Essential Statistics for Medical Practice A case-study approach D.C Rees Senior Lecturer in Statistics Oxford Brookes University UK SPRINGER-SCIENCE+BUSINESS MEDIA, B.V First edition 1994 © D G.Rees1994 Originally published by Chapman & Hall in 1994 Typeset in 10/12pt Palatino by Best-set Typesetter Ltd., Hong Kong ISBN 978-0-412-59930-9 ISBN 978-1-4899-4505-1 (eBook) DOI 10.1007/978-1-4899-4505-1 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the UK Copyright Designs and Patents Act, 1988, this publication may not be reproduced, stored, or transmitted, in any form or by any means, without the prior permission in writing of the publishers, or in the case of reprographic reproduction only in accordance with the terms of the licences issued by the Copyright Licensing Agency in the UK, or in accordance with the terms of licences issued by the appropriate Reproduction Rights Organization outside the UK Enquiries concerning reproduction outside the terms stated here should be sent to the publishers at the London address printed on this page The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made A catalogue record for this book is available from the British Library Library of Congress Catalog Card Number: 94-71200 Printed on permanent acid-free text paper, manufactured in accordance with ANSI/NISO Z39.48-1992 and ANSI/NISO Z39.48-1984 (Permanence of Paper) To the memory of Florence Nightingale, her work and her inspiration With Miss Nightingale statistics were a passion and not merely a hobby But she loved statistics not for their own sake, but for their practical uses It was by the statistical method that she had driven home the lessons of the Crimean hospitals It was the study of statistics that had opened her eyes to the preventable mortality among the Army at home She was in very serious, and even in bitter, earnest a passionate statistician Contents Preface Acknowledgements Overview of the use of basic statistical methods in medical studies Part One Discussion of Case Studies Preliminary trial of the effect of general practice based nutritional advice 1.1 Discussion Randomized controlled trial of anti-smoking advice by nurses in general practice 2.1 Discussion Psychological distress: outcome and consultation rates in one general practice 3.1 Discussion xi xiii xv 18 23 33 37 48 Use of regression analysis to explain the variation in prescribing rates and costs between family practitioner committees 4.1 Discussion 53 66 Hidden psychiatric illness: use of the general health questionnaire in general practice 5.1 Discussion 71 83 A randomized controlled trial of surgery for glue ear 6.1 Discussion 85 106 vi Contents Part Two Statistical Methods Data, tables, graphs, summary statistics and 109 probability 7.1 Data 7.2 Tables and graphs 7.3 Summary statistics for numerical variables 7.4 Summary statistics for non-numerical variables 7.5 Probability 111 111 113 114 Hypothesis tests and confidence intervals for means 8.1 Introduction 8.2 Confidence interval for a population mean (large samples) 8.3 Interpretation of a confidence interval 8.4 Confidence interval for a population mean (small samples) 8.5 Hypothesis test for a population mean (small or large samples) 8.6 The confidence interval and hypothesis test approaches compared 8.7 Confidence interval and hypothesis test for comparing two means (paired t-test) 8.8 Confidence interval and hypothesis test for comparing two means (unpaired t-test) 8.9 Practical and statistical significance 8.10 What if the assumptions of the methods in this chapter are not valid? 127 127 10 119 121 128 129 130 131 134 134 137 140 141 More on comparing means, the analysis of variance and the F-test 9.1 Introduction 9.2 Why not carry out t-tests to compare the means in pairs? 9.3 A numerical example of one-way ANOVA 9.4 A posterior test after ANOVA The F-test to compare two variances 9.5 144 144 147 148 Hypothesis tests and confidence intervals for percentages 10.1 In trod uction 10.2 Confidence interval for a percentage 151 151 152 143 143 Contents 10.3 Hypothesis test for a percentage 10.4 Confidence interval for the difference vii 153 between two percentages 154 two percentages 155 10.5 Hypothesis test for the difference between 11 Further tests for percentages 11.1 The Fisher exact test 11.2 X2 (chi-square) trend test 163 163 165 12 Regression and correlation 12.1 Introduction 12.2 Simple linear regression 12.3 Correlation coefficient 12.4 ANOVA applied to simple linear regression analysis 12.5 How useful is the regression equation? 12.6 Introduction to multiple regression analysis 12.7 How good is our predicted value of y in simple linear regression analysis? 