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.

Table of Contents:
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 τ 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 predictive checks 131 6.6 Summary key points 134 6.7 Further reading 134 6.8 Exercises 134 References 137 7 Evidence synthesis in a decision modelling framework 138 7.1 Introduction 138 7.2 Evaluation of decision models: One-stage vs two-stage approach 139 7.3 Sensitivity analyses (of model inputs and model specifications) 147 7.4 Summary key points 147 7.5 Further reading 147 7.6 Exercises 147 References 149 8 Multi-parameter evidence synthesis 151 8.1 Introduction 151 8.2 Prior and posterior simulation in a probabilistic model: Maple Syrup Urine Disease (MSUD) 152 8.3 A model for prenatal HIV testing 155 8.4 Model criticism in multi-parameter models 161 8.5 Evidence-based policy 163 8.6 Summary key points 164 8.7 Further reading 165 8.8 Exercises 166 References 167 9 Mixed and indirect treatment comparisons 169 9.1 Why go beyond ‘direct’ head-to-head trials? 169 9.2 A fixed treatment effects model for MTC 172 9.2.1 Absolute treatment effects 176 9.2.2 Relative treatment efficacy and ranking 176 9.3 Random Effects MTC models 178 9.4 Model choice and consistency of MTC evidence 179 9.4.1 Techniques for presenting and understanding the results of MTC 180 9.5 Multi-arm trials 181 9.6 Assumptions made in mixed treatment comparisons 182 9.7 Embedding an MTC within a cost-effectiveness analysis 183 9.8 Extension to continuous, rate and other outcomes 185 9.9 Summary key points 187 9.10 Further reading 187 9.11 Exercises 189 References 190 10 Markov models 193 10.1 Introduction 193 10.2 Continuous and discrete time Markov models 195 10.3 Decision analysis with Markov models 196 10.3.1 Evaluating Markov models 197 10.4 Estimating transition parameters from a single study 199 10.4.1 Likelihood 202 10.4.2 Priors and posteriors for multinomial probabilities 202 10.5 Propagating uncertainty in Markov parameters into a decision model 206 10.6 Estimating transition parameters from a synthesis of several studies 209 10.6.1 Challenges for meta-analysis of evidence on Markov transition parameters 209 10.6.2 The relationship between probabilities and rates 211 10.6.3 Modelling study effects 213 10.6.4 Synthesis of studies reporting aggregate data 215 10.6.5 Incorporating studies that provide event history data 217 10.6.6 Reporting results from a Random Effects model 219 10.6.7 Incorporating treatment effects 220 10.7 Summary key points 224 10.8 Further reading 224 10.9 Exercises 224 References 225 11 Generalised evidence synthesis 227 11.1 Introduction 227 11.2 Deriving a prior distribution from observational evidence 230 11.3 Bias allowance model for the observational data 233 11.4 Hierarchical models for evidence from different study designs 238 11.5 Discussion 244 11.6 Summary key points 244 11.7 Further reading 245 11.8 Exercises 246 References 248 12 Expected value of information for research prioritisation and study design 251 12.1 Introduction 251 12.2 Expected value of perfect information 256 12.3 Expected value of partial perfect information 259 12.3.1 Computation 261 12.3.2 Notes on EVPPI 264 12.4 Expected value of sample information 264 12.4.1 Computation 265 12.5 Expected net benefit of sampling 266 12.6 Summary key points 267 12.7 Further reading 268 12.8 Exercises 268 References 268 Appendix 1 Abbreviations 270 Appendix 2 Common distributions 272 A2.1 The Normal distribution 272 A2.2 The Binomial distribution 273 A2.3 The Multinomial distribution 273 A2.4 The Uniform distribution 274 A2.5 The Exponential distribution 274 A2.6 The Gamma distribution 275 A2.7 The Beta distribution 276 A2.8 The Dirichlet distribution 277 Index 278