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Disease Mapping with Winbugs and Mlwin Disease Mapping with WinBUGS and MLwiN Andrew B. Lawson Department of Epidemiology and Biostatistics University of South Carolina, USA William J. Browne School of Mathematical Sciences University of Nottingham, UK Carmen L. Vidal Rodeiro Department of Epidemiology and Biostatistics University of South Carolina, USA Disease Mapping with WinBUGS and MLwiN STATISTICS IN PRACTICE Advisory Editor Stephen Senn University College London, UK Founding Editor Vic Barnett Nottingham Trent University, UK Statistics in Practice is an important international series of texts which provide detailed coverage of statistical concepts, methods and worked case studies in specific fields of investigation and study. With sound motivation and many worked practical examples, the books show in down-to-earth terms how to select and use an appropriate range of statistical techniques in a particular practical field within each title’s special topic area. The books provide statistical support for professionals and research workers across a range of employment fields and research environments. Subject areas covered include medicine and pharmaceutics; industry, finance and commerce; public services; the earth and environmental sciences, and so on. The books also provide support to students studying statistical courses applied to the above areas. The demand for graduates to be equipped for the work environment has led to such courses becoming increasingly prevalent at uni- versities and colleges. It is our aim to present judiciously chosen and well-written workbooks to meet everyday practical needs. Feedback of views from readers will be most valuable to monitor the success of this aim. A complete list of titles in this series appears at the end of the volume. Disease Mapping with WinBUGS and MLwiN Andrew B. Lawson Department of Epidemiology and Biostatistics University of South Carolina, USA William J. Browne School of Mathematical Sciences University of Nottingham, UK Carmen L. Vidal Rodeiro Department of Epidemiology and Biostatistics University of South Carolina, USA Copyright # 2003 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (þ44) 1243 779777 Email (for orders and customer service enquiries): cs-bookswiley.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 permreqwiley.co.uk, or faxed to (þ44) 1243 770571. 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 Offices 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 129809 John Wiley & Sons Canada Ltd, 22 Worcester Road, Etobicoke, Ontario, Canada M9W 1L1 Library of Congress Cataloging-in-Publication Data Lawson, Andrew (Andrew B.) Disease mapping with WinBUGS and MLwiN / Andrew B. Lawson, William J. Browne, Carmen L. Vidal Rodeiro. p. cm. – (Statistics in practice) Includes bibliographical references and index. ISBN 0-470-85604-1 (hbk. : alk. paper) 1. Medical geography. 2. Medical geography – Maps – Data processing. 3. Epidemiology – Statistical methods. 4. Epidemiology – Data processing. 5. Public health surveillance. I. Browne, William J., Ph.D. II. Vidal Rodeiro, Carmen L. III. Title. IV. Statistics in practice (Chichester, England). RA792.5.L388 2003 615.4’2’0727–dc21 2003053782 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 0–470–85604–1 Typeset in 10/12 pt by Kolam Information Services Pvt. Ltd, Pondicherry, India Printed and bound in Great Britain by T J International Ltd, Padstow, Cornwall 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. Contents Preface ix Notation xi 0.1 Standard notation for multilevel modelling xi 0.2 Spatial multiple-membership models and the MMMC notation xii 0.3 Standard notation for WinBUGS models xii 1 Disease mapping basics 1 1.1 Disease mapping and map reconstruction 2 1.2 Disease map restoration 3 2 Bayesian hierarchical modelling 17 2.1 Likelihood and posterior distributions 17 2.2 Hierarchical models 18 2.3 Posterior inference 19 2.4 Markov chain Monte Carlo methods 20 2.5 Metropolis and Metropolis–Hastings algorithms 21 2.6 Residuals and goodness of fit 26 