A practical guide to network meta-analysis with examples and codeIn 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 xiiiList of Abbreviations xxiAbout the Companion Website xxv1 Introduction to Evidence Synthesis 11.1 Introduction 11.2 Why Indirect Comparisons and Network Meta?-Analysis? 21.3 Some Simple Methods 41.4 An Example of a Network Meta?-Analysis 61.5 Assumptions Made by Indirect Comparisons and Network Meta?-Analysis 91.6 Which Trials to Include in a Network 121.6.1 The Need for a Unique Set of Trials 121.7 The Definition of Treatments and Outcomes: Network Connectivity 141.7.1 Lumping and Splitting 141.7.2 Relationships Between Multiple Outcomes 151.7.3 How Large Should a Network Be? 151.8 Summary 161.9 Exercises 162 The Core Model 192.1 Bayesian Meta?-Analysis 192.2 Development of the Core Models 202.2.1 Worked Example: Meta?-Analysis of Binomial Data 212.2.1.1 Model Specification: Two Treatments 212.2.1.2 WinBUGS Implementation: Two Treatments 252.2.2 Extension to Indirect Comparisons and Network Meta?-Analysis 322.2.2.1 Incorporating Multi?-Arm Trials 352.2.3 Worked Example: Network Meta?-Analysis 362.2.3.1 WinBUGS Implementation 372.3 Technical Issues in Network Meta?-Analysis 502.3.1 Choice of Reference Treatment 502.3.2 Choice of Prior Distributions 512.3.3 Choice of Scale 532.3.4 Connected Networks 542.4 Advantages of a Bayesian Approach 552.5 Summary of Key Points and Further Reading 562.6 Exercises 573 Model Fit, Model Comparison and Outlier Detection 593.1 Introduction 593.2 Assessing Model Fit 603.2.1 Deviance 603.2.2 Residual Deviance 613.2.3 Zero Counts* 623.2.4 Worked Example: Full Thrombolytic Treatments Network 623.2.4.1 Posterior Mean Deviance, Dmodel 623.2.4.2 Posterior Mean Residual Deviance, Dres 643.3 Model Comparison 663.3.1 Effective Number of Parameters, pD 683.3.2 Deviance Information Criterion (DIC) 693.3.2.1 *Leverage Plots 703.3.3 Worked Example: Full Thrombolytic Treatments Network 703.4 Outlier Detection in Network Meta?-Analysis 753.4.1 Outlier Detection in Pairwise Meta?-Analysis 753.4.2 Predictive Cross?-Validation for Network Meta?-Analysis 793.4.3 Note on Multi?-Arm Trials 853.4.4 WinBUGS Code: Predictive Cross?-Validation for Network Meta?-Analysis 863.5 Summary and Further Reading 893.6 Exercises 904 Generalised Linear Models 934.1 A Unified Framework for Evidence Synthesis 934.2 The Generic Network Meta?-Analysis Models 944.3 Univariate Arm?-Based Likelihoods 994.3.1 Rate Data: Poisson Likelihood and Log Link 994.3.1.1 WinBUGS Implementation 1004.3.1.2 Example: Dietary Fat 1014.3.1.3 Results: Dietary Fat 1044.3.2 Rate Data: Binomial Likelihood and Cloglog Link 1054.3.2.1 WinBUGS Implementation 1074.3.2.2 Example: Diabetes 1094.3.2.3 Results: Diabetes 1124.3.3 Continuous Data: Normal Likelihood and Identity Link 1144.3.3.1 Before/After Studies: Change from Baseline Measures 1154.3.3.2 Standardised Mean Differences 1154.3.3.3 WinBUGS Implementation 1164.3.3.4 Example: Parkinson's 1174.3.3.5 Results: Parkinson's 1194.4 Contrast?-Based Likelihoods 1204.4.1 Continuous Data: Treatment Differences 1214.4.1.1 Multi?-Arm Trials with Treatment Differences (Trial?-Based Summaries) 1224.4.1.2 *WinBUGS Implementation 1234.4.1.3 Example: Parkinson's (Treatment Differences as Data) 1254.4.1.4 Results: Parkinson's (Treatment Differences as Data) 1274.5 *Multinomial Likelihoods 1274.5.1 Ordered Categorical Data: Multinomial Likelihood and Probit Link 1284.5.1.1 WinBUGS Implementation 1324.5.1.2 Example: Psoriasis 1334.5.1.3 Results: Psoriasis 1374.5.2 Competing Risks: Multinomial Likelihood and Log Link 1384.5.2.1 WinBUGS Implementation 1404.5.2.2 Example: Schizophrenia 1414.5.2.3 Results: Schizophrenia 1434.6 *Shared Parameter Models 1464.6.1 Example: Parkinson's (Mixed Treatment Difference and Arm?