Statistical_Aspects_Of_The_Design_And_Analysis_Of_Clinical_Trials_（1999）.pdf

STATISTI(AL ASPKTS O F THE DlSlGN AND ANAlYSlS Of(lINI(A1 TRIALS STATISTICAL ASPECTS O F THE DESIGN AND ANAlYSlS O F (llNKA1 TRlAlS I Brian 5.Everitt Andrew Picklei lnrtitute of Piychiatry,London Univetrity of Monchertet Imperial College Press Published by Imperial College Press 57 Shelton Street Covent Garden London WC2H 9HE Distributed by World Scientific Publishing Co.Re.Ltd.P 0 Box 128,Farrer Road,Singapore 912805 USA ofice:Suite lB,1060 Main Street,River Edge,NJ 07661 UKofJice:57 Shelton Street,Covent Garden,London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.STATISTICAL ASPECTS OF THE DESIGN AND ANALYSIS OF CLINICAL TRIALS Copyright 0 1999 by Imperial College Press All rights reserved.This book,or parts thereof;may not be reproduced in any form or by any means,electronic or mechanical,including photocopying,recording or any information storage and retrieval system now known or to be invented,without written permission from the Publisher.For photocopying of material in this volume,please pay a copying fee through the Copyright Clearance Center,Inc.,222 Rosewood Drive,Danvers,MA 01923,USA.In this case permission to photocopy is not required from the publisher.ISBN 1-86094-153-2 This book is printed on acid-free paper.Printed in Singapore by Regal Press(S)Re.Ltd.PREFACE According to Sir David Cox,the randomised controlled clinical trial is perhaps the outstanding contribution of statistics to 20th century medical research.Nowadays about 8000 such trials are undertaken annually in all areas of medicine from the treatment of acne to the prevention of cancer.Although the vast majority of these trials take place away from the glare of public interest,some deal with issues that are controversial enough to make even the popular press;an obvious example is the use of AZT for the treatment of AIDS.There are many excellent books available which give comprehen-sive accounts of how clinical trials should be carried out and organ-ised.Our aim is somewhat different;we attempt to give relatively concise descriptions of the more statistical aspects of the design and analysis of clinical trials,particularly those methods developed over the last decade or so.Topics discussed in this text include randomi-sation,interim analyses,sample size determination,the analysis of longitudinal data,Bayesian methods,survival analysis and meta-analysis.Many examples are included alongside some of the neces-sary technical material,the more difficult parts of which are confined to tables.An Appendix gives details of relevant software.We hope that our book will be useful to medical statisticians and others faced with the often difficult problems of designing and analysing clinical trials.Our thanks are due to Dr Sophia Rabe-Hesketh and Dr Sabine Landau for reading the text and making many helpful suggestions,to Professor Elizabeth Kuipers for allowing us to use the economic data from her CBT trial in Chapter 4 and to Mrs Harriet Meteyard for help in compiling the references.Brian S.Everitt and Andrew Pickles London,1999 V CONTENTS PREFACE CHAPTER 1.An Introduction to Clinical Trials 1.1 INTRODUCTION 1.2 A BRIEF HISTORY OF CLINICAL TRIALS 1.3 TYPES OF CLINICAL TRIAL 1.4 ETHICS OF CLINICAL TRIALS 1.5 CLINICAL TRIAL PROTOCOLS 1.6 SUMMARY CHAPTER 2.Treatment Allocation,the Size of Trials and Reporting Results 2.1 INTRODUCTION 2.2 TREATMENT ASSIGNMENT METHODS 2.2.1 Simple Randomisation 2.2.2 Blocked Randomisation 2.2.3 Stratified Randomisation 2.2.4 Minimisation Method 2.2.5 Unequal Randomisation THE SIZE OF A CLINICAL TRIAL 2.3 2.4 REPORTING RESULTS 2.5 SUMMARY V 1 1 2 5 9 16 16 18 18 18 21 22 24 26 27 29 33 35 vii viii Design and