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Statistics in Practice Statistical Issues in Drug Development StatisticalIssuesinDrugDevelopment, 2ndEdition. StephenSenn ©2007JohnWiley&Sons,Ltd. ISBN: 978-0-470-01877-4 Statistics in Practice Advisory Editor Stephen Senn University of Glasgow, UK Founding Editor Vic Barnett Nottingham Trent University, UK Statistics in Practice is an important international series of texts which provide detailed coverage of statistical concepts, methods and worked case studies in specific fields of investigation and study. With sound motivation and many worked practical examples, the books show in down-to-earth terms how to select and use an appropriate range of statistical techniques in a particular practical field within each title’s special topic area. The books provide statistical support for professionals and research workers across a range of employment fields and research environments. Subject areas covered include medicine and pharmaceutics; industry, finance and commerce; public services; the earth and environmental sciences, and so on. The books also provide support to students studying statistical courses applied to the above areas. The demand for graduates to be equipped for the work environment has led to such courses becoming increasingly prevalent at universities and colleges. It is our aim to present judiciously chosen and well-written workbooks to meet everyday practical needs. Feedback of views from readers will be most valuable to monitor the success of this aim. A complete list of titles in this series appears at the end of the volume. Statistical Issues in Drug Development Second Edition Stephen Senn Department of Statistics University of Glasgow, UK Copyright © 2007 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777 Email (for orders and customer service enquiries): [email protected] Visit our Home Page on www.wiley.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to [email protected], or faxed to (+44) 1243 770620. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA Wiley-VCH Verlag GmbH, Boschstr. 12, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 42 McDougall Street, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons Canada Ltd, 6045 Freemont Blvd, Mississauga, Ontario, L5R 4J3 Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Anniversary Logo Design: Richard J. Pacifico British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 978-0-470-01877-4 Typeset in 10/12pt Times by Integra Software Services Pvt. Ltd, Pondicherry, India Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production. To Victoria, Helen and Mark Contents Preface to the Second Edition xiii Preface to the First Edition xvii Acknowledgements xxi 1 Introduction 1 1.1 Drug development 1 1.2 The role of statistics in drug development 2 1.3 The object of this book 3 1.4 The author’s knowledge of statistics in drug development 4 1.5 The reader and his or her knowledge of statistics 4 1.6 How to use the book 5 References 6 Part 1 Four Views of Statistics in Drug Development: Historical, Methodological, Technical and Professional 9 2 A Brief and Superficial History of Statistics for Drug Developers 11 2.1 Introduction 11 2.2 Early Probabilists 12 2.3 James Bernoulli (1654–1705) 13 2.4 John Arbuthnott (1667–1753) 14 2.5 The mathematics of probability in the late 17th, the 18th and early 19th centuries 14 2.6 Thomas Bayes (1701–1761) 15 2.7 Adolphe Quetelet (1796–1874) 16 2.8 Francis Galton (1822–1911) 16 2.9 Karl Pearson (1857–1936) 17 2.10 ‘Student’ (1876–1937) 17 2.11 R.A. Fisher (1890–1962) 17 2.12 Modern mathematical statistics 18 2.13 Medical statistics 19 2.14 Statistics in clinical trials today 20 2.15 The current debate 21 2.16 A living science 21 2.17 Further reading 23 References 23 viii Contents 3 Design and Interpretation of Clinical Trials as Seen by a Statistician 27 3.1 Prefatory warning 27 3.2 Introduction 27 3.3 Defining effects 28 3.4 Practical problems in using the counterfactual argument 28 3.5 Regression to the mean 29 3.6 Control in clinical trials 33 3.7 Randomization 34 3.8 Blinding 36 3.9 Using concomitant observations 37 3.10 Measuring treatment effects 38 3.11 Data generation models 39 3.12 In conclusion 41 3.13 Further reading 41 References 41 4 Probability, Bayes, P-values, Tests of Hypotheses and Confidence Intervals 43 4.1 Introduction 43 4.2 An example 44 4.3 Odds and sods 44 4.4 The Bayesian solution to the example 45 4.5 Why don’t we regularly use the Bayesian approach in clinical trials? 