Repeated_Measures_Design_with_Generalized linear mixed models for RCTs.pdf

Toshiro TangoCenter for Medical Statistics Minato-ku Tokyo Japan Harry YangRepeated Measures Design with Generalized Linear Mixed Models for Randomized Controlled TrialsEditor-in-ChiefShein-Chung Chow,Ph.D.,Professor,Department of Biostatistics and Bioinformatics,Duke University School of Medicine,Durham,North Carolina Series Editors Byron Jones,Biometrical Fellow,Statistical Methodology,Integrated Information Sciences,Novartis Pharma AG,Basel,SwitzerlandJen-pei Liu,Professor,Division of Biometry,Department of Agronomy,National Taiwan University,Taipei,TaiwanKarl E.Peace,Georgia Cancer Coalition,Distinguished Cancer Scholar,Senior Research Scientist and Professor of Biostatistics,Jiann-Ping Hsu College of Public Health,Georgia Southern University,Statesboro,Georgia Bruce W.Turnbull,Professor,School of Operations Research and Industrial Engineering,Cornell University,Ithaca,New YorkPublished TitlesAdaptive Design Methods in Clinical Trials,Second Edition Shein-Chung Chow and Mark ChangAdaptive Designs for Sequential Treatment Allocation Alessandro Baldi Antognini and Alessandra GiovagnoliAdaptive Design Theory and Implementation Using SAS and R,Second EditionMark ChangAdvanced Bayesian Methods for Medical Test Accuracy Lyle D.BroemelingAnalyzing Longitudinal Clinical Trial Data:A Practical Guide Craig Mallinckrodt and Ilya LipkovichApplied Biclustering Methods for Big and High-Dimensional Data Using R Adetayo Kasim,Ziv Shkedy,Sebastian Kaiser,Sepp Hochreiter,and Willem TalloenApplied Meta-Analysis with R Ding-Geng(Din)Chen and Karl E.PeaceApplied Surrogate Endpoint Evaluation Methods with SAS and R Ariel Alonso,Theophile Bigirumurame,Tomasz Burzykowski,Marc Buyse,Geert Molenberghs,Leacky Muchene,Nolen Joy Perualila,Ziv Shkedy,and Wim Van der Elst Basic Statistics and Pharmaceutical Statistical Applications,Second Edition James E.De MuthBayesian Adaptive Methods for Clinical Trials Scott M.Berry,Bradley P.Carlin,J.Jack Lee,and Peter Muller Bayesian Analysis Made Simple:An Excel GUI for WinBUGS Phil Woodward Bayesian Designs for Phase III Clinical Trials Ying Yuan,Hoang Q.Nguyen,and Peter F.Thall Bayesian Methods for Measures of Agreement Lyle D.BroemelingBayesian Methods for Repeated Measures Lyle D.BroemelingBayesian Methods in Epidemiology Lyle D.BroemelingBayesian Methods in Health Economics Gianluca BaioBayesian Missing Data Problems:EM,Data Augmentation and Noniterative Computation Ming T.Tan,Guo-Liang Tian,and Kai Wang NgBayesian Modeling in Bioinformatics Dipak K.Dey,Samiran Ghosh,and Bani K.MallickBenefit-Risk Assessment in Pharmaceutical Research and Development Andreas Sashegyi,James Felli,and Rebecca NoelBenefit-Risk Assessment Methods in Medical Product Development:Bridging Qualitative and Quantitative Assessments Qi Jiang and Weili HeBioequivalence and Statistics in Clinical Pharmacology,Second Edition Scott Patterson and Byron JonesBiosimilar Clinical Development:Scientific Considerations and New Methodologies Kerry B.Barker,Sandeep M.Menon,Ralph B.DAgostino,Sr.,Siyan Xu,and Bo JinBiosimilars:Design and Analysis of Follow-on Biologics Shein-Chung ChowBiostatistics:A Computing Approach Stewart J.AndersonCancer Clinical Trials:Current and Controversial Issues in Design and Analysis Stephen L.George,Xiaofei Wang,and Herbert Pang Causal Analysis in Biomedicine and Epidemiology:Based on Minimal Sufficient Causation Mikel AickinClinical and Statistical Considerations in Personalized Medicine Claudio Carini,Sandeep Menon,and Mark ChangClinical Trial Data Analysis using R Ding-Geng(Din)Chen and Karl E.PeaceClinical Trial Methodology Karl E.Peace and