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Medical Statistics Book Medical Statistics at a Glance Flow charts indicating appropriate techniques in different circumstances* Flow chart for hypothesis tests I I Numerical data Categorical data I I I 1 I 2 categories 1 group 2 groups > 2 groups (investigating proportions) I I I I 1 I I I One-sample Chi-squared t-test (19) Paired Independent Independent 2 groups 1 group > 2 groups test (25) Sign test (19) I I i Paired t-test (20) Unpaired One-way Chi-squared z test for a Wilcoxon signedl t-test (2" ANOVA (22) I I test (25) I ranks test (20) Wicoxon rank Kroskal-Wallis proponion (23) I Independent Chi-squared , Sign test (19) sum test (21) , test (22) Sign test (23) trend test (25) , I I paid , , Chi-squared McNemar's Flow chart for further analyses Longitudinal 1 Additional 1 studies topics Systematic reviews and Agreement - kappa (36) Survival analysis (41) meta-analyses (38) Bayesian methods (42) Correlation coefficients Pearson's (26) Multiple (29) Spearman's (26) Logistic (30) Modelling (31) "Relevant topic numbers shown in parenthesis Medical Statistics at a Glance AVIVA PETRIE Senior Lecturer in Statistics Biostatistics Unit Eastman Dental Institute for Oral Health Care Sciences University College London 256 Grays Inn Road London WClX 8LD and Honorary Lecturer in Medical Statistics Medical Statistics Unit London School of Hygiene and Tropical Medicine Keppel Street London WClE 7HT CAROLINE SABIN Senior Lecturer in Medical Statistics and Epidemiology Department of Primary Care and Population Sciences The Royal Free and University College Medical School Royal Free Campus Rowland Hill Street London NW3 2PF Blackwell Science O 2000 by The right of the Author to be DISTRIBUTORS Blackwell Science Ltd identified as the Author of this Work Marston Book Services Ltd Editorial Offices: has been asserted in accordance PO Box 269 Osney Mead, Oxford OX2 OEL with the Copyright, Designs and Abingdon, Oxon OX14 4YN 25 John Street, London WClN 2BL Patents Act 1988. (Orders: Tel: 01235 465500 23 Ainslie Place, Edinburgh EH3 6AJ Fax: 01235 465555) 350 Main Street, Malden All rights reserved. No part of MA 02148-5018,USA this publication may be reproduced, USA 54 University Street, Carlton stored in a retrieval system, or Blackwell Science, Inc. Victoria 3053, Australia transmitted, in any form or by any Commerce Place 10,rue Casimir Delavigne means, electronic, mechanical, 350 Main Street 75006 Paris, France photocopying, recording or otherwise, Malden, MA 02148-5018 except as permitted by the UK (Orders: Tel: 800 759 6102 Other Editorial Offices: Copyright, Designs and Patents Act 781 388 8250 Blackwell Wissenschafts-Verlag GmbH 1988,without the prior permission Fax: 781 388 8255) Kurfiirstendamm 57 of the copyright owner. Canada 10707 Berlin, Germany Login Brothers Book Company Blackwell Science KK A catalogue record for this title 324 Saulteaux Crescent MG Kodenmacho Building is available from the British Library Winnipeg, Manitoba R3J 3T2 7-10 Kodenmacho Nihombashi (Orders: Tel: 204 837 2987) ISBN 0-632-05075-6 Chuo-ku,Tokyo 104,Japan Australia Blackwell Science Pty Ltd First published 2000 Library of Congress 54 University Street Cataloging-in-publication Data Carlton,Victoria 3053 Set by Excel Typesetters Co., Hong Kong Petrie, Aviva. (Orders: Tel: 3 9347 0300 Printed and bound in Great Britain at Medical statistics at a glance / Aviva the Alden Press, Oxford and Northampton Fax: 3 9347 5001) Petrie, Caroline Sabin. p. cm.. The Blackwell Science logo is a For further information on Includes index. trade mark of Blackwell Science Ltd, Blackwell Science, visit our website: ISBN 0-632-05075-6 registered at the United Kingdom www.blackwell-science.com 1. Medical statistics. 2. Medicine - Trade Marks Registry Statistical methods. I. Sabin, Caroline. 11. Title. R853.S7 P476 2000 610'.7'27 -dc21 99-045806 Contents Preface, 6 Regression and correlation: 26 Correlation, 67 Handling data 27 The theory of linear regression, 70 Types of data, 8 28 Performing a linear regression analysis, 72 Data entry, 10 29 Multiple linear regression, 75 Error checking and outliers, 12 30 Polynomial and logistic regression, 78 Displaying data graphically, 14 31 Statistical modelling, 80 Describing data (1): the 'average', 16 Describing data (2): the 'spread', 18 Important considerations: Theoretical distributions (1): the Normal 32 Checking assumptions, 82 distribution, 20 33 Sample size calculations, 84 Theoretical distributions (2): other distributions, 22 34 Presenting results, 87 Transformations, 24 Additional topics Sampling and estimation Diagnostic tools, 90 Sampling and sampling distributions, 26 Assessing agreement, 93 Confidence intervals, 28 Evidence-based medicine, 96 Systematic reviews and meta-analysis, 98 Study design Methods for repeated measures, 101 Study design I, 30 Time series, 104 Study design II,32 Survival analysis, 106 Clinical trials, 34 Bayesian methods, 109 Cohort studies, 37 Case-control studies, 40 Appendices A Statistical tables, 112 Hypothesis testing B Altman's nomogram for sample size calculations, 119 