Planning and Analyzing Clinical Trials with Composite Endpoints.pdf

Springer Series in Pharmaceutical StatisticsGeraldineRauchSvenjaSchlerMeinhardKieserPlanning and Analyzing Clinical Trials with Composite EndpointsSpringer Series in Pharmaceutical StatisticsEditorsF.BretzP.MllerT.PermuttJ.PinheiroMore information about this series at http:/ Rauch Svenja SchR uler Meinhard KieserPlanning and AnalyzingClinical Trialswith Composite Endpoints123Geraldine RauchInstitute of Biometry and ClinicalEpidemiologyCharit-UniversitR atsmedizin BerlinBerlin,GermanySvenja SchR ulerInstitute of Medical Biometry andInformaticsUniversity of HeidelbergHeidelberg,GermanyMeinhard KieserInstitute of Medical Biometry andInformaticsUniversity of HeidelbergHeidelberg,GermanyISSN 2366-8695ISSN 2366-8709(electronic)Springer Series in Pharmaceutical StatisticsISBN 978-3-319-73769-0ISBN 978-3-319-73770-6(eBook)https:/doi.org/10.1007/978-3-319-73770-6Library of Congress Control Number:2017964233Mathematics Subject Classification(2010):62L05,62P10 Springer International Publishing AG,part of Springer Nature 2017This work is subject to copyright.All rights are reserved by the Publisher,whether the whole or part ofthe material is concerned,specifically the rights of translation,reprinting,reuse of illustrations,recitation,broadcasting,reproduction on microfilms or in any other physical way,and transmission or informationstorage and retrieval,electronic adaptation,computer software,or by similar or dissimilar methodologynow known or hereafter developed.Theuseofgeneral descriptive names,registered names,trademarks,service marks,etc.in this publicationdoes not imply,even in the absence of a specific statement,that such names are exempt from the relevantprotective laws and regulations and therefore free for general use.The publisher,the authors and the editors are safe to assume that the advice and information in this bookare believed to be true and accurate at the date of publication.Neither the publisher nor the authors orthe editors give a warranty,express or implied,with respect to the material contained herein or for anyerrors or omissions that may have been made.The publisher remains neutral with regard to jurisdictionalclaims in published maps and institutional affiliations.Printed on acid-free paperThis Springer imprint is published by the registered company Springer International Publishing AG partof Springer Nature.The registered company address is:Gewerbestrasse 11,6330 Cham,SwitzerlandWe would like to thank our colleagues fromthe Institute of Medical Biometry andInformatics,University of Heidelberg,formany discussions on the topic of compositeendpoints and for reviewing parts of the text,especially Eva Dlger,Ann-Kathrin Ozga,and Stella Preussler.In addition,we aregrateful to Springer Publishers for thedecision to publish this book.A specialthanks goes to our editor Dr.Eva Hiripi forher continuous encouragement and supportfor this project.PrefaceComposite endpoints are often used as primary efficacy variables for clinical trials,particularly in the field of oncology and cardiology.These endpoints combineseveral variablesof interest within a single composite measure.By this,all variableswhich are of major clinical relevance can be considered in the primary analysiswithout the need to adjust for multiplicity.Moreover,it is intended to enlarge thenumber 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 ofinterest correspond to rather rare events.This concept can be illustrated by meansof a fairytale.Each of the following animalsdonkey,dog,cat,and cocktakenon its own has a relatively small height.Putting these animals on top of each other,they form the“Bremer Town Musicians”(Bremer Stadtmusikanten)which are nowvery large and impressive.Coming back to real clinical trial applications in oncology and cardiology,themost relevant endpoint often corresponds to“death”.However,if the survivalprognosis of the patient population of interest is not too bad,then it might notbe feasible to wait until an effect in the death rates can be observed.To resolvethis problem,the outcome“death”might be combined with other disease-relatedevents which occur more frequently.There exist some major challenges whenusing 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 isbased on more parameter assumptions as compared to a clinical trial with asingle-variable primary endpoint.Thus,the target sample size is often subjectto a high level of uncertainty.This is due to the fact that the assumed effectfor the composite endpoint which is used for sample size calculation dependsboth on the effects in the single components and on the correlation betweenthem.On the other hand,the interpretation of composite endpoints can be dif-ficult,as the observed effect for the composite does not necessarily reflectsthe effects for the single components.Therefore,it