Analysis of Clinical Trials CHAPTER 3.Monitoring Trial Progress:Outcome Measures,Compliance,Dropouts and Interim Analyses 3.1 INTRODUCTION 3.2 OUTCOME MEASURES 3.3 COMPLIANCE,DROPOUTS AND INTENTION-TO-TREAT 3.3.1 Int,ention-tc-Treat 3.3.2 A Taxonomy of Dropouts 3.4 INTERIM ANALYSES IN CLINICAL TRIALS 3.4.1 Group Sequential Procedures-A Bayesian Perspective 3.5 SUMMARY CHAPTER 4.Basic Analyses of Clinical Trials,the Generalized Linear Model and the Economic Evaluation of Trials 4.1 INTRODUCTION STATISTICS MODELS 4.3.1 Models for Counts:the 4.2 A BRIEF REVIEW OF ELSIC 4.3 GENERALIZED LINEAR Treatment of Familial Adenomatous Poiyposis(FAP)wit.h a Non-Steroidal Anti-Inflammatory Drug 4.3.2 Ordinal Response Models:A Clinical Trial in Lymphoma 4.3.2.1 Models with parallel 4.3.2.2 Non-parallel models 4.3.2.3 Model estimation linear predictors 37 37 39 41 45 50 54 65 67 69 69 70 77 83 89 89 90 91 Contents 4.4 MULTIPLE EIYDPOINTS 4.5 ECONOMIC EVALUATION OF TRTALS 4.5.1 Measuring Costs 4.5.2 Analysis of Cost Data 4.5.3 Cost-Benefit Analysis 4.5.4 An Example:Cognitive Behavioral Therapy 4.6 SUMMARY CHAPTER 5.Simple Approaches to the Analysis of Longitudinal Data from Clinical Trials 5.1 5.2 5.3 5.4 5.5 INTRODUCTION GRAPHICAL METHODS FOR DISPLAYING LONGITUDINAL DATA TIME-BY-TIME ilNALYSIS OF LONGITUDINAL DATA RESPONSE FEATURE ANALYSIS OF LONGITUDINAL DATA 5.4.1 Choosing Summary Measures 5.4.2 Incorporating Pre-Randomisation,Baseline Measures int,o the Response Approach 5.4.3 Response Feature Analysis when the Response Variable is Binary SUMMARY i x 93 97 97 99 101 101 106 108 108 109 118 120 121 129 134 142 CHAPTER 6.Multivariate Normal Regression Models for Longitudinal Data from Clinical Trials 143 6.1 INTRODUCTION 143 6.2 SOME GENERAL COMMENTS ABOUT MODELS FOR LONGITUDINAL DATA 144 X Design and Analysis of Clinical Trials 6.3 MISSING VALUES AND LIKELIHO OD-B ASED INFERENCE FOR LONGITUDINAL DATA 6.4 MAXIMUM LIKELIHOOD ESTIMATION ASSUMING NORMALITY 149 6.5 NUMERICAL EXAMPLES 151 6.5.1 Oestrogen Patches in the Treatment of Post*-N atal Depression 151 6.5.2 Post-Surgical Recovery in Young Children 161 6.6 ANOVA AND MANOVA APPROACHES TO THE ANALYSIS OF LONGITUDINAL DATA4 167 6.7 INFORMATIVE DROP OUTS 168 6.8 OTHER METHODS FOR THE ANALYSIS OF LONGITUDINAL DATA 6.9 SUMMA4RY 147 173 175 CHAPTER 7.Models for Non-Normal Longitudinal Data from Clinical Trials 7.1 INTRODUCTION 7.2 MARGINAL MODELS 7.2.1 Marginal Modelling using Generalised Estimating Equations 7.3 RANDOM EFFECTS MODELS 7.4 TRANSITION MODELS 7.5 A COMPARISON OF METHODS 7.6 MISSING DATA AND WEIGHTED ESTIMATING EQUATIONS 178 178 179 183 193 197 201 202 Contents x i 7.6.1 Missing Data in a Longitudinal Clinical Trial with an Ordinal Response 7.7 SUMMARY CHAPTER 8.Survival Analysis 8.1 INTRODUCTIOK 8.2 THE SURVIVOR FUNCTION AND THE HAZARD FUNCTION 8.2.1 Survivor Function 8.2.2 The Hazard Function 8.3 REGRESSION MODELS FOR SURVIVAL DATA 8.4 ACCELERATED FAILURE TIME MODELS 8.5 PROPORTIONAL HAZARDS MODEL 8.5.1 Proportional Hazards 8.5.2 The Semi-parametric Proportional Hazard or Cox Model 5.5.3 Cox Model Example 8.5.4 Checking the Specification 8.5.5 Goodness-of-fi t Tests 8.5.6 Influence TI ME-17ARYlhG C OVARI ATE S 8.6.1 Modelling with Time-Varying 8.6.2 of a Cox Model 8.6 Covariates The Probiem of Int,ernal or Endogeneous Covariates 8.6.3 Treatment Waiting Times 8.7 STRATIFICATION,MATCHING AND CLUSTER SAMPLING 203 206 208 208 209 2 09 219 220 222 225 225 226 229 232 240 241 242 242 243 244 245 xii Design and Analysis of Clinical Trials 8.7.1 Stratification 245 8.7.2 Matching 246 8.7.3 Cluster Sampling 247 RISKS 248 8.9 AUXILIARY VARIABLES 249 8.10 FRAILTY MODELS 250 8.11 INTERIM ANALYSIS FOR 8.8 CENSORING AND COMPETING SURVIVAL TIME DATA 251 