3 Multilevel modelling 29 3.1 Continuous response models 30 3.2 Estimation procedures for multilevel models 35 3.3 Poisson response models 38 3.4 Incorporating spatial information 42 3.5 Discussion 43 4 WinBUGS basics 45 4.1 About WinBUGS 45 4.2 Start using WinBUGS 47 4.3 Specification of the model 50 4.4 Model fitting 59 4.5 Scripts 64 4.6 Checking convergence 65 v vi Contents 4.7 Spatial modelling: GeoBUGS 67 4.8 Conclusions 72 5 MLwiN basics 75 5.1 About MLwiN 75 5.2 Getting started 77 5.3 Fitting statistical models 84 5.4 MCMC estimation in MLwiN 94 5.5 Spatial modelling 104 5.6 Conclusions 113 6 Relative risk estimation 115 6.1 Relative risk estimation using WinBUGS 115 6.2 Spatial prediction 137 6.3 An analysis of the Ohio dataset using MLwiN 139 7 Focused clustering: the analysis of putative health hazards 155 7.1 Introduction 155 7.2 Study design 156 7.3 Problems of inference 158 7.4 Modelling the hazard exposure risk 160 7.5 Models for count data 164 7.6 Bayesian models 166 7.7 Focused clustering in WinBUGS 167 7.8 Focused clustering in MLwiN 190 8 Ecological analysis 197 8.1 Introduction 197 8.2 Statistical models 198 8.3 WinBUGS analyses of ecological datasets 199 8.4 MLwiN analyses of ecological datasets 219 9 Spatially-correlated survival analysis 235 9.1 Survival analysis in WinBUGS 235 9.2 Survival analysis in MLwiN 237 10 Epilogue 251 Appendix 1: WinBUGS code for focused clustering models 253 A.1 Falkirk example 253 A.2 Ohio example 256 Contents vii Appendix 2: S-Plus function for conversion to GeoBUGS format 263 Bibliography 267 Index 275 Statistics in Practice Human and Biological Sciences Brown and Prescott – Applied Mixed Models in Medicine Ellenberg, Fleming and DeMets – Data Monitoring in Clinical Trials: A Practical Perspective Lawson, Browne and Vidal Rodeiro – Disease Mapping with WinBUGS and MLwiN Marubini and Valsecchi – Analysing Survival Data from Clinical Trials and Observation Studies Parmigiani – Modeling in Medical Decision Making: A Bayesian Approach Senn – Cross-over Trials in Clinical Research, Second Edition Senn – Statistical Issues in Drug Development Whitehead – Design and Analysis of Sequential Clinical Trials, Revised Second Edition Whitehead – Meta-analysis of Controlled Clinical Trials Earth and Environmental Sciences Buck, Cavanagh and Litton – Bayesian Approach to Intrepreting Archaeological Data Glasbey and Horam – Image Analysis for the Biological Sciences Webster and Oliver – Geostatistics for Environmental Scientists Industry, Commerce and Finance Aitken – Statistics and the Evaluation of Evidence for Forensic Scientists Lehtonen and Pahkinen – Practical Methods for Design and Analysis of Complex Surveys, Second Edition Ohser and Mu¨cklich – Statistical Analysis of Microstructures in Materials Science Preface The analysis of disease maps has seen considerable development over the last decade. This development has been reflected in a fast-increasing literature and has been matched by the development of software tools. The intersecting areas of spatial statistical methods development and geographical information systems (GIS) have both witnessed this growth. With increasing public health concerns about environmental risks and even bioterrorism, the need for good methods for analysing spatial health data is immediate. Two major software tools have now been developed, which allow the modelling of spatially-refer- enced small area health data. These tools, MLwiN and WinBUGS, both provide facilities for sophisticated modelling of realistically complex health data. Win- BUGS was developed to allow the application of a wide range of hierarchical Bayesian models, exploiting modern computational advances, in particular Gibbs sampling. MLwiN was developed to allow the fitting of models to multi- level data where a natural parameter hierarchy exists. Originally, this was implemented using iterative likelihood and quasi-likelihood estimation methods. However, the most recent versions of the package have implemented Bayesian computational methodology and
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