OTE/SPH OTE/SPH JWBK220-FM November 28, 2007 11:13 Char Count= 0 Medical Statistics from Scratch An Introduction for Health Professionals Second Edition David Bowers Honorary Lecturer, School of Medicine, University of Leeds, UK iii OTE/SPH OTE/SPH JWBK220-FM November 28, 2007 11:13 Char Count= 0 Medical Statistics from Scratch Second Edition i OTE/SPH OTE/SPH JWBK220-FM November 28, 2007 11:13 Char Count= 0 ii OTE/SPH OTE/SPH JWBK220-FM November 28, 2007 11:13 Char Count= 0 Medical Statistics from Scratch An Introduction for Health Professionals Second Edition David Bowers Honorary Lecturer, School of Medicine, University of Leeds, UK iii OTE/SPH OTE/SPH JWBK220-FM November 28, 2007 11:13 Char Count= 0 Copyright C 2008 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.wileyeurope.com or www.wiley.com All Rights Reserved. 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Library of Congress Cataloging-in-Publication Data Bowers, David, 1938– Medical statistics from scratch : an introduction for health professionals / David Bowers. — 2nd ed. p. ; cm. Includes bibliographical references and index. ISBN 978-0-470-51301-9 (cloth : alk, paper) 1. Medical statistics. 2. Medicine—Research—Statistical methods. I. Title. [DNLM: 1. Biometry. 2. Statistics—methods. WA 950 B786m 2007] RA409.B669 2007 610.72’7—dc22 2007041619 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 978-0-470-51301-9 Typeset in 10/12pt Minion by Aptara Inc., New Delhi, India 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. iv OTE/SPH OTE/SPH JWBK220-FM November 28, 2007 11:13 Char Count= 0 This book is for Susanne v OTE/SPH OTE/SPH JWBK220-FM November 28, 2007 11:13 Char Count= 0 vi OTE/SPH OTE/SPH JWBK220-FM November 28, 2007 11:13 Char Count= 0 Contents Preface to the 2nd Edition xi Preface to the 1st Edition xiii Introduction xv I Some Fundamental Stuff 1 1 First things first – the nature of data 3 Learning Objectives 3 Variables and data 3 The good, the bad, and the ugly – types of variable 4 Categorical variables 4 Metric variables 7 How can I tell what type of variable I am dealing with? 9 II Descriptive Statistics 15 2 Describing data with tables 17 Learning Objectives 17 What is descriptive statistics? 17 The frequency table 18 3 Describing data with charts 29 Learning Objectives 29 Picture it! 29 Charting nominal and ordinal data 30 Charting discrete metric data 34 Charting continuous metric data 35 Charting cumulative data 37 4 Describing data from its shape 43 Learning Objectives 43 The shape of things to come 43 vii OTE/SPH OTE/SPH JWBK220-FM November 28, 2007 11:13 Char Count= 0 viii CONTENTS 5 Describing data with numeric summary values 51 Learning Objectives 51 Numbers R us 52 Summary measures of location 54 Summary measures of spread 57 Standard deviation and the Normal distribution 65 III Getting the Data 69 6 Doing it right first time – designing a study 71 Learning Objectives 71 Hey ho! Hey ho! It’s off to work we go 72 Collecting the data – types of sample 74 Types of study 75 Confounding 81 Matching 81 Comparing cohort and case-control designs 83 Getting stuck in – experimental studies 83 IV From Little to Large – Statistical Inference 91 7 From samples to populations – making inferences 93 Learning Objectives 93 Statistical inference 93 8 Probability, risk and odds 97 Learning Objectives 97 Chance would be a fine thing – the idea of probability 98 Calculating probability 99 Probability and the Normal distribution 100 Risk 100 Odds 101 Why you can’t calculate risk in a case-control study 102 The link between probability and odds 103 The risk ratio 104 The odds ratio 105 Number needed to treat (NNT) 106 V The Informed Guess – Confidence Interval Estimation 109 9 Estimating the value of a single population parameter – the idea of confidence intervals 111 Learning Objectives 111 Confidence interval estimation for a population mean 112 Confidence interval for a population proportion 116 Estimating a confidence interval for the median of a single population 117 OTE/SPH OTE/SPH JWBK220-FM November 28, 2007 11:13 Char Count= 0 CONTENTS ix 10 Estimating the difference between two population parameters 119 Learning Objectives 119 What’s the difference? 120 Estimating the difference between the means of two independent populations – using a method based on the two-sample t test 120 Estimating the difference between two matched population means – using a method based on the matched-pairs t test 125 Estimating the difference between two independent population proportions 126 Estimating the difference between two independent population medians – the Mann–Whitney rank-sums method 127 Estimating the difference between two matched population medians – Wilcoxon signed-ranks method 131 11 Estimating the ratio of two population parameters 133 Learning Objectives 133 Estimating ratios of means, risks and odds 133 VI Putting it to the Test 139 12 Testing hypotheses about the difference between two population parameters 141 Learning Objectives 141 The research question and the hypothesis test 142 A brief summary of a few of the commonest tests 144 Some examples of hypothesis tests from practice 146 Confidence intervals versus hypothesis testing 149 Nobody’s perfect – types of error 149 The power of a test 151 Maximising power – calculating sample size 152 Rules of thumb 152 13 Testing hypotheses about the ratio of two population parameters 155 Learning Objectives 155 Testing the risk ratio 155 Testing the odds ratio 158 14 Testing hypotheses about the equality of population proportions: the chi-squared test 161 Learning Objectives 161 Of all the tests in all the world...thechi-squared (χ 2) test 162 VII Getting up Close 169 15 Measuring the association between two variables 171 Learning Objectives 171 Association 171 The correlation coefficient 175 OTE/SPH OTE/SPH JWBK220-FM November 28, 2007 11:13 Char Count= 0 x CONTENTS 16 Measuring agreement 181 Learning Objectives 181 To agree or not agree: that is the question 181 Cohen’s kappa 182 Measuring agreement with ordinal data – weighted kappa 184 Measuring the agreement between two metric continuous variables 184 VIII Getting into a Relationship 187 17 Straight line models: linear regression 189 Learning Objectives 189 Health warning! 190 Relationship and association 190 The linear regression model 192 Model building and variable selection 200 18 Curvy models: logistic regression 213 Learning Objectives 213 A second health warning! 213 Binary dependent variables 214 The logistic regression model 215 IX Two More Chapters 225 19 Measuring survival 227 Learning Objectives 227 Introduction 227 Calculating survival probabilities and the proportion surviving: the Kaplan-Meier table 228 The Kaplan-Meier chart 230 Determining median survival time 231 Comparing survival with two groups 232 20 Systematic review and meta-analysis 239 Learning Objectives 239 Introduction 240 Systematic review 240 Publication and other biases 244 The funnel plot 244 Combining the studies 246 Appendix: Table of random numbers 251 Solutions to Exercises 253 References 273 Index 277 OTE/SPH OTE/SPH JWBK220-FM November 28, 2007 11:13 Char Count= 0 Preface to the 2nd Edition This book is a ‘not-too-mathematical’ introduction to medical statistics. It should appeal to anyone training or working in the health care arena – whatever their particular discipline – who wants either a simple introduction to the subject, or a gentle reminder of stuff they might have forgotten.