Ding-Geng(Din)ChenComputational Methods in Biomedical Research Ravindra Khattree and Dayanand N.NaikComputational Pharmacokinetics Anders KllnConfidence Intervals for Proportions and Related Measures of Effect Size Robert G.NewcombeControversial Statistical Issues in Clinical Trials Shein-Chung ChowData Analysis with Competing Risks and Intermediate States Ronald B.GeskusData and Safety Monitoring Committees in Clinical Trials,Second Edition Jay HersonDesign and Analysis of Animal Studies in Pharmaceutical Development Shein-Chung Chow and Jen-pei LiuDesign and Analysis of Bioavailability and Bioequivalence Studies,Third Edition Shein-Chung Chow and Jen-pei LiuDesign and Analysis of Bridging Studies Jen-pei Liu,Shein-Chung Chow,and Chin-Fu HsiaoDesign&Analysis of Clinical Trials for Economic Evaluation&Reimbursement:An Applied Approach Using SAS&STATA Iftekhar Khan Design and Analysis of Clinical Trials for Predictive Medicine Shigeyuki Matsui,Marc Buyse,and Richard Simon Design and Analysis of Clinical Trials with Time-to-Event Endpoints Karl E.Peace Design and Analysis of Non-Inferiority Trials Mark D.Rothmann,Brian L.Wiens,and Ivan S.F.ChanDifference Equations with Public Health Applications Lemuel A.Moy and Asha Seth KapadiaDNA Methylation Microarrays:Experimental Design and Statistical Analysis Sun-Chong Wang and Arturas PetronisPublished TitlesDNA Microarrays and Related Genomics Techniques:Design,Analysis,and Interpretation of Experiments David B.Allison,Grier P.Page,T.Mark Beasley,and Jode W.EdwardsDose Finding by the Continual Reassessment Method Ying Kuen CheungDynamical Biostatistical Models Daniel Commenges and Hlne Jacqmin-GaddaElementary Bayesian Biostatistics Lemuel A.MoyEmerging Non-Clinical Biostatistics in Biopharmaceutical Development and Manufacturing Harry YangEmpirical Likelihood Method in Survival Analysis Mai ZhouEssentials of a Successful Biostatistical Collaboration Arul EarnestExposureResponse Modeling:Methods and Practical Implementation Jixian Wang Frailty Models in Survival Analysis Andreas WienkeFundamental Concepts for New Clinical Trialists Scott Evans and Naitee Ting Generalized Linear Models:A Bayesian Perspective Dipak K.Dey,Sujit K.Ghosh,and Bani K.MallickHandbook of Regression and Modeling:Applications for the Clinical and Pharmaceutical Industries Daryl S.PaulsonInference Principles for Biostatisticians Ian C.MarschnerInterval-Censored Time-to-Event Data:Methods and Applications Ding-Geng(Din)Chen,Jianguo Sun,and Karl E.PeaceIntroductory Adaptive Trial Designs:A Practical Guide with R Mark ChangJoint Models for Longitudinal and Time-to-Event Data:With Applications in R Dimitris RizopoulosMeasures of Interobserver Agreement and Reliability,Second Edition Mohamed M.ShoukriMedical Biostatistics,Third Edition A.IndrayanMeta-Analysis in Medicine and Health Policy Dalene Stangl and Donald A.Berry Methods in Comparative Effectiveness Research Constantine Gatsonis and Sally C.Morton Mixed Effects Models for the Population Approach:Models,Tasks,Methods and Tools Marc Lavielle Modeling to Inform Infectious Disease Control Niels G.BeckerModern Adaptive Randomized Clinical Trials:Statistical and Practical Aspects Oleksandr Sverdlov Monte Carlo Simulation for the Pharmaceutical Industry:Concepts,Algorithms,and Case Studies Mark ChangMultiregional Clinical Trials for Simultaneous Global New Drug Development Joshua Chen and Hui QuanMultiple Testing Problems in Pharmaceutical Statistics Alex Dmitrienko,Ajit C.Tamhane,and Frank Bretz Noninferiority Testing in Clinical Trials:Issues and Challenges Tie-Hua Ng Optimal Design for Nonlinear Response Models Valerii V.Fedorov and Sergei L.Leonov Published TitlesPublished