might not be adequate toviiviiiPrefacejudge the efficacy of a new intervention exclusively based on the compositeeffect.This book is structuredinto six parts.In Part I,the general concepts of compositeendpoints are introduced.In Chap.1,we begin by defining composite endpointsand by providing the rationale for the application of composite primary endpointsin clinical practice.In Chap.2,the challenges resulting from the use of compositeendpoints are introduced and discussed.Chapter 3 presents recommendations andopen issues related to composite endpoints which are discussed by current guide-lines in the field of clinical trial methodology,benefit-risk and health technologyassessment,as well as by disease-specific guidelines.Part I concludes with Chap.4where an overview of some exemplary clinical trials is given which illustratedifferent aspects related to composite endpoints.In Part II,we formulate the mathematical background of the underlying testproblem.In this part of the book,we focus on a confirmatory test problem whichis formulated for a single(composite)endpoint.The underlying test hypotheses,the test statistics,as well as strategies for sample size calculation are provided forcomposite binary endpoints as well as for composite time-to-first-event endpointswithinthecontextofclassical single-stagedesigns(Chap.5)andingroup-sequentialor adaptive designs(Chap.6).In Chap.7,exemplary source code written in thesoftware R implementing the different approaches introduced in Part II is providedto ease the application in practice.In Part III,the focus lies on multiple test problems which are of interest ifthe composite endpoint alone is not sufficient to provide enough information ontreatment efficacy and is therefore simultaneously tested along with its individual(main)components to ease the interpretation of the results.Chapter 8 providesa general mathematical introduction on how to derive the correlation betweenthe test statistics of a composite endpoint and an individual component.Thiscorrelation structure can be implemented within a multiple test procedure inseveral ways.As before in Part II,the test hypotheses,the test statistics,as wellas the sample size calculation algorithms are provided for classical single-stagedesigns in Chap.9 and for group-sequential or adaptive designs in Chap.10.Again,Part III concludes with a Chap.11 providing R code to implement the differentmethods.A completely different approach to ease the interpretation of a compositeendpointwithoutformulatinga multipletest problemis to directlydefinea weightedcompositeeffect measure,where the weights reflect the clinical relevanceof the dif-ferent components.Part IV presents weighted effect measures for composite binaryendpoints in Chap.12 and for composite time-to-first-event endpoints in Chap.13.Moreover,alternative weighting strategies which are prominently discussed in thePrefaceixstatistical and medical literature are critically reviewed in Chap.14.As in theprevious parts,Part IV concludes with a Chap.15 providing the related R code ofthe different methodologies.Whereas Parts IIIV are dedicated to the formulation of an adequate teststrategy for the confirmatory efficacy proof based on the composite endpoint,theaim of Part V is to address the issue of additionally evaluating the individualcomponents which is a standard guideline recommendation.In Chap.16,severalcommonly met descriptive methods to assess the impact of the treatment underinvestigation on the individual components are discussed.In contrast,Chap.17investigates simple confirmatory analysis strategies to potentially obtain additionalconfirmatory evidence for the components even if the underlying multiple testproblem does not correspond to the formal efficacy claim for which the trial ispowered.As before,Chap.18 provides the corresponding R code of the discussedmethods.Finally,Part VI is dedicated to illustrate all methods presented within thisbook by means of real clinical trial scenarios.As for a specific clinical trial thedefinition of an adequate planning and analysis strategy requires implementation ofseveral aspects and methods discussed within this book,we decided to provide anentire exemplary part at the end of the book instead of illustrating each methodseparately.Moreover,there often exist several alternative planning or analysisapproaches to address the trial-specific challenges which should be comparedand outweighed against each other.We therefore decided to recall the exemplaryclinical trials first introduced in Chap.4 in Part I and to present different planningand analysis strategies for each of them subsequently.By this,the differentstatistical approaches along with their advantages and challenges can be directlycompared.Part VI is divided into Chap.19 describing clinical trial scenarios for(composite)binary endpoints and Chap.20 