A practical guide to network meta-analysis with examples and code

In the evaluation of healthcare, rigorous methods of quantitative assessment are necessary to establish which interventions are effective and cost-effective. Often a single study will not provide the answers and it is desirable to synthesise evidence from multiple sources, usually randomised controlled trials. This book takes an approach to evidence synthesis that is specifically intended for decision making when there are two or more treatment alternatives being evaluated, and assumes that the purpose of every synthesis is to answer the question "for this pre-identified population of patients, which treatment is 'best'?"

A comprehensive, coherent framework for network meta-analysis (mixed treatment comparisons) is adopted and estimated using Bayesian Markov Chain Monte Carlo methods implemented in the freely available software WinBUGS. Each chapter contains worked examples, exercises, solutions and code that may be adapted by readers to apply to their own analyses.

This book can be used as an introduction to evidence synthesis and network meta-analysis, its key properties and policy implications. Examples and advanced methods are also presented for the more experienced reader.

* Methods used throughout this book can be applied consistently: model critique and checking for evidence consistency are emphasised.

* Methods are based on technical support documents produced for NICE Decision Support Unit, which support the NICE Methods of Technology Appraisal.

* Code presented is also the basis for the code used by the ISPOR Task Force on Indirect Comparisons.

* Includes extensive carefully worked examples, with thorough explanations of how to set out data for use in WinBUGS and how to interpret the output.

Network Meta-Analysis for Decision Making will be of interest to decision makers, medical statisticians, health economists, and anyone involved in Health Technology Assessment including the pharmaceutical industry.

SOFIA DIAS, University of Bristol, UK
A.E. ADES, University of Bristol, UK
NICKY J. WELTON, University of Bristol, UK
JEROEN P. JANSEN, Precision Health Economics, USA
ALEXANDER J. SUTTON, University of Leicester, UK

A practical guide to network meta-analysis with examples and code

In the evaluation of healthcare, rigorous methods of quantitative assessment are necessary to establish which interventions are effective and cost-effective. Often a single study will not provide the answers and it is desirable to synthesise evidence from multiple sources, usually randomised controlled trials. This book takes an approach to evidence synthesis that is specifically intended for decision making when there are two or more treatment alternatives being evaluated, and assumes that the purpose of every synthesis is to answer the question "for this pre-identified population of patients, which treatment is 'best'?"

A comprehensive, coherent framework for network meta-analysis (mixed treatment comparisons) is adopted and estimated using Bayesian Markov Chain Monte Carlo methods implemented in the freely available software WinBUGS. Each chapter contains worked examples, exercises, solutions and code that may be adapted by readers to apply to their own analyses.

This book can be used as an introduction to evidence synthesis and network meta-analysis, its key properties and policy implications. Examples and advanced methods are also presented for the more experienced reader.

• Methods used throughout this book can be applied consistently: model critique and checking for evidence consistency are emphasised.
• Methods are based on technical support documents produced for NICE Decision Support Unit, which support the NICE Methods of Technology Appraisal.
• Code presented is also the basis for the code used by the ISPOR Task Force on Indirect Comparisons.
• Includes extensive carefully worked examples, with thorough explanations of how to set out data for use in WinBUGS and how to interpret the output.

Network Meta-Analysis for Decision Making will be of interest to decision makers, medical statisticians, health economists, and anyone involved in Health Technology Assessment including the pharmaceutical industry.

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

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, D¯model 62

3.2.4.2 Posterior Mean Residual Deviance, D¯res 64

3.3 Model Comparison 66

3.3.1 Effective Number of Parameters, pD 68

3.3.2 Deviance Information Criterion (DIC) 69

3.3.2.1 *Leverage Plots 70

3.3.3 Worked Example: Full Thrombolytic Treatments Network 70

3.4 Outlier Detection in Network Meta?-Analysis 75

3.4.1 Outlier Detection in Pairwise Meta?-Analysis 75

3.4.2 Predictive Cross?-Validation for Network Meta?-Analysis 79

3.4.3 Note on Multi?-Arm Trials 85

3.4.4 WinBUGS Code: Predictive Cross?-Validation for Network Meta?-Analysis 86

3.5 Summary and Further Reading 89

3.6 Exercises 90

4 Generalised Linear Models 93

4.1 A Unified Framework for Evidence Synthesis 93

4.2 The Generic Network Meta?-Analysis Models 94

4.3 Univariate Arm?-Based Likelihoods 99

4.3.1 Rate Data: Poisson Likelihood and Log Link 99

4.3.1.1 WinBUGS Implementation 100

4.3.1.2 Example: Dietary Fat 101

4.3.1.3 Results: Dietary Fat 104

4.3.2 Rate Data: Binomial Likelihood and Cloglog Link 105

4.3.2.1 WinBUGS Implementation 107

4.3.2.2 Example: Diabetes 109

4.3.2.3 Results: Diabetes 112

4.3.3 Continuous Data: Normal Likelihood and Identity Link 114

4.3.3.1 Before/After Studies: Change from Baseline Measures 115

4.3.3.2 Standardised Mea…