TitlesPatient-Reported Outcomes:Measurement,Implementation and Interpretation Joseph C.Cappelleri,Kelly H.Zou,Andrew G.Bushmakin,Jose Ma.J.Alvir,Demissie Alemayehu,and Tara Symonds Quantitative Evaluation of Safety in Drug Development:Design,Analysis and Reporting Qi Jiang and H.Amy Xia Quantitative Methods for Traditional Chinese Medicine Development Shein-Chung Chow Randomized Clinical Trials of Nonpharmacological Treatments Isabelle Boutron,Philippe Ravaud,and David Moher Randomized Phase II Cancer Clinical Trials Sin-Ho Jung Repeated Measures Design with Generalized Linear Mixed Models for Randomized Controlled Trials Toshiro Tango Sample Size Calculations for Clustered and Longitudinal Outcomes in Clinical Research Chul Ahn,Moonseong Heo,and Song ZhangSample Size Calculations in Clinical Research,Second Edition Shein-Chung Chow,Jun Shao,and Hansheng WangStatistical Analysis of Human Growth and Development Yin Bun CheungStatistical Design and Analysis of Clinical Trials:Principles and Methods Weichung Joe Shih and Joseph AisnerStatistical Design and Analysis of Stability Studies Shein-Chung ChowStatistical Evaluation of Diagnostic Performance:Topics in ROC Analysis Kelly H.Zou,Aiyi Liu,Andriy Bandos,Lucila Ohno-Machado,and Howard RocketteStatistical Methods for Clinical Trials Mark X.NorleansStatistical Methods for Drug Safety Robert D.Gibbons and Anup K.AmatyaStatistical Methods for Healthcare Performance Monitoring Alex Bottle and Paul AylinStatistical Methods for Immunogenicity Assessment Harry Yang,Jianchun Zhang,Binbing Yu,and Wei ZhaoStatistical Methods in Drug Combination Studies Wei Zhao and Harry YangStatistical Testing Strategies in the Health Sciences Albert Vexler,Alan D.Hutson,and Xiwei Chen Statistics in Drug Research:Methodologies and Recent Developments Shein-Chung Chow and Jun ShaoStatistics in the Pharmaceutical Industry,Third Edition Ralph Buncher and Jia-Yeong TsaySurvival Analysis in Medicine and Genetics Jialiang Li and Shuangge MaTheory of Drug Development Eric B.HolmgrenTranslational Medicine:Strategies and Statistical Methods Dennis Cosmatos and Shein-Chung ChowCRC PressTaylor&Francis Group6000 Broken Sound Parkway NW,Suite 300Boca Raton,FL 33487-2742 2017 by Taylor&Francis Group,LLCCRC Press is an imprint of Taylor&Francis Group,an Informa businessNo claim to original U.S.Government worksPrinted on acid-free paperVersion Date:20170125International Standard Book Number-13:978-1-4987-4789-9(Hardback)This book contains information obtained from authentic and highly regarded sources.Reasonable efforts have been made to publish reliable data and information,but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use.The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained.If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint.Except as permitted under U.S.Copyright Law,no part of this book may be reprinted,reproduced,transmitted,or utilized in any form by any electronic,mechanical,or other means,now known or hereafter invented,including photocopying,microfilming,and recording,or in any information storage or retrieval system,without written permission from the publishers.For permission to photocopy or use material electronically from this work,please access (http:/ contact the Copyright Clearance Center,Inc.