In the evaluation of healthcare, rigorous methods of quantitative assessment are necessary to establish interventions that are both effective and cost-effective. Usually a single study will not fully address these issues and it is desirable to synthesize evidence from multiple sources. This book aims to provide a practical guide to evidence synthesis for the purpose of decision making, starting with a simple single parameter model, where all studies estimate the same quantity (pairwise meta-analysis) and progressing to more complex multi-parameter structures (including meta-regression, mixed treatment comparisons, Markov models of disease progression, and epidemiology models). A comprehensive, coherent framework is adopted and estimated using Bayesian methods.

Key features:

* A coherent approach to evidence synthesis from multiple sources.

* Focus is given to Bayesian methods for evidence synthesis that can be integrated within cost-effectiveness analyses in a probabilistic framework using Markov Chain Monte Carlo simulation.

* Provides methods to statistically combine evidence from a range of evidence structures.

* Emphasizes the importance of model critique and checking for evidence consistency.

* Presents numerous worked examples, exercises and solutions drawn from a variety of medical disciplines throughout the book.

* WinBUGS code is provided for all examples.

Evidence Synthesis for Decision Making in Healthcare is intended for health economists, decision modelers, statisticians and others involved in evidence synthesis, health technology assessment, and economic evaluation of health technologies.

Nicky Welton, Department of Social Medicine, University of Bristol
Dr Welton's research includes Bayesian statistical modeling in epidemiology and evidence synthesis and evidence consistency.

Alex Sutton, Department of Health Sciences, University of Leicester
Dr Sutton, senior lecture in medical statistics, has a primary research interest in meta-analysis. This specifically includes methods to combine evidence from disparate sources, and methods to deal with the problem of publication bias. With numerous published papers in a variety of journals he has also collaborated on over 15 substantive evidence synthesis projects. He is lead author on one of the first textbooks on meta-analysis in medicine and is co-editor on a recently published Wiley book on publication bias.

Nicola Cooper, Department of Health Sciences, University of Leicester
Dr Cooper's primary research interest is in the interface and integration of medical statistics and health economics. This specifically includes methods for statistical modelling of cost data, integration of evidence synthesis within a decision-modelling context, handling of missing data in economic evaluations conducted alongside clinical trials, and the application of Bayesian statistical methods to all of the above.

Keith Abrams, Department of Health Sciences, University of Leicester
Professor Abrams' research interests include the development and application of Bayesian methods in healthcare evaluation, systematic reviews and meta-analysis, and the joint modeling of longitudinal and time-to-event data. He has published dozens of articles in numerous international journals and is the co-author of two Wiley books in this area.

Anthony E Ades, Department of Social Medicine, University of Bristol with over 30 published articles in the last three years, Professor Ades' research interests include statistical methods for multi-parameter evidence synthesis in epidemiology, disease mapping and economic evaluation; Bayesian decision theory and the expected value of information; statistical and epidemiological methods in infectious disease surveillance.

Preface xi

1 Introduction 1

1.1 The rise of health economics 1

1.2 Decision making under uncertainty 4

1.2.1 Deterministic models 4

1.2.2 Probabilistic decision modelling 6

1.3 Evidence-based medicine 9

1.4 Bayesian statistics 10

1.5 NICE 11

1.6 Structure of the book 12

1.7 Summary key points 13

1.8 Further reading 13

References 14

2 Bayesian methods and WinBUGS 17

2.1 Introduction to Bayesian methods 17

2.1.1 What is a Bayesian approach? 17

2.1.2 Likelihood 18

2.1.3 Bayes' theorem and Bayesian updating 19

2.1.4 Prior distributions 22

2.1.5 Summarising the posterior distribution 23

2.1.6 Prediction 24

2.1.7 More realistic and complex models 24

2.1.8 MCMC and Gibbs sampling 25

2.2 Introduction to WinBUGS 26

2.2.1 The BUGS language 26

2.2.2 Graphical representation 31

2.2.3 Running WinBUGS 32

2.2.4 Assessing convergence in WinBUGS 33

2.2.5 Statistical inference in WinBUGS 36

2.2.6 Practical aspects of using WinBUGS 39

2.3 Advantages and disadvantages of a Bayesian approach 39

2.4 Summary key points 40

2.5 Further reading 41

2.6 Exercises 41

References 42

3 Introduction to decision models 43

3.1 Introduction 43

3.2 Decision tree models 44

3.3 Model parameters 45

3.3.1 Effects of interventions 45

3.3.2 Quantities relating to the clinical epidemiology of the clinical condition being treated 50

3.3.3 Utilities 52

3.3.4 Resource use and costs 52

3.4 Deterministic decision tree 52

3.5 Stochastic decision tree 56

3.5.1 Presenting the results of stochastic economic decision models 60

3.6 Sources of evidence 66

3.7 Principles of synthesis for decision models (motivation for the rest of the book) 70

3.8 Summary key points 70

3.9 Further reading 71

3.10 Exercises 71

References 72

4 Meta-analysis using Bayesian methods 76

4.1 Introduction 76

4.2 Fixed Effect model 78

4.3 Random Effects model 81

4.3.1 The predictive distribution 83

4.3.2 Prior specification for 84

4.3.3 'Exact' Random Effects model for Odds Ratios based on a Binomial likelihood 84

4.3.4 Shrunken study level estimates 86

4.4 Publication bias 87

4.5 Study validity 88

4.6 Summary key points 88

4.7 Further reading 88

4.8 Exercises 89

References 92

5 Exploring between study heterogeneity 94

5.1 Introduction 94

5.2 Random effects meta-regression models 95

5.2.1 Generic random effect meta-regression model 95

5.2.2 Random effects meta-regression model for Odds Ratio (OR) outcomes using a Binomial likelihood 98

5.2.3 Autocorrelation and centring covariates 100

5.3 Limitations of meta-regression 104

5.4 Baseline risk 105

5.4.1 Model for including baseline risk in a meta-regression on the (log) OR scale 107

5.4.2 Final comments on including baseline risk as a covariate 109

5.5 Summary key points 110

5.6 Further reading 110

5.7 Exercises 110

References 113

6 Model critique and evidence consistency in random effects meta-analysis 115

6.1 Introduction 115

6.2 The Random Effects model revisited 117

6.3 Assessing model fit 121

6.3.1 Deviance 121

6.3.2 Residual deviance 122

6.4 Model comparison 124

6.4.1 Effective number of parameters, pD 125

6.4.2 Deviance Information Criteria 126

6.5 Exploring inconsistency 127

6.5.1 Cross-validation 128

6.5.2 Mixed...