-Level Data) 1474.6.2 Results: Parkinson's (Mixed Treatment Difference and Arm?-Level Data) 1484.7 Choice of Prior Distributions 1494.8 Zero Cells 1494.9 Summary of Key Points and Further Reading 1504.10 Exercises 1515 Network Meta?-Analysis Within Cost?-Effectiveness Analysis 1555.1 Introduction 1555.2 Sources of Evidence for Relative Treatment Effects and the Baseline Model 1565.3 The Baseline Model 1585.3.1 Estimating the Baseline Model in WinBUGS 1585.3.2 Alternative Computation Methods for the Baseline Model 1625.3.3 *Arm?-Based Meta?-Analytic Models 1625.3.4 Baseline Models with Covariates 1645.3.4.1 Using Aggregate Data 1645.3.4.2 Risk Equations for the Baseline Model Basedon Individual Patient Data 1655.4 The Natural History Model 1655.5 Model Validation and Calibration Through Multi?-Parameter Synthesis 1675.6 Generating the Outputs Required for Cost?-Effectiveness Analysis 1695.6.1 Generating a CEA 1695.6.2 Heterogeneity in the Context of Decision?-Making 1705.7 Strategies to Implement Cost?-Effectiveness Analyses 1735.7.1 Bayesian Posterior Simulation: One?-Stage Approach 1745.7.2 Bayesian Posterior Simulation: Two?-Stage Approach 1745.7.3 Multiple Software Platforms and Automation of Network Meta?-Analysis 1755.8 Summary and Further Reading 1775.9 Exercises 1786 Adverse Events and Other Sparse Outcome Data 1796.1 Introduction 1796.2 Challenges Regarding the Analysis of Sparse Data in Pairwise and Network Meta?-Analysis 1806.2.1 Network Structure and Connectivity 1826.2.2 Assessing Convergence and Model Fit 1826.3 Strategies to Improve the Robustness of Estimation of Effects from Sparse Data in Network Meta?-Analysis 1836.3.1 Specifying Informative Prior Distributions for Response in Trial Reference Groups 1836.3.2 Specifying an Informative Prior Distribution for the Between Study Variance Parameters 1846.3.3 Specifying Reference Group Responses as Exchangeable with Random Effects 1846.3.4 Situational Modelling Extensions 1856.3.5 Specification of Informative Prior Distributions Versus Use of Continuity Corrections 1866.4 Summary and Further Reading 1866.5 Exercises 1877 Checking for Inconsistency 1897.1 Introduction 1897.2 Network Structure 1907.2.1 Inconsistency Degrees of Freedom 1917.2.2 Defining Inconsistency in the Presence of Multi?-Arm Trials 1927.3 Loop Specific Tests for Inconsistency 1957.3.1 Networks with Independent Tests for Inconsistency 1957.3.1.1 Bucher Method for Single Loops of Evidence 1957.3.1.2 Example: HIV 1967.3.1.3 Extension of Bucher Method to Networks with Multiple Loops: Enuresis Example 1977.3.1.4 Obtaining the 'Direct' Estimates of Inconsistency 1997.3.2 Methods for General Networks 2007.3.2.1 Repeat Application of the Bucher Method 2017.3.2.2 A Back?-Calculation Method 2027.3.2.3 *Variance Measures of Inconsistency 2027.3.2.4 *Node?-Splitting 2037.4 A Global Test for Loop Inconsistency 2057.4.1 Inconsistency Model with Unrelated Mean Relative Effects 2067.4.2 Example: Full Thrombolytic Treatments Network 2107.4.2.1 Adjusted Standard Errors for Multi?-Arm Trials 2147.4.3 Example: Parkinson's 2157.4.4 Example: Diabetes 2187.5 Response to Inconsistency 2197.6 The Relationship between Heterogeneity and Inconsistency 2217.7 Summary and Further Reading 2237.8 Exercises 2258 Meta?-Regression for Relative Treatment Effects 2278.1 Introduction 2278.2 Basic Concepts 2298.2.1 Types of Covariate 2298.3 Heterogeneity, Meta?-Regression and Predictive Distributions 2328.3.1 Worked Example: BCG Vaccine 2338.3.2 Implications of Heterogeneity in Decision Making 2368.4 Meta?-Regression Models for Network Meta?-Analysis 2388.4.1 Baseline Risk 2418.4.2 WinBUGS Implementation 2428.4.3 Meta?-Regression with a Continuous Covariate 2458.4.3.1 BCG Vaccine Example: Pairwise Meta?-Regression with a Continuous Covariate 2458.4.3.2 Certolizumab Example: Network Meta?