Title Details

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 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