12.8 Correlation, further discussion 167 167 168 170 13 Sensitivity and specificity 13.1 Definitions 13.2 Example from case study 183 183 184 14 Study design 14.1 Introduction 14.2 Study size 187 187 189 15 Calculators and computers 15.1 Introduction 15.2 MINIT AB examples 195 195 196 Appendix A Further reading Appendix B Statistical tables 207 209 Index 217 171 174 175 178 180 Preface Books on medical statistics usually start with elementary statistical techniques of data presentation and analysis, building up to more advanced techniques Relevant examples from the literature, for example medical journals, are quoted as each technique is introduced This book is different! I start from where the medical professional starts when reading the literature, namely with a medical investigation which nearly always contains some use of statistical methods So in Part One I have taken six real case studies from recent medical journals and discussed each in turn, using a common format, with particular emphasis on the statistics Forward references are made from the case studies to examples in Part Two, which draws together similar examples and discusses the background assumptions, limitations and applicability of the statistical methods described I have limited this book to only the most basic, but nevertheless useful, methods, because my aim is to provide a readable and relatively short primer, rather than a long text which might deter the busy health professional Acknowledgements Miss Nightingale's mastery of the art of marshalling facts to logical conclusions was recognised by her election in 1858 as a member of the Statistical Society I would like to thank the editor of the British Journal of General Practice (formerly the Journal of the Royal College of General Practitioners) for permission to reproduce five articles (case studies 1-5), and the production director of the British Medical Journal for permission to reproduce one article (case study 6) I would further like to thank the following authors and publishers for their kind permission to adapt from the following tables: Pearson, E.S and Hartley, H.O (1966), Biometrika Tables for Statisticians, vol I, 3rd edition, Cambridge University Press, Cambridge (Tables B.1-B.4); and Mead, R and Curnow, R.N (1983), Statistical Methods in Agriculture and Experimental Biology, Chapman & Hall, London (Table B.5) The quotations before or after various sections and chapters are taken from a biography written by Sir Edward Cook (1913), The Life of Florence Nightingale, Vol I 1820-1861 and Vol II 1862-1910, Macmillan, London, with permission from the publishers The quotations are the biographer's words unless otherwise stated Thanks also to David Mant, Department of Community Medicine and General Practice, University of Oxford, and to Peter Anderson, formerly Director of HEA Primary Health Care Unit, Churchill Hospital, Oxford, for initial discussions and assistance with the choice of relevant case studies Most of all, I am grateful to my wife, Merilyn, for her help in the production of the various drafts and for her support and encouragement throughout Overview of the use of basic statistical methods in medical studies Data are collected from patients in order to diagnose and treat their medical conditions, and to make them well again In medical studies we usually need to collect data from one or more groups of patients who have something in common, such as suffering from the same disease We may then wish to compare sub-groups of patients, for example those treated by one method and those treated by another method The simplest way to compare the sub-groups will probably be in terms of means or percentages, depending on the type of variable of interest For example, if the treatments given to sub-groups and are one of two drugs designed to reduce blood pressure, we would wish to compare the mean reduction in blood pressure for each of the sub-groups Whereas, if the two treatments given result in either 'success' (disease cured) or 'failure' (disease not cured) for each patient, we would wish to compare the percentages achieving success for the treatments Means and percentages are examples of summary (or 'descriptive') statistics, and these and others are discussed in the first chapter of Part Two (Chapter 7) The other aspect of the medical data we collect is that they represent only some of the possible data that we could have collected We, of course, restrict ourselves to collecting only data for variables which are relevant to the objectives of our study Even so, if our objective is, for example, to 'compare the reduction in blood pressure resulting from the applications of drugs A and B' we will have to restrict ourselves to collecting ... surgery for glue ear 6.1 Discussion 85 106 vi Contents Part Two Statistical Methods Data, tables, graphs, summary statistics and 109 probability 7.1 Data 7.2 Tables and graphs 7.3 Summary statistics. .. blood-pressure data for the patients we actually include in our study The statistician regards the 'sample data' as 'known', in the sense that he can calculate various statistics from them He also regards... medical statistics usually start with elementary statistical techniques of data presentation and analysis, building up to more advanced techniques Relevant examples from the literature, for example