Sample Size Tables for Clinical Studies

Transcription

1 Sample Size Tables for Clinical Studies Sample Size Tables for Clinical Studies, 3rd edition. D. M., M. J. Campbell, S. B. Tan, and S. H. Tan 2009 D. Machin, M.J. Campbell, S.B. Tan, S.H. Tan. ISBN:

2 To Oliver, Joshua and Sophie David, John and Joseph Lisa and Sophie Kim San, Geok Yan and Janet Companion CD-ROM A companion CD-ROM is included with this book. The CD contains software that will enable you to implement the sample size calculation methods discussed in the book. The CD content is referenced throughout the text where you see this symbol S S S See Chapter 17 for full details of the software on the CD and how to install and use it. Technical requirements: Operating System: Windows XP, 2000; CPU: 500 MHz; RAM: 128 MB; Disc drive: 16 CD drive; Hard drive: 10 MB of free space

3 Sample Size Tables for Clinical Studies David Machin Children s Cancer and Leukaemia Group University of Leicester, UK; Division of Clinical Trials and Epidemiological Sciences National Cancer Centre, Singapore; Medical Statistics Unit School of Health and Related Sciences University of Sheffield, UK Michael J. Campbell Medical Statistics Unit School of Health and Related Research University of Sheffield, UK Say Beng Tan Singapore Clinical Research Institute, Singapore Duke NUS Graduate Medical School, Singapore Sze Huey Tan Division of Clinical Trials and Epidemiological Sciences National Cancer Centre, Singapore THIRD EDITION A John Wiley & Sons, Ltd., Publication

4 This edition first published 2009, 2009 by D. Machin, M.J. Campbell, S.B. Tan, S.H. Tan Previous editions: 1987, 1997 Blackwell Publishing was acquired by John Wiley & Sons in February Blackwell s publishing program has been merged with Wiley s global Scientific, Technical and Medical business to form Wiley-Blackwell. Registered office: John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK Editorial offices: 9600 Garsington Road, Oxford, OX4 2DQ, UK The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK 111 River Street, Hoboken, NJ , USA For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 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 or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. 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. The contents of this work are intended to further general scientific research, understanding, and discussion only and are not intended and should not be relied upon as recommending or promoting a specific method, diagnosis, or treatment by physicians for any particular patient. The publisher and the author make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of fitness for a particular purpose. In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of medicines, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each medicine, equipment, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. Readers should consult with a specialist where appropriate. The fact that an organization or Website is referred to in this work as a citation and/or a potential source of further information does not mean that the author or the publisher endorses the information the organization or Website may provide or recommendations it may make. Further, readers should be aware that Internet Websites listed in this work may have changed or disappeared between when this work was written and when it is read. No warranty may be created or extended by any promotional statements for this work. Neither the publisher nor the author shall be liable for any damages arising herefrom. Library of Congress Cataloging-in-Publication Data Sample size tables for clinical studies / David Machin...[et al.].a3rd ed. p. ; cm. Includes bibliographical references and index. ISBN Clinical trialsastatistical methodsatables. I. Machin, David, 1939 [DNLM: 1. Research DesignaTables. 2. Clinical Trials as TopicaTables. 3. Sample SizeaTables. 4. Statistics as TopicaTables. W 16 S ] R853. C55S adc ISBN: A catalogue record for this book is available from the British Library. Set in 9.5/13pt Minion by Graphicraft Limited, Hong Kong Printed and bound in Singapore by COS Printers Pte Ltd

5 Contents Preface, viii 1 Basic design considerations, 1 2 Distributions and confidence intervals, 14 Table 2.1 The Normal distribution functionaprobability that a Normally distributed variable is less than z, 27 Table 2.2 Percentage points of the Normal distribution for α and 1 β, 28 Table 2.3 Values of θ(α, β) = (z 1 α/2 + z 1 β ) 2, 28 Table 2.4 The t-distribution, 29 3 Comparing two independent groups for binary data, 30 Table 3.1 Sample size for the comparison of two proportions, 38 Table 3.2 Sample size for the comparison of two proportions using the odds ratio (OR), 40 4 Comparing two independent groups for ordered categorical data, 42 5 Comparing two independent groups for continuous data, 47 Table 5.1 Sample sizes for the two sample t-test with two-sided α = 0.05, 54 Table 5.2 Sample sizes for the two sample t-test with unequal variances, 55 Table 5.3 Sample sizes for the one sample t-test with two-sided α = 0.05, 57 6 Cluster designs, repeated measures data and more than two groups, 58 Table 6.1 Multiplying factor for repeated measures designs, 66 7 Comparing paired groups for binary, ordered categorical and continuous outcomes, 67 Table 7.1 Sample sizes for paired binary data, 82 Table 7.2 Sample sizes for paired continuous data with two-sided α = 0.05, 83 8 Comparing survival curves, 84 Table 8.1 Number of critical events for comparison of survival rates (Logrank test), 97 Table 8.2 Number of subjects for comparison of survival rates (Logrank test), 99 Table 8.3 Number of critical events for comparison of two exponential survival distributions with two-sided α = 0.05, 101 v