Hypothesis testing, 42 C Typical computer output, 120 Errors in hypothesis testing, 44 D Glossary of terms, 127 Basic techniques for analysing data Index, 135 Numerical data: A single group, 46 Two related groups, 49 Two unrelated groups, 52 More than two groups, 55 Categorical data: A single proportion, 58 Two proportions, 61 More than two categories, 64 Medical Statistics at a Glance is directed at undergraduate guide to the most commonly used statistical procedures. medical students, medical researchers, postgraduates in the Epidemiology is closely allied to medical statistics. Hence biomedical disciplines and at pharmaceutical industry per- some of the main issues in epidemiology, relating to study sonnel. All of these individuals will, at some time in their design and interpretation, are discussed. Also included are professional lives, be faced with quantitative results (their topics that the reader may find useful only occasionally, but own or those of others) that will need to be critically which are, nevertheless, fundamental to many areas of evaluated and interpreted, and some, of course, will have to medical research; for example, evidence-based medicine, pass that dreaded statistics exam! A proper understanding systematic reviews and meta-analysis, time series, survival of statistical concepts and methodology is invaluable for analysis and Bayesian methods. We have explained the these needs. Much as we should like to fire the reader with principles underlying these topics so that the reader will be an enthusiasm for the subject of statistics, we are pragmatic. able to understand and interpret the results from them Our aim is to provide the student and the researcher, as when they are presented in the literature. More detailed well as the clinician encountering statistical concepts in discussions may be obtained from the references listed on the medical literature, with a book that is sound, easy to our Web site. read, comprehensive, relevant, and of useful practical There is extensive cross-referencing throughout the text application. to help the reader link the various procedures.The Glossary We believe Medical Statistics at a Glance will be particu- of terms (Appendix D) provides readily accessible expla- larly helpful as a adjunct to statistics lectures and as a refer- nations of commonly used terminology. A basic set of sta- ence guide. In addition, the reader can assess hislher tistical tables is contained in Appendix A. Neave, H.R. progress in self-directed learning by attempting the exer- (1981) Elemementary Statistical Tables Routledge, and cises on our Web site (www.medstatsaag.com), which can be Geigy Scientific Tables Vol. 2, 8th edn (1990) Ciba-Geigy accessed from the 1nternet.This Web site also contains a full Ltd., amongst others, provide fuller versions if the reader set of references (some of which are linked directly to requires more precise results for hand calculations. Medline) to supplement the references quoted in the text We know that one of the greatest difficulties facing non- and provide useful background information for the exam- statisticians is choosing the appropriate technique. We have ples. For those readers who wish to gain a greater insight therefore produced two flow-charts which can be used both into particular areas of medical statistics, we can recom- to aid the decision as to what method to use in a given situa- mend the following books: tion and to locate a particular technique in the book easily. They are displayed prominently on the inside cover for easy Altman, D.G. (1991) Practical Statistics for Medical access. Research. Chapman and Hall, London. Every topic describing a statistical technique is accompa- Armitage, P., Berry, G. (1994) Statistical Methods in Medical nied by an example illustrating its use. We have generally Research, 3rd edn. Blackwell Scientific Publications, obtained the data for these examples from collaborative Oxford. studies in which we or colleagues have been involved; in Pocock, S.J. (1983) Clinical Trials: A Practical Approach. some instances, we have used real data from published Wiley, Chichester. papers. Where possible, we have utilized the same data set In line with other books in the At a Glance series, we lead in more than one topic to reflect the reality of data analysis, the reader through a number of self-contained, two- and which is rarely restricted to a single technique or approach. three-page topics, each covering a different aspect of Although we believe that formulae should be provided and medical statistics. We have learned from our own teaching the logic of the approach explained as an aid to understand- experiences, and have taken account of the difficulties that ing, we have avoided showing the details of complex calcu- our students have encountered when studying medical sta- lations-most readers will have access to computers and tistics. For this reason, we have chosen to limit the theoreti- are unlikely to perform any but the simplest calculations by cal content of the book to a level that is sufficient for hand.
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