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This page intentionally left blank, Medical Statistics. Fourth Edition, This page intentionally left blank. Medical Statistics, Fourth Edition, A Textbook for the Health Sciences. David Machin, Division of Clinical Trials and Epidemiological Sciences National Cancer. Centre Singapore, Medical Statistics Group School of Health and Related Research University of.
Shef eld UK, Children s Cancer and Leukaemia Group University of Leicester UK. Michael J Campbell, Medical Statistics Group School of Health and Related Research University of. Shef eld UK, Stephen J Walters, Medical Statistics Group School of Health and Related Research University of. Shef eld 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 cs books wiley co uk. Visit our Home Page on www wileyeurope com or 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 permreq. wiley co uk or faxed to 44 1243 770620, 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. Other Wiley Editorial Of ces, 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 33 Park Road Milton Queensland 4064 Australia. John Wiley Sons Asia Pte Ltd 2 Clementi Loop 02 01 Jin Xing Distripark Singapore. John Wiley Sons Canada Ltd 6045 Freemont Blvd Mississauga Ontario L5R 4J3 Canada. 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 Paci co. Library of Congress Cataloging in Publication Data. Campbell Michael J PhD, Medical statistics a textbook for the health sciences Michael J.
Campbell David Machin Stephen J Walters 4th ed, Includes bibliographical references. ISBN 978 0 470 02519 2 cloth alk paper, 1 Medical statistics 2 Medicine Research Statistical methods I Machin David. 1939 II Walters Stephen John III Title, DNLM 1 Biometry methods 2 Research Design 3 Statistics WA 950 C189m 2007. R853 S7C36 2007, 610 72 7 dc22, British Library Cataloguing in Publication Data. A catalogue record for this book is available from the British Library. ISBN 978 0 470 02519 2, Typeset in 10 5 12 5 Times by SNP Best set Typesetter Ltd Hong Kong.
Printed and bound in Great Britain by Antony Rowe Ltd Chippenham Wilts. 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. Preface to the Fourth Edition xi, 1 Uses and abuses of medical statistics 1. 1 1 Introduction 2, 1 2 Why use statistics 3, 1 3 Statistics is about common sense and good design 4. 1 4 Types of data 5, 1 5 How a statistician can help 9. 1 6 Further reading 11, 1 7 Exercises 12, 2 Describing and displaying categorical data 13. 2 1 Summarising categorical data 14, 2 2 Displaying categorical data 21.
2 3 Points when reading the literature 23, 2 4 Exercises 24. 3 Describing and displaying quantitative data 27, 3 1 Summarising continuous data 28. 3 2 Displaying continuous daa 34, 3 3 Within subject variability 39. 3 4 Presentation 42, 3 5 Points when reading the literature 43. 3 6 Exercises 43, vi CONTENTS, 4 Probability and decision making 45.
4 1 Types of probability 46, 4 2 Diagnostic tests 49. 4 3 Bayes Theorem 51, 4 4 Relative receiver operating characteristic ROC curve 57. 4 5 Points when reading the literature 59, 4 6 Exercises 60. 5 Distributions 63, 5 1 Introduction 64, 5 2 The Binomial distribution 64. 5 3 The Poisson distribution 66, 5 4 Probability for continuous outcomes 68.
5 5 The Normal distribution 69, 5 6 Reference ranges 73. 5 7 Points when reading the literature 75, 5 8 Technical details 75. 5 9 Exercises 76, 6 Populations samples standard errors and con dence. intervals 79, 6 1 Populations 80, 6 2 Samples 81, 6 3 The standard error 82. 6 4 The Central Limit Theorem 84, 6 5 Standard errors for proportions and rates 85.
6 6 Standard errors of differences 87, 6 7 Con dence intervals for an estimate 89. 6 8 Con dence intervals for differences 93, 6 9 Points when reading the literature 94. 6 10 Technical details 94, 6 11 Exercises 96, 7 p values and statistical inference 99. 7 1 Introduction 100, 7 2 The null hypothesis 100, 7 3 The p value 103. 7 4 Statistical inference 105, 7 5 Statistical power 108.
7 6 Con dence intervals rather than p values 110, 7 7 One sided and two sided tests 112. 7 8 Points when reading the literature 113, 7 9 Technical details 114. 7 10 Exercises 114, CONTENTS vii, 8 Tests for comparing two groups of categorical or. continuous data 117, 8 1 Introduction 118, 8 2 Comparison of two groups of paired observations. continuous outcomes 119, 8 3 Comparison of two independent groups.
continuous outcomes 125, 8 4 Comparison of two independent groups. categorical outcomes 132, 8 5 Comparison of two groups of paired observations. categorical outcomes 136, 8 6 Non Normal distributions 138. 8 7 Degrees of freedom 139, 8 8 Points when reading the literature 140. 8 9 Technical details 140, 8 10 Exercises 144, 9 Correlation and linear regression 149.
9 1 Introduction 150, 9 2 Correlation 151, 9 3 Linear regression 156. 9 4 Comparison of assumptions between correlation and. regression 165, 9 5 Multiple regression 166, 9 6 Logistic regression 169. 9 7 Correlation is not causation 174, 9 8 Points when reading the literature 175. 9 9 Technical details 175, 9 10 Exercises 179, 10 Survival analysis 181. 10 1 Time to event data 182, 10 2 Kaplan Meier survival curve 185.