addressing(composite)time-to-first-event endpoints.In conclusion,this book gives a comprehensive overview on all importantissues on how to plan and evaluate clinical trials with a composite primaryendpoint to assure the choice of proper and efficient methods as well as aclinically meaningful and valid interpretation of the results.The book givespractical advice for statisticians and for medical experts involved in the plan-ning and analysis of clinical trials.For readers from the mathematical field,wealso 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 easyxPrefaceimplementation.The book also discusses all presented methods in the context ofrelevant guidelines related to the topic.Therefore,the book addresses many issueswhich are relevant for biostatisticians and medical experts involved in clinicalresearch.Berlin,GermanyGeraldine RauchHeidelberg,GermanySvenja SchlerHeidelberg,GermanyMeinhard KieserFebruary 2018ContentsPart IGeneral Introduction to Composite Endpoints1Definition and Rationale.31.1Definitions and Types of Composite Endpoints.31.1.1Composite Binary Event Endpoints.31.1.2Composite Time-to-First-Event Endpoints.41.1.3A Note on Clinical Scores.51.2Rationale for the Use of Composite Endpoints.51.2.1Augmenting Power.61.2.2Avoiding Multiplicity.6References.62Challenges of Composite Endpoints.92.1Uncertainties in the Planning Stage.92.2Interpretation of Results.92.3Competing Risks as a Source of Bias.102.4Follow-Up Beyond the First Event.11References.123Guideline View:Recommendations and Requirements.133.1Guidelines Related to Composite Endpoints.133.2Guideline Recommendations.153.3Beyond the Guidelines:Open Issues.17References.184Clinical Trial Examples.214.1The Osteoporosis Trial.214.2The MOMS Trial.224.3The OMEGA Trial.224.4The RENAAL Trial.234.5The DREAM Trial.24xixiiContents4.6The CAPRICORN Trial.244.7The LIFE Trial.25References.26Part IIConfirmatory Test Problem for a Single(Composite)Endpoint5The Single-Stage Design.315.1Binary Endpoints.315.1.1Test Problem.335.1.2Test Statistics.345.1.3Sample Size Calculation.365.1.3.1Standard Sample Size Calculation.365.1.3.2Robust Sample Size Calculation.385.2Time-to-Event Endpoints Under Proportional Hazards.395.2.1Test Problem.405.2.2Test Statistics.415.2.3Sample Size Calculation.425.2.3.1Standard Sample Size Calculation.425.2.3.2Robust Sample Size Calculation.445.3Time-to-Event Endpoints for Non-proportionalHazards.455.3.1Test Problem.475.3.2Test Statistics.485.3.3Sample Size Calculation.485.4Recurrent Event Analysis.48References.506Group-Sequential and Adaptive Designs.536.1Stage-Wise Local Levels.546.1.1Choice of Stage-Wise Local Levels.546.2Stage-Wise Test Statistics for Binary Endpoints.556.3Stage-Wise Test Statistics for Time-to-Event Endpoints.566.4Incorporating Stopping for Futility.586.4.1Choice of Futility Boundaries.606.5Sample Size Calculation.616.5.1Sample Size Calculation for Group-SequentialDesigns.616.5.2Sample Size Recalculation for Adaptive Designs.62References.637Related Software Code.657.1Sample Size Calculation Based on Expected Powerfor a Binary Endpoint.657.2Sample Size Calculation for the Average Hazard Ratio.69Contentsxiii7.3Calculation of the OCS Futility Boundary.737.3.1OCS Futility Boundary for a Binary Endpoint.737.3.2OCS Futility Boundary for a Time-to-EventEndpoint.78Part IIIConfirmatory Multiple Test Problem8Correlation Between Test Statistics.878.1Composite Binary Endpoints.878.2Composite Time-To-First-Event Endpoints.89References.909The Single-Stage Design.919.1Formulation of the Multiple Test Problem.919.1.1Intersection-Union Test.919.1.1.1Sample Size Calculation for the IUT.929.1.2Union-Intersection Test.939.1.2.1Sample Size Calculation for the UIT.959.1.3Effect Consistency Approach.969.1.3.1Sample Size Calculation for the ECA.99References.9910Group-Sequential and Adaptive Designs.10110.1Intersection-Union Test.10110.1.1Sample Size Calculation for the IUT.10210.2Union-Intersection Test.10210.2.1Sample Size Calculation for Group-SequentialDesigns.10410.2.2Sample Size Recalculation Within Adaptive Designs.104References.10611Related Software Code.10711.1Sample Size Calculation for the IUT.10711.2Sample Size Calculation for the UIT.11111.3Correlation-Adjusted Local Levels.11511.4Implementation of the ECA.11711.4.1ECA for Binary Endpoints.11711.4.2ECA for Time-to-Event Endpoints.12411.5Adaptive Bonferroni and Bonferroni-Holm.13111.5.1Adaptive Bonferroni and Bonferroni-Holmfor Binary Endpoints.13111.5.2Adaptive Bonferroni and Bonferroni-Holmfor Time-to-Event Endpoints.136xivContentsPart IVConfirmatory Test Problem for a Weighted CompositeEndpoint12Weighted Composite Binary Endpoint.14512.1Weighted Risk Difference.14512.1.1Considerations on the Choice of Weights.14712.1.2Test Problem.14712.1.3Test Statistic.14712.1.4Sample Size Calculation.148References.14913Weighted Composite Time-to-Event Endpoint.1511