-Regression with Continuous Covariate 2478.4.3.3 Certolizumab Example: Network Meta?-Regression on Baseline Risk 2528.4.4 Subgroup Effects 2558.4.4.1 Statins Example: Pairwise Meta?-Analysis with Subgroups 2568.5 Individual Patient Data in Meta?-Regression 2578.6 Models with Treatment?-Level Covariates 2618.6.1 Accounting for Dose 2618.6.2 Class Effects Models 2638.6.3 Treatment Combination Models 2648.7 Implications of Meta?-Regression for Decision Making 2668.8 Summary and Further Reading 2688.9 Exercises 2699 Bias Adjustment Methods 2739.1 Introduction 2739.2 Adjustment for Bias Based on Meta?-Epidemiological Data 2759.3 Estimation and Adjustment for Bias in Networks of Trials 2789.3.1 Worked Example: Fluoride Therapies for the Prevention of Caries in Children 2799.3.2 Extensions 2859.3.3 Novel Agent Effects 2869.3.4 Small?-Study Effects 2879.3.5 Industry Sponsor Effects 2879.3.6 Accounting for Missing Data 2889.4 Elicitation of Internal and External Bias Distributions from Experts 2899.5 Summary and Further Reading 2909.6 Exercises 29110 *Network Meta?-Analysis of Survival Outcomes 29310.1 Introduction 29310.2 Time?-to?-Event Data 29410.2.1 Individual Patient Data 29410.2.2 Reported Summary Data 29510.2.3 Kaplan-Meier Estimate of the Survival Function 29510.3 Parametric Survival Functions 29610.4 The Relative Treatment Effect 29810.5 Network Meta?-Analysis of a Single Effect Measure per Study 30010.5.1 Proportion Alive, Median Survival and Hazard Ratio as Reported Treatment Effects 30010.5.2 Network Meta?-Analysis of Parametric Survival Curves: Single Treatment Effect 30010.5.3 Shared Parameter Models 30110.5.4 Limitations 30210.6 Network Meta?-Analysis with Multivariate Treatment Effects 30210.6.1 Multidimensional Network Meta?-Analysis Model 30210.6.1.1 Weibull 30210.6.1.2 Gompertz 30310.6.1.3 Log?-Logistic and Log?-Normal 30310.6.1.4 Fractional Polynomial 30410.6.1.5 Splines 30410.6.2 Evaluation of Consistency 30410.6.3 Meta?-Regression 30510.7 Data and Likelihood 30510.7.1 Likelihood with Individual Patient Data 30510.7.2 Discrete or Piecewise Constant Hazards as Approximate Likelihood 30610.7.3 Conditional Survival Probabilities as Approximate Likelihood 30710.7.4 Reconstructing Kaplan-Meier Data 30710.7.5 Constructing Interval Data 30810.8 Model Choice 30810.9 Presentation of Results 30910.10 Illustrative Example 31010.11 Network Meta?-Analysis of Survival Outcomes for Cost?-Effectiveness Evaluations 31910.12 Summary and Further Reading 32010.13 Exercises 32211 *Multiple Outcomes 32311.1 Introduction 32311.2 Multivariate Random Effects Meta?-Analysis 32411.3 Multinomial Likelihoods and Extensions of Univariate Methods 32711.4 Chains of Evidence 32811.4.1 A Decision Tree Structure: Coronary Patency 32811.4.2 Chain of Evidence with Relative Risks: Neonatal Early Onset Group B Strep 33011.5 Follow?-Up to Multiple Time Points: Gastro?-Esophageal Reflux Disease 33211.6 Multiple Outcomes Reported in Different Ways: Influenza 33511.7 Simultaneous Mapping and Synthesis 33711.8 Related Outcomes Reported in Different Ways: Advanced Breast Cancer 34211.9 Repeat Observations for Continuous Outcomes: Fractional Polynomials 34411.10 Synthesis for Markov Models 34511.11 Summary and Further Reading 34711.12 Exercises 34912 Validity of Network Meta?-Analysis 35112.1 Introduction 35112.2 What Are the Assumptions of Network Meta?-Analysis? 35212.2.1 Exchangeability 35212.2.2 Other Terminologies and Their Relation to Exchangeability 35312.3 Direct and Indirect Comparisons: Some Thought Experiments 35512.3.1 Direct Comparisons 35612.3.2 Indirect Comparisons 35912.3.3 Under What Conditions Is Evidence Synthesis Likely to Be Valid? 36212.4 Empirical Studies of the Consistency Assumption 36312.5 Quality of Evidence Versus Reliability of Recommendation 