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Network Meta‐Analysis for Decision-Making Wiley Series in Statistics in Practice Network Meta‐Analysis for Decision-Making Wiley Series in Statistics in Practice Advisory Editor, Marian Scott, University of Glasgow, Scotland, UK Founding Editor, Vic Barnett, Nottingham Trent University, UK Statistics in Practice is an important international series of texts that 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 universities 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. Wiley Series in Statistics in Practice Advisory Editor, Marian Scott, University of Glasgow, Gibbons, Bhaumik, and Aryal · Statistical Methods Scotland, UK for Groundwater Monitoring, Second Edition Founding Editor, Vic Barnett, Nottingham Trent Glasbey and Horgan · Image Analysis in the University, UK Biological Sciences Helsel · Nondetects and Data Analysis: Statistics for Human and Biological Sciences Censored Environmental Data Brown and Prescott · Applied Mixed Models in Medicine Helsel · Statistics for Censored Environmental Data Ellenberg, Fleming and DeMets · Data Monitoring Using Minitab® and R, Second Edition Committees in Clinical Trials: McBride · Using Statistical Methods for Water A Practical Perspective Quality Management: Issues, Problems and Lawson, Browne and Vidal Rodeiro · Disease Solutions Mapping With WinBUGS and MLwiN Ofungwu · Statistical Applications for Environmental Lui · Statistical Estimation of Epidemiological Risk Analysis and Risk Assessment *Marubini and Valsecchi · Analysing Survival Data Webster and Oliver · Geostatistics for Environmental from Clinical Trials and Observation Studies Scientists Parmigiani · Modeling in Medical Decision Making: A Bayesian Approach Industry, Commerce and Finance Senn · Cross‐over Trials in Clinical Research, Aitken and Taroni · Statistics and the Evaluation of Second Edition Evidence for Forensic Scientists, Second Edition Senn · Statistical Issues in Drug Development Brandimarte · Numerical Methods in Finance and Spiegelhalter, Abrams and Myles · Bayesian Approaches Economics: A MATLAB‐Based Introduction, to Clinical Trials and Health‐Care Evaluation Second Edition Turner · New Drug Development: Design, Brandimarte and Zotteri · Introduction to Methodology, and Analysis Distribution Logistics Whitehead · Design and Analysis of Sequential Chan and Wong · Simulation Techniques in Financial Clinical Trials, Revised Second Edition Risk Management, Second Edition Whitehead · Meta‐Analysis of Controlled Clinical Jank · Statistical Methods in eCommerce Research Trials Jank and Shmueli · Modeling Online Auctions Zhou, Zhou, Liu and Ding · Applied Missing Data Lehtonen and Pahkinen · Practical Methods for Design Analysis in the Health Sciences and Analysis of Complex Surveys, Second Edition Earth and Environmental Sciences Lloyd · Data Driven Business Decisions Buck, Cavanagh and Litton · Bayesian Approach to Ohser and Mücklich · Statistical Analysis of Interpreting Archaeological Data Microstructures in Materials Science Cooke · Uncertainty Modeling in Dose Response: Rausand · Risk Assessment: Theory, Methods, and Bench Testing Environmental Toxicity Applications Network Meta‐Analysis for Decision-Making Sofia Dias University of Bristol Bristol, UK A. E. Ades University of Bristol Bristol, UK Nicky J. Welton University of Bristol Bristol, UK Jeroen P. Jansen Precision Health Economics Oakland, CA Alexander J. Sutton University of Leicester Leicester, UK This edition first published 2018 © 2018 John Wiley & Sons Ltd 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 or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions. The right of Sofia Dias, A. E. Ades, Nicky J. Welton, Jeroen P. Jansen and Alexander J. Sutton to be identified as the authors of this work has been asserted in accordance with law. Registered Offices John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK Editorial Office 9600 Garsington Road, Oxford, OX4 2DQ, UK For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com. Wiley also publishes its books in a variety of electronic formats and by print‐on‐demand. Some content that appears in standard print versions of this book may not be available in other formats. Limit of Liability/Disclaimer of Warranty While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. Library of Congress Cataloging‐in‐Publication Data Names: Dias, Sofia, 1977- author. Title: Network meta-analysis for decision-making / by Sofia Dias, University of Bristol, Bristol, UK [and four others]. Description: Hoboken, NJ : Wiley, 2018. | Includes bibliographical references and index. | Identifiers: LCCN 2017036441 (print) | LCCN 2017048849 (ebook) | ISBN 9781118951712 (pdf) | ISBN 9781118951729 (epub) | ISBN 9781118647509 (cloth) Subjects: LCSH: Meta-analysis. | Mathematical analysis. Classification: LCC R853.M48 (ebook) | LCC R853.M48 N484 2018 (print) | DDC 610.72/7–dc23 LC record available at https://lccn.loc.gov/2017036441 Cover Design: Wiley Cover Image: © SergeyNivens/Gettyimages Set in 10/12pt Warnock by SPi Global, Pondicherry, India 10 9 8 7 6 5 4 3 2 1 v Contents Preface xiii List of Abbreviations xxi About the Companion Website xxv 1 Introduction to Evidence Synthesis 1 1.1 Introduction 1 1.2 Why Indirect Comparisons and Network Meta‐Analysis? 2 1.3 Some Simple Methods 4 1.4 An Example of a Network Meta‐Analysis 6 1.5 Assumptions Made by Indirect Comparisons and Network Meta‐Analysis 9 1.6 Which Trials to Include in a Network 12 1.6.1 The Need for a Unique Set of Trials 12 1.7 The Definition of Treatments and Outcomes: Network Connectivity 14 1.7.1 Lumping and Splitting 14 1.7.2 Relationships Between Multiple Outcomes 15 1.7.3 How Large Should a Network Be? 15 1.8 Summary 16 1.9 Exercises 16 2 The Core Model 19 2.1 Bayesian Meta‐Analysis 19 2.2 Development of the Core Models 20 2.2.1 Worked Example: Meta‐Analysis of Binomial Data 21 2.2.1.1 Model Specification: Two Treatments 21 2.2.1.2 WinBUGS Implementation: Two Treatments 25 2.2.2 Extension to Indirect Comparisons and Network Meta‐Analysis 32 2.2.2.1 Incorporating Multi‐Arm Trials 35 2.2.3 Worked Example: Network Meta‐Analysis 36 vi Contents 2.2.3.1 WinBUGS Implementation 37 2.3 Technical Issues in Network Meta‐Analysis 50 2.3.1 Choice of Reference Treatment 50 2.3.2 Choice of Prior Distributions 51 2.3.3 Choice of Scale 53 2.3.4 Connected Networks 54 2.4 Advantages of a Bayesian Approach 55 2.5 Summary of Key Points and Further Reading 56 2.6 Exercises 57 3 Model Fit, Model Comparison and Outlier Detection 59 3.1 Introduction 59 3.2 Assessing Model Fit 60 3.2.1 Deviance 60 3.2.2 Residual Deviance 61 3.2.3 Zero Counts* 62 3.2.4 Worked Example: Full Thrombolytic Treatments Network 62 ̅ 3.2.4.1 Posterior Mean Deviance, Dmodel 62 ̅ 3.2.4.2 Posterior Mean Residual Deviance, Dres 64 3.3 Model Comparison 66 3.3.1 Effective Number of Parameters, pD 68 3.3.2 Deviance Information
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