8.11.1 An Example of the Application of an Interim Analysis Procedure for Survival Data 251 8.12 DESCRIBING THE RESULTS OF A SURVIVAL ANALYSIS OF A CLINICAL TRIAL 8.13 SUMMARY 252 253 CHAPTER 9.Bayesian Methods 9.1 INTRODUCTION 9.2 BAYESIAN ESTIMATION 9.3 MARKOV CHAIN MONTE CARL0(MCMC)9.4 ADVANTAGES OF THE MCMC APPROACH 9.4.1 Model Parametrisation and Scientific Inference 9.4.2 Missing Data 9.4.3 Prior Distributions as a Numerical Device 9.4.4 Alternative Models and Model Selection 9.5 A NUMERICAL EXAMPLE OF 9.6 INFORMATIVE PRIORS USING BAYESIAN ESTIMATION 255 255 257 259 260 261 262 262 263 264 268 Contents.Xlll 9.7 PRIORS AND STOPPING RULES FOR TRIAL MONITORING 9.7.1 Clinical Demands 9.7.2 Clinical Beliefs 9.8 MONITORING 9.8.1 9.8.2 Recognising Heterogeneity in The Prior as a Handicap Priors:Enthusiasts and Sceptics 9.9 SAMPLE SIZE ESTIMATION FOR EARLY PHASE TRIALS 9.10 REPORTING OF RESULTS 9.11 SUMMARY CHAPTER 10.Meta-Analysis 10.1 10.2 10.3 10.4 10.5 INTRODUCTION SELECTION OF STUDIES-WHAT TO INCLUDE THE STATISTICS OF META-ANALY SIS TWO EXAMPLES OF THE APPLICATION OF META-ANALYSIS 10.4.1 The Comparison of Sodium Monofluorophosphate(SMFP)and Sodium Fluoride(NaF)Toothpastes in the Prevention of Caries Development 10.4.2 The Effectiveness of Aspirin in Preventing Death after a Myocardial Infarction BAYESIAN META-ANALYSIS 268 269 271 272 272 273 275 278 279 280 280 282 290 297 297 297 300 xiv Design and Analysis of Clinical Rials 10.6 META-ANALYSIS IN MORE COMPLEX SETTINGS 10.7 SUMMARY APPENDIX A.Software REFERENCES INDEX 302 303 305 311 333 CHAPTER 1 An Introduction to Clinical Trials 1.1.INTRODUCTION Avicenna,an Arabian physician and philospher(98&1037),in his encyclopedic Canon of Medicine,set down seven rules to evaluate the effect of drugs on diseases.He suggested that a remedy should be used in its natural state,with uncomplicated disease,and should be observed in two contrary types of disease.His Canon also sug-gested that the time of action and reproducibility of the treatment effect should be studied(Crombie,1952;Meinert,1986).But for several centuries Avicennas advice appears to have been largely ignored,with most ideas affecting choice of treatment depend-ing largely on serendipity rather then planned experiments.Only in recent years(although see next section)has it become widely recog-nised that properly conducted clinical trials,which follow the prin-ciple of scientific experimentation provide the only reliable basis for evaluating the efficacy and safety of new treatments.And just what constitutes a clinical trial?There are several pos-sible definitions,but for our purposes the term will be used for any form of planned experiment designed to assess the most appropri-ate treatment of future patients with a particular medical condition,where the outcome in a group of patients treated with the test treat-ment are compared with those observed in a similar group of pa-tients receiving a control treatment,and patients in both groups are 1 2 Design and Analysis of Clinical Trials enrolled,treated and followed over the same time period.The groups may be established through randomisation or some other method of assignment.The outcome measure may be the result of a laboratory test,a quality of life assessment,a rating of some characteristic or,in some cases,the death of a patient.As a consequence of this somewhat restricted definition,compar-ative studies involving animals,or studies that are carried out in vitro using biological substances from man do not qualify as clinical trials.The definition also rules out detailed consideration of investigations involving historical controls.1.2.A BRIEF HISTORY OF CLINICAL TRIALS It is almost de rigeur in books on clinical trials to include