Table Of Content

This guide may be used to indicate appropriate statistical methods. It is advisable to read the details of all these tests after consulting this table Design or aim of study Type of data/assumptions Statistical method COMPARE TWO INDEPENDENT SAMPLES Compare two means Continuous, Normal distribution, same variance t test for two independent means Compare two proportions Categorical, two categories, all expected values greater than 5 Chi-squared test Compare two proportions Categorical, two categories, some expected values less than 5 Fisher’s exact test Compare distributions Ordinal Wilcoxon two-sample signed rank test equivalent to Mann Whitney U test Compare time to an event (e.g. survival) in two groups Continuous Logrank test COMPARE SEVERAL INDEPENDENT SAMPLES Compare several means Continuous, Normal distribution, same variance One-way analysis of variance Compare time to an event (e.g. survival) in several groups Continuous Logrank test A guide to unifactorial statistical methods COMPARE DIFFERENCES IN A PAIRED SAMPLE Test mean difference Continuous, Normal distribution for differences t test for two paired (matched) means Compare two paired proportions Categorical, two categories (binary) McNemar’s test Distribution of differences Ordinal, symmetrical distribution Wilcoxon matched pairs test Distribution of differences Ordinal Sign test RELATIONSHIPS BETWEEN TWO VARIABLES Test strength of linear relationship between two variables Continuous, at least one has Normal distribution Pearson’s correlation Test strength of relationship between two variables Ordinal Spearman’s rank correlation, Kendall’s tau (if many ties) Examine nature of linear relationship between two variables Continuous, residuals from Normal distribution, constant variance Simple linear regression Test association between two categorical variables Categorical, more than two categories for either or both variables, at least 80% of expected frequencies greater than 5 Chi-squared test Test for trend in proportions Categorical, one variable has two categories and the other has several categories which are ordered, sample greater than 30 Chi-squared test for trend OXFORD MEDICAL PUBLICATIONS Oxford Handbook of Medical Statistics Published and forthcoming Oxford Handbooks Oxford Handbook for the Foundation Programme 2e Oxford Handbook of Acute Medicine 2e Oxford Handbook of Anaesthesia 2e Oxford Handbook of Applied Dental Sciences Oxford Handbook of Cardiology Oxford Handbook of Clinical and Laboratory Investigation 2e Oxford Handbook of Clinical Dentistry 4e Oxford Handbook of Clinical Diagnosis 2e Oxford Handbook of Clinical Examination and Practical Skills Oxford Handbook of Clinical Haematology 3e Oxford Handbook of Clinical Immunology and Allergy 2e Oxford Handbook of Clinical Medicine—Mini Edition 7e Oxford Handbook of Clinical Medicine 7e Oxford Handbook of Clinical Pharmacy Oxford Handbook of Clinical Rehabilitation 2e Oxford Handbook of Clinical Specialties 8e Oxford Handbook of Clinical Surgery 3e Oxford Handbook of Complementary Medicine Oxford Handbook of Critical Care 3e Oxford Handbook of Dental Patient Care 2e Oxford Handbook of Dialysis 3e Oxford Handbook of Emergency Medicine 3e Oxford Handbook of Endocrinology and Diabetes 2e Oxford Handbook of ENT and Head and Neck Surgery Oxford Handbook of Expedition and Wilderness Medicine Oxford Handbook of Gastroenterology & Hepatology Oxford Handbook of General Practice 3e Oxford Handbook of Genitourinary Medicine, HIV and AIDS 2e Oxford Handbook of Geriatric Medicine Oxford Handbook of Infectious Diseases and Microbiology Oxford Handbook of Key Clinical Evidence Oxford Handbook of Medical Sciences Oxford Handbook of Nephrology and Hypertension Oxford Handbook of Neurology Oxford Handbook of Nutrition and Dietetics Oxford Handbook of Obstetrics and Gynaecology 2e Oxford Handbook of Occupational Health Oxford Handbook of Oncology 2e Oxford Handbook of Ophthalmology Oxford Handbook of Paediatrics Oxford Handbook of Palliative Care 2e Oxford Handbook of Practical Drug Therapy Oxford Handbook of Pre-Hospital Care Oxford Handbook of Psychiatry 2e Oxford Handbook of Public Health Practice 2e Oxford Handbook of Reproductive Medicine and Family Planning Oxford Handbook of Respiratory Medicine 2e Oxford Handbook of Rheumatology 2e Oxford Handbook of Sport and Exercise Medicine Oxford Handbook of Tropical Medicine 3e Oxford Handbook of Urology 2e Oxford Handbook of Medical Statistics Janet L. Peacock Professor of Medical Statistics University of Southampton UK Philip J. Peacock Academic Clinical Fellow in Paediatrics University of Bristol UK 1 1 Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offi ces in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York © Oxford University Press, 2011 The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2011 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, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose this same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available Typeset by Glyph International, Bangalore, India Printed in China on acid-free paper through Asia Pacifi c Offset Ltd. ISBN 978–0–19–955128–6 10 9 8 7 6 5 4 3 2 1 Oxford University Press makes no representation, express or implied, that