6 vi Contents 9 Equivalence, 102 Table 9.1 Sample sizes for bioequivalence studiesadifference between two means or ratio of two means, 117 Table 9.2 Sample sizes for testing the equivalence of two means, 118 Table 9.3 Sample sizes for testing the equivalence of two proportions, Confidence intervals, 122 Table 10.1 Sample sizes required to observe a given confidence interval width for a given proportion in a sample from a large population, 136 Table 10.2 Sample sizes required to observe a given confidence interval width for the difference between two proportionsaindependent groups, 137 Table 10.3 Sample sizes required to observe a proportionate confidence interval width for the difference between two groups expressed via the odds ratio (OR), 138 Table 10.4 Sample sizes required to observe a given confidence interval width for the difference between two proportions from paired or matched groups, 139 Table 10.5 Sample sizes required to observe a given confidence interval width to estimate a single mean or the difference between two means for independent or matched groups, Post-marketing surveillance, 142 Table 11.1 Sample sizes required to observe a total of a adverse reactions with a given probability 1 β and anticipated incidence λ, 149 Table 11.2 Sample sizes required for detection of a specific adverse reaction with background incidence, λ 0, known, 150 Table 11.3 Sample sizes required for detection of a specific adverse reaction with background incidence unknown, 151 Table 11.4 Number of cases to be observed in a case-control study, The correlation coefficient, 153 Table 12.1 Sample sizes for detecting a statistically significant correlation coefficient, Reference intervals and receiver operating curves, 158 Table 13.1 Sample sizes in order to obtain a required reference intervalanormal distribution, 169 Table 13.2 Sample sizes in order to obtain a required reference intervalanon-normal distribution, 170 Table 13.3 Sample sizes required to observe a given sensitivity or specificity in diagnostic accuracy studiesasingle sample, 171 Table 13.4 Sample sizes required to observe a given sensitivity or specificity in diagnostic accuracy studiesatwo sample unpaired design, 173 Table 13.5 Sample sizes required to observe a given sensitivity or specificity in diagnostic accuracy studiesatwo sample matched paired design, 175 Table 13.6 Sample sizes required to observe a given confidence interval width for receiver operating curves (ROC), 177

7 Contents vii 14 Observer agreement studies, 179 Table 14.1 Sample sizes required to observe a given confidence interval to estimate the proportion of disagreements between two observers, 189 Table 14.2 Sample sizes required to observe a given confidence interval to estimate the within observer variation, 190 Table 14.3 Sample sizes required to observe a given confidence interval to minimise the number of subjects required to achieve the desired precision in the probability of their disagreement, Θ Dis, 191 Table 14.4 Sample sizes required to observe a given confidence interval width for inter-observer agreement using Cohen s Kappa, κ, 192 Table 14.5 Sample sizes required to observe a given intra-class correlation, ρ, using the confidence interval approach, 193 Table 14.6 Sample sizes required to observe a given intra-class correlation using the hypothesis testing approach with two-sided α = 0.05, Dose finding studies, Phase II trials, 207 Table 16.1 Fleming A Hern single-stage Phase II design, 225 Table 16.2 Gehan two-stage Phase II designastage 1, 226 Table 16.3 Gehan two-stage Phase II designastage 2, 227 Table 16.4 Simon Optimal and Minimax designs, 228 Table 16.5 Bayesian single threshold design (STD), 229 Table 16.6 Bayesian dual threshold design (DTD), 230 Table 16.7 Case and Morgan EDA design with α = 0.05, 231 Table 16.8 Case and Morgan ETSL design with α = 0.05, 232 Table 16.9 Simon, Wittes and Ellenberg design, 233 Table Bryant and Day design, Sample size software S S S, 237 Cumulative references, 239 Author index, 249 Subject index, 253 A companion CD-ROM of the sample size software S S S is included in the inside back cover of this book

8 Preface It is now more than 20 years since the first edition of this book and 10 years from the second. The need for evidence-based estimates of the required size of a study is now universally recognized. Since the second edition the methodology for sample-size calculation has been widely extended, which is the main reason for a third edition. A second reason is the vastly improved computing power available. For the first edition, the tabulations were extensive to obviate separate calculations. A computer program to extend the range of the tables was available for the second edition. This edition comes with sample size software S S S, which we hope will give the user even greater flexibility and easy access to a wide range of designs, and allow design parameters to be tailored more readily to specific problems. Further, as some early phase designs are adaptive in nature and require knowledge of earlier patients response to determine the relevant options for the next patient, a (secure) database is provided for these. Designing modern clinical research studies requires the involvement of multidisciplinary teams, with the process of sample size determination not being something that can be done by the statistician alone. So while software is available that can compute sample sizes (even from the internet), we feel that it is necessary that such software be complemented with a book that clearly explains and illustrates the methodology, along with tables. Feedback from users of earlier editions suggests that this can facilitate planning discussions within the research team. Thus a major consideration has been to present the details, which are often complex, as clearly as possible and to illustrate these with appropriate examples. One objective of this approach is to encourage the wider use of sample size issues at the design stage in areas such as laboratory studies, which have been relatively neglected compared to epidemiological studies and clinical trials. David Machin Michael J. Campbell Say Beng Tan Sze Huey Tan Singapore; Leicester and Sheffield, UK viii