a section tracing their history.Our book is no exception!Table 1.1(taken from Meinert,1986)lists some important dates in the development of such trials,the first of which relates to the often described exper-iment of James Lind carried out in 1747 while at sea on board the Salisbury.Bradford Hill(1962)gives the following quotation from Linds account.On the 20th May 1747,I took twelve patients in the scurvy,on board the Salisbury at sea.Their cases were as similar as I could have them.They all in general had putrid gums,the spots and lassitude,with weakness of their knees.They lay together in one place,being a proper apartment for the sick in the fore-hold;and had one diet in common to all,viz.water-gruel sweetened with sugar in the morning;fresh mutton broth often times for dinner;at other times puddings,boiled biscuit with sugar etc.And for supper,barley and raisins,rice and currants,sago and wine,or the like.Two of these were ordered each a quart of cider a day.Two others took twenty-five gutts of elixir vitriol three times a day,upon an empty stomach;using a gargle strongly acidulated with it for their mouths.Two others took two spoonfuls of vinegar three times a day,upon an empty stomach:having their gruels and their other food well acidulated with it,as also the gargle An Introduction to Clinical Trials Table 1.1.Historical Events in the Development of Clinical Trials.3 Date Author Event 1747 1799 1800 1863 1923 1931 1931 1937 1944 1946 1962 1962 1966 1967 1979 1980 Lind Haygarth Waterhouse Gull Fisher-Amberson-Hill Kefauver and Harris-Chalmers-Experiment with untreated control group(Lind,1753)Use of sham procedure(Haygarth,1800)U.S.-based smallpox trial(Waterhouse,1800,1802)Use of placebo treatment(Sutton,1865)Application of randomisation to experimentation(Fisher and MacKenzie.1923)Special committee on clinical trial created by the Medical Research Council of Great Britain(Medical Research Council,1931)Random allocation of treatment to groups of patients(Amberson et al.,1931)Start of NIH grant support with creation of the National Cancer Institute(National Institutes of Health.1981b)Publication of multicenter trial on treatment for common cold(Patulin Clinical Trials Committee,1944)Promulgation of Nurernberg Code for Human Experimentation(Curran and Shapiro,1970)Publication of book on clinical trials(Hill,1962)Amendments to the Food,Drug and Cosmetic Act of 1938(United States Congress,1962)Publication of U.S.Public Health Service regulations leading to creation of Institutional Review Boards for research involving humans(Levine,1981)Structure for separating the treatment monitoring and treatment administration process(Coronary Drug Project Research Group,1973a)Establishment of Society for Clinical Trials(Society for Clinical Trials,Inc.,1980)First issue of Controlled Clinical Trials(Taken with permission from Meinert,1986.)4 Design and Analysis of Clinical Trials for their mouths.Two of the worst patients,with the tendons in the ham rigid(a symptom none of the rest had)were put under a course of sea-water.Of this they drank half a pint every day,and sometimes more or less as it operated,by way of a gentle physic.Two others had each two oranges and one lemon given them every day.These they eat with greediness,at different times,upon an empty stomach.They continued but six days under this course,having consumed the quantity that could be spared.The two remaining patients,took the bigness of a nutmeg three times a day of an electuary recommended by a hospital-surgeon,made of garlic,mustard-feed,rad.raphan.balsam of Peru,and gum myrr;using for common drink barley water well acidulated with tamarinds;by a decoction of which,with the addition of cremor tartar,they were greatly pur