the drug dosages in this book are correct. Readers must therefore always check the product information and clinical procedures with the most up-to-date published product information and data sheets provided by the manufacturers and the most recent codes of conduct and safety regulations. The authors and publishers do not accept responsibility or legal liability for any errors in the text or for the misuse or misap- plication of material in this work. Except where otherwise stated, drug dosages and recommendations are for the non-pregnant adult who is not breastfeeding. StormRG v All health care professionals want to provide safe and effective care to their patients. This means that everyone has to keep up with the speed of innovation and be in a position to apply the fi ndings of new research. Historically individuals have tended to delegate the assessment of the quality of research to journal editors, the peer review system and guideline developers. However for many reasons this may not be suffi cient. All professionals have to make a judgement call on whether the research fi ndings or guideline recommendations that they are assessing are relevant to the patient in front of them. They will have to decide whether the drug trial designed to determine the short term safety and effi cacy against placebo in a selected population in the USA is really relevant to the elderly, ethnically diverse population with multiple co-morbidities facing them on a Friday afternoon. To make things even more complicated, many of the questions raised in day to day practice will never be answered by randomized controlled trials. So other methods need to be applied, all with their own challenges and potential biases. This means, like it or not, that a sound understanding of medical statistics is essential for all health professionals. Many doctors and medical students fi nd statistics diffi cult to understand, and voice the need for a concise but thorough account of the subject. They plead for the statistical analysis to draw on real life situations and to use examples that they can understand. This book responds completely to that plea by providing an accessible format that allows individual topics to be easily found and understood. It takes the reader, not only through the theory of the underlying statistics, but also the practical steps to set up and interpret all the key research designs. The authors are an experienced academic medical statistician who has conducted many collaborative research studies and taught statistics to students and doctors (to a very high standard—I should know— she taught me), and a junior academic doctor who has published his own work. They have written a book that meets all the needs of doctors and students carrying out their own research, and for those appraising others’ research. Professor Peter Littlejohns Clinical and Public Health Director National Institute for Health and Clinical Excellence Foreword vi To practice evidence-based medicine, doctors need to critically appraise research evidence. The majority of medical research involves quantita- tive methods and so it is essential to be able to understand and interpret statistics. In addition, many doctors conduct research which requires the use of statistics throughout the research process – from design, to data collection and analysis, and to the interpretation and dissemination. Doctors study statistics at undergraduate and postgraduate level and there is an increasing move towards teaching programmes that are based on real clinical problems and real data. However, in our experience both as teacher and former medical student, courses do not always fully equip doctors to critically appraise research evidence or to conduct research and communicate the fi ndings. We have written this book to help bridge this gap by covering a wide span of topics from research design, through collecting and handling data, to both simple and complex statistical analyses. We have aimed to be as comprehensive as possible in this handbook and so we have included all commonly-used statistical methods as well as more advanced methods such as multifactorial regression, mixed models, GEEs, and Bayesian models that are seen in medical papers. However, medical statistics is a broad and ever-growing discipline and so it is inevitable that some newer or less commonly-used topics have not found their way into this edition. For all methods we have provided clear guidance on when methods may be used and how the results of analyses are inter- preted using examples from the medical literature and our own research. We have chosen to give formulae and worked examples for the ‘simpler’ methods as we know that the more mathematically minded readers may want to understand where the numbers come from. For those who do not wish to know, or who simply don’t have time, these can be ignored without loss of continuity. This book is written in the popular Oxford Handbook style with one topic per double page spread, providing easy access to discrete topics for busy doctors and students. Writing in this format has provided a challenge to us since many topics in medical statistics build on other topics and therefore assume prior knowledge. For this reason we have included many