46 4.6 A frequentist approach 47 4.7 Hypothesis testing in controlled clinical trials 48 4.8 Significance tests and P-values 49 4.9 Confidence intervals and limits and credible intervals 50 4.10 Some Bayesian criticism of the frequentist approach 51 4.11 Decision theory 51 4.12 Conclusion 52 4.13 Further reading 52 References 53 5 The Work of the Pharmaceutical Statistician 55 5.1 Prefatory remarks 55 5.2 Introduction 56 5.3 In the beginning 57 5.4 The trial protocol 57 5.5 The statistician’s role in planning the protocol 58 5.6 Sample size determination 59 5.7 Other important design issues 60 5.8 Randomization 60 5.9 Data collection preview 61 5.10 Performing the trial 61 5.11 Data analysis preview 61 5.12 Analysis and reporting 62 5.13 Other activities 63 Contents ix 5.14 Statistical research 63 5.15 Further reading 64 References 65 Part 2 Statistical Issues: Debatable and Controversial Topics in Drug Development 67 6 Allocating Treatments to Patients in Clinical Trials 69 6.1 Background 69 6.2 Issues 71 References 87 6.A Technical appendix 88 7 Baselines and Covariate Information 95 7.1 Background 95 7.2 Issues 98 References 108 7.A Technical appendix 109 8 The Measurement of Treatment Effects 113 8.1 Background 113 8.2 Issues 114 References 129 8.A Technical appendix 130 9 Demographic Subgroups: Representation and Analysis 133 9.1 Background 133 9.2 Issues 134 References 144 9.A Technical appendix 145 10 Multiplicity 149 10.1 Background 149 10.2 Issues 150 References 161 10.A Technical appendix 162 11 Intention to Treat, Missing Data and Related Matters 165 11.1 Background 165 11.2 Issues 167 References 178 11.A Technical appendix 180 12 One-sided and Two-sided Tests and other Issues to Do with Significance and P-values 183 12.1 Background 183 12.2 Issues 184 References 192 x Contents 13 Determining the Sample Size 195 13.1 Background 195 13.2 Issues 198 References 211 14 Multicentre Trials 213 14.1 Background 213 14.2 Issues 213 References 230 14.A Technical appendix 231 15 Active Control Equivalence Studies 235 15.1 Background 235 15.2 Issues 237 References 247 15.A Technical appendix 249 16 Meta-Analysis 251 16.1 Background 251 16.2 Issues 253 References 268 16.A Technical appendix 270 17 Cross-over Trials 273 17.1 Background 273 17.2 Issues 275 References 284 18 n-of-1 Trials 287 18.1 Background 287 18.2 Issues 289 References 293 19 Sequential Trials 295 19.1 Background 295 19.2 Issues 302 References 313 20 Dose-finding 317 20.1 Background 317 20.2 Issues 319 References 334 21 Concerning Pharmacokinetics and Pharmacodynamics 337 21.1 Background 337 21.2 Issues 343 References 358 Contents xi 22 Bioequivalence Studies 361 22.1 Background 361 22.2 Issues 362 References 379 23 Safety Data, Harms, Drug Monitoring and Pharmaco-epidemiology 383 23.1 Background 383 23.2 Issues 388 References 403 24 Pharmaco-economics and Portfolio Management 405 24.1 Background 405 24.2 Issues 407 References 429 25 Concerning Pharmacogenetics, Pharmacogenomics and Related Matters 433 25.1 Background 433 25.2 Issues 437 References 450 25.A Technical appendix 451 Glossary 453 Index 483 Preface to the Second Edition There have been many developments since the first edition of this book and it was high time for a second. My own period working in the pharmaceutical industry is now a distant memory but the ten years working as an academic since the first edition has had its compensations.
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