10 3 The logrank test 189, 10 4 The hazard ratio 190. 10 5 Modelling time to event data 193, 10 6 Points when reading the literature 197. 10 7 Exercises 198, 11 Reliability and method comparison studies 201. 11 1 Introduction 202, 11 2 Repeatability 203, 11 3 Agreement 206. viii CONTENTS, 11 4 Validity 209, 11 5 Method comparison studies 210.
11 6 Points when reading the literature 212, 11 7 Technical details 213. 11 8 Exercises 215, 12 Observational studies 217, 12 1 Introduction 218. 12 2 Risk and rates 218, 12 3 Taking a random sample 220. 12 4 Questionnaire and form design 221, 12 5 Cross sectional surveys 222. 12 6 Non randomised studies 224, 12 7 Cohort studies 227.
12 8 Case control studies 231, 12 9 Association and causality 237. 12 10 Points when reading the literature 238, 12 11 Technical details 238. 12 12 Exercises 239, 13 The randomised controlled trial 241. 13 1 Introduction 242, 13 2 Why randomise 242, 13 3 Methods of randomisation 244. 13 4 Design features 247, 13 5 Design options 250, 13 6 Meta analysis 254.
13 7 The protocol 255, 13 8 Checklists for design analysis and reporting 256. 13 9 Number needed to treat NNT 258, 13 10 Points when reading the literature 259. 13 11 Exercises 260, 14 Sample size issues 261, 14 1 Introduction 262. 14 2 Study size 263, 14 3 Continuous data 267, 14 4 Binary data 268. 14 5 Prevalence 270, 14 6 Subject withdrawals 271, 14 7 Internal pilot studies 272.
14 8 Points when reading the literature 272, 14 9 Technical details 273. 14 10 Exercises 274, CONTENTS ix, 15 Common pitfalls 277. 15 1 Introduction 278, 15 2 Using the t test 278, 15 3 Plotting change against initial value 280. 15 4 Repeated measures 284, 15 5 Clinical and statistical signi cance 288. 15 6 Exploratory data analysis 288, 15 7 Points when reading the literature 290.
15 8 Exercises 290, References 291, Solutions to exercises 297. Statistical tables 315, Table T1 The Normal distribution 316. Table T2 Random numbers 318, Table T3 Student s t distribution 319. Table T4 The 2 distribution 320, Table T5 Normal ordinates for cumulative probabilities 321. This page intentionally left blank, Preface to the Fourth Edition.
Revised editions of books are often only minor departures from previous. editions In this edition however with the aid of a new co author we have. attempted a total revamp of our previously successful textbook We did this. because not only have twenty years passed but the statistical requirements. of medical journals are now more rigorous and there has been an increasing. demand for the newer statistical methods to meet new scienti c challenges. Despite this we have retained the popular approach of explaining medical. statistics with as little technical detail as possible so as to make the textbook. accessible to a wide audience In general we have placed the sometimes. unavoidable more technical aspects at the end of each chapter We have. updated many of the examples to give a more modern approach but have. retained a few classics from the earlier editions because they so well illustrate. the point we wish to make, To aid the individual learner exercises are included at the end of each. chapter with answers provided at the end of the book We have concentrated. the design issues into three chapters concerning the design of observational. studies randomised clinical trials and sample size issues Many health scien. tists will have to validate their methods of measurement and a new feature. in this book is a chapter on reliability and validity. Students of the health sciences such as medicine nursing dentistry physio. therapy occupational therapy and radiography should nd the book useful. with examples relevant to their disciplines The aim of training courses in. medical statistics pertinent to these areas is not to turn the students into. medical statisticians but rather to help them interpret the published scienti c. literature and appreciate how to design studies and analyse data arising from. their own projects, We envisage the book being useful in two areas First for consumers of. statistics who need to be able to read the research literature in the eld with. xii PREFACE TO THE FOURTH EDITION, a critical eye All health science professionals need to be able to do this but. for many this is all they will need We suggest that Chapters 1 7 would form. the basis of a course for this purpose However some perhaps trainee pro. fessionals will go on to design studies and analyse data from projects and so. secondly the book will be useful to doers of statistics who need relatively. straightforward methods that they can be con dent of using Chapters 8 15. are aimed at this audience though clearly they also need to be familiar with. the earlier chapters These students will be doing statistics on computer pack. ages so we have given generic output which is typical of the major packages. to aid in the interpretation of the results, We thank Lucy Sayer from Wiley for her patience for what initially was. simply a revision but is now essentially a new textbook. David Machin, Singapore and Shef eld and Leicester UK.
Michael J Campbell, Shef eld UK, Stephen J Walters. Shef eld UK, November 2006, 1 Uses and abuses of, medical statistics. 1 1 Introduction 2, 1 2 Why use statistics 3, 1 3 Statistics is about common sense and good design 4. 1 4 Types of data 5, 1 5 How a statistician can help 9. 1 6 Further reading 11, 1 7 Exercises 12, Medical Statistics Fourth Edition David Machin Michael J Campbell Stephen J Walters.
Medical Statistics Fourth Edition 9 Correlation and linear regression 149 9 1 Introduction 150 13 6 Meta analysis 254

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