cross- references to other sections of the book so that other relevant information is clearly signposted. We have also included references for further reading where we believe that readers may wish to explore the topic in more detail. Writing any material in a punchy, brief style carries the danger of omitting material or ‘dumbing it down’. We have fought hard to avoid doing this, not excluding material but making the format both accessible and thorough. We hope that you agree that we have managed to make this work. Preface vii Acknowledgements So many people have helped us in so many ways with the design, writing and publication of this book. Unfortunately it is inevitable that in naming people we may have missed some out, but we are incredibly grateful to everyone who has helped in any way. Our fi rst thanks go to the OUP clinical reviewers, Tom Turmeziei, Kam Cheong Wong and Ryckie Wade, who provided invaluable feedback on the manuscript, especially in the early days, which helped us to shape the book. Our statistical colleagues, Jenny Freeman and Andrew Smith, gave us very thorough reviews of the draft script and their comments have made the book so much better. We wish to thank Diane Morrison who proof-read the fi rst draft for us to a very short deadline. Of course any errors which remain are our own. We are very grateful to the OUP editors, Catherine Barnes, Sara Chare, Liz Reeve, and Selby Marshall for agreeing with us that this book needed to be written and for helping us to make it happen, and to Kate Wanwimolruk for guiding us through the production process. We especially want to express our appreciation to Anna Winstanley for the tremendous encouragement and enthusiastic support she has given us throughout the project, as well as her patience when we didn’t always make our writing deadlines. We want to thank colleagues at Dartmouth College New Hampshire, USA, where we both have links, especially Margaret Karagas, who hosted Janet so generously to enable her to make a start writing the book. We thank our senior academic colleagues, Paul Roderick for his encouragement and support, and Martin Bland who has always been such a help and inspiration to us both. Finally we wish to say a huge thank you to our spouses, Eric and Becky, for all their helpful comments and suggestions during the writing and proof- reading process, but most of all for their continued confi dence in us and graciousness when at times we neglected them so this book could be completed. This page intentionally left blank ix Detailed contents xi Symbols xix 1 Research design 1 2 Collecting data 75 3 Handling data: what steps are important 101 4 Presenting research fi ndings 127 5 Choosing and using statistical software for analysing data 155 6 Summarizing data 173 7 Probability and distributions 203 8 Statistical tests 237 9 Diagnostic studies 339 10 Other statistical methods 353 11 Analysing multiple observations per subject 377 12 Analysing multiple variables per subject 393 13 Meta-analysis 447 14 Bayesian statistics 477 15 Glossary of terms 499 Index 507 Contents This page intentionally left blank xi Symbols xix 1 Research design 1 Introduction 2 Introduction to research 3 Research questions 4 Interventional studies 6 Randomized controlled trials 8 Randomization in RCTs 10 Patient consent in research studies 12 Blinding in RCTs 14 RCTs: parallel groups and crossover designs 16 Zelen randomized consent design 18 Superiority and equivalence trials 20 Intention to treat analysis 22 Case–control studies 24 Cohort studies 28 Cross-sectional studies 32 Case study and series 34 Deducing causal effects 36 Designing an audit 38 Data collection in audit 40 Research versus audit 41 Data collection: sources of data 42 Data collection: outcomes 44 Outcomes: continuous and categorical 46 Collecting additional data 50 The study protocol 52 Sampling strategies 54 Choosing a sample size 56 Sample size for estimation studies: means 58 Sample size for estimation studies: proportions 60 Sample size for comparative studies 62 Detailed contents xii DETAILED CONTENTS Sample size for comparative studies: means 64 Sample size for comparative studies: proportions 66 Sample size calculations: further issues 68 Sample size: other issues 70 Using a statistical program to do the calculations 72 2 Collecting data 75 Data collection forms 76 Form fi lling and coding 78 Examples of questions with possible coding 80 Data quality 81 Questions and questionnaires 82 Designing good questions 84 Sensitive topics 86 Designing questionnaires 88 Example of a validated questionnaire 90 Designing a new measurement tool: psychometrics 92 Measuring reliability 94 Questionnaire measurement scales 96 Visual analogue scales 98 3 Handling data: what steps are important 101 Data entry 102 Forms that can be automatically scanned for data entry 106 Variable names and labels 108 Joining datasets 110 Joining datasets: examples 112 Storing and transporting data 114 Data checking and errors 116 Data checking: examples 118 Formal data monitoring 122 Statistical issues in data monitoring 124 4 Presenting research fi ndings 127 Communicating statistics 128 Producing journal articles 130 Research articles: abstracts 132 Research articles: introduction and methods sections 134