(CCC),222 Rosewood Drive,Danvers,MA 01923,978-750-8400.CCC is a not-for-profit organization that provides licenses and registration for a variety of users.For organizations that have been granted a photocopy license by the CCC,a separate system of payment has been arranged.Trademark Notice:Product or corporate names may be trademarks or registered trademarks,and are used only for identification and explanation without intent to infringe.Visit the Taylor&Francis Web site athttp:/and the CRC Press Web site athttp:/ContentsPrefacexiii1Introduction11.1Repeated measures design.11.2Generalized linear mixed models.41.2.1Model for the treatment effect at each scheduled visit41.2.2Model for the average treatment effect.91.2.3Model for the treatment by linear time interaction.101.3Superiority and non-inferiority.112Naive analysis of animal experiment data172.1Introduction.172.2Analysis plan I:Difference in means at each time point.182.3Analysis plan II:Difference in mean changes from baseline ateach time point.182.4Analysis plan III:Analysis of covariance at the last time point192.5Discussion.233Analysis of variance models253.1Introduction.253.2Analysis of variance model.253.3Change from baseline.283.4Split-plot design.323.5Selecting a good fit covariance structure using SAS.363.6Heterogeneous covariance.443.7ANCOVA-type models.474From ANOVA models to mixed-effects repeated measuresmodels534.1Introduction.534.2Shift to mixed-effects repeated measures models.544.3ANCOVA-type mixed-effects models.594.4Unbiased estimator for treatment effects.604.4.1Difference in mean changes from baseline.604.4.2Difference in means.604.4.3Adjustment due to regression to the mean.61viiviiiContents5Illustration of the mixed-effects models655.1Introduction.655.2The Growth Data.655.2.1Linear regression model.655.2.2Random intercept model.675.2.3Random intercept plus slope model.695.2.4Analysis using SAS.695.3The Rat Data.735.3.1Random intercept model.735.3.2Random intercept plus slope model.775.3.3Random intercept plus slope model with slopes varyingover time.786Likelihood-based ignorable analysis for missing data816.1Introduction.816.2Handling of missing data.816.3Likelihood-based ignorable analysis.846.4Sensitivity analysis.856.5The Growth Data.866.6The Rat Data.896.7MMRM vs.LOCF.907Mixed-effects normal linear regression models937.1Example:The Beat the Blues Data with 1:4 design.937.2Checking the missing data mechanism via a graphical procedure957.3Data format for analysis using SAS.967.4Models for the treatment effect at each scheduled visit.977.4.1Model I:Random intercept model.987.4.2Model II:Random intercept plus slope model.1007.4.3Model III:Random intercept plus slope model withslopes varying over time.1017.4.4Analysis using SAS.1017.5Models for the average treatment effect.1087.5.1Model IV:Random intercept model.1097.5.2Model V:Random intercept plus slope model.1107.5.3Analysis using SAS.1107.5.4Heteroscedastic models.1127.6Models for the treatment by linear time interaction.1147.6.1Model VI:Random intercept model.1157.6.2Model VII:Random intercept plus slope model.1167.6.3Analysis using SAS.1167.6.4Checking the goodness-of-fit of linearity.1187.7ANCOVA-type models adjusting for baseline measurement.1227.7.1Model VIII:Random intercept model for the treatmenteffect at each visit.122Contentsix7.7.2Model IX:Random intercept model for the averagetreatment effect.1247.7.3Analysis using SAS.1247.8Sample size.1297.8.1Sample size for the average treatment effect.1297.8.1.1Sample size assuming no missing data.1297.8.1.2Sample size allowing for missing data.1347.8.2Sample size for the treatment by linear time interaction 1447.9Discussion.1478Mixed-effects logistic regression models1498.1Example 1:The Respiratory Data with 1:4 design.1498.2Odds ratio.1518.3Logistic regression models.1528.4Models for the treatment effect at each scheduled visit.1558.4.1Model I:Random intercept model.1558.4.2Model II:Random intercept plus slope model.1578.4.3Analysis using SAS.1588.5Models for the average treatment effect.1678.5.1Model IV:Random intercept model.1678.5.2Mode