretation of composite endpoints can be dif-
ficult, as the observed effect for the composite does not necessarily reflects
the effects for the single components. Therefore, it might not be adequate to
vii
viii Preface
judge the efficacy of a new intervention exclusively based on the composite
effect.
Thisbookisstructuredintosixparts.InPartI,thegeneralconceptsofcomposite
endpoints are introduced. In Chap.1, we begin by defining composite endpoints
and byprovidingthe rationalefor the applicationof compositeprimaryendpoints
in clinicalpractice.In Chap.2,the challengesresultingfromthe use ofcomposite
endpointsare introducedand discussed. Chapter 3 presents recommendationsand
open issues related to composite endpointswhich are discussed by currentguide-
lines in the field of clinical trial methodology, benefit-risk and health technology
assessment,aswellasbydisease-specificguidelines.PartIconcludeswithChap.4
where an overview of some exemplary clinical trials is given which illustrate
differentaspectsrelatedtocompositeendpoints.
In Part II, we formulate the mathematical background of the underlying test
problem.In this partof the book,we focus on a confirmatorytest problemwhich
is formulated for a single (composite) endpoint. The underlying test hypotheses,
the teststatistics, as wellas strategiesforsample size calculationare providedfor
composite binary endpointsas well as for composite time-to-first-eventendpoints
withinthecontextofclassicalsingle-stagedesigns(Chap.5)andingroup-sequential
or adaptive designs (Chap.6). In Chap.7, exemplary source code written in the
softwareRimplementingthedifferentapproachesintroducedinPartIIisprovided
toeasetheapplicationinpractice.
In Part III, the focus lies on multiple test problems which are of interest if
the composite endpoint alone is not sufficient to provide enough information on
treatment efficacy and is therefore simultaneously tested along with its individual
(main) components to ease the interpretation of the results. Chapter 8 provides
a general mathematical introduction on how to derive the correlation between
the test statistics of a composite endpoint and an individual component. This
correlation structure can be implemented within a multiple test procedure in
several ways. As before in Part II, the test hypotheses, the test statistics, as well
as the sample size calculation algorithms are provided for classical single-stage
designsinChap.9andforgroup-sequentialoradaptivedesignsinChap.10.Again,
Part III concludes with a Chap.11 providing R code to implement the different
methods.
A completely different approach to ease the interpretation of a composite
endpointwithoutformulatingamultipletestproblemistodirectlydefineaweighted
compositeeffectmeasure,wheretheweightsreflecttheclinicalrelevanceofthedif-
ferentcomponents.PartIVpresentsweightedeffectmeasuresforcompositebinary
endpointsinChap.12andforcompositetime-to-first-eventendpointsinChap.13.
Moreover,alternative weightingstrategieswhich are prominentlydiscussed in the
Preface ix
statistical and medical literature are critically reviewed in Chap.14. As in the
previousparts, Part IV concludeswith a Chap.15 providingthe related R code of
thedifferentmethodologies.
Whereas Parts II–IV are dedicated to the formulation of an adequate test
strategy for the confirmatory efficacy proof based on the composite endpoint, the
aim of Part V is to address the issue of additionally evaluating the individual
components which is a standard guideline recommendation. In Chap.16, several
commonly met descriptive methods to assess the impact of the treatment under
investigation on the individual components are discussed. In contrast, Chap.17
investigatessimpleconfirmatoryanalysisstrategiestopotentiallyobtainadditional
confirmatory evidence for the components even if the underlying multiple test
problem does not correspond to the formal efficacy claim for which the trial is
powered.As before,Chap.18 providesthe correspondingR code of the discussed
methods.
Finally, Part VI is dedicated to illustrate all methods presented within this
book by means of real clinical trial scenarios. As for a specific clinical trial the
definitionofanadequateplanningandanalysisstrategyrequiresimplementationof
severalaspectsandmethodsdiscussedwithin thisbook,we decidedto providean
entire exemplary part at the end of the book instead of illustrating each method
separately. Moreover, there often exist several alternative planning or analysis
approaches to address the trial-specific challenges which should be compared
and outweighed against each other. We therefore decided to recall the exemplary
clinicaltrialsfirst introducedin Chap.4 in PartI andto presentdifferentplanning
and analysis strategies for each of them subsequently. By this, the different
statistical approaches along with their advantages and challenges can be directly
compared. Part VI is divided into Chap.19 describing clinical trial scenarios for
(composite) binary endpoints and Chap.20 addressing (composite) time-to-first-
eventendpoints.
In conclusion, this book gives a comprehensive overview on all important
issues on how to plan and evaluate clinical trials with a composite primary
endpoint to assure the choice of proper and efficient methods as well as a
clinically meaningful and valid interpretation of the results. The book gives
practical advice for statisticians and for medical experts involved in the plan-
ning and analysis of clinical trials. For readers from the mathematical field, we
also provide the underlying statistical theory in order to give a sound math-
ematical background. For readers which are mainly interested in the applica-
tion of the methods, we illustrate all approaches with real clinical trial ex-
amples and moreover provide the required software code for a fast and easy
x Preface
implementation. The book also discusses all presented methods in the context of
relevantguidelinesrelatedtothetopic.Therefore,thebookaddressesmanyissues
which are relevant for biostatisticians and medical experts involved in clinical
research.
Berlin,Germany GeraldineRauch
Heidelberg,Germany SvenjaSchüler
Heidelberg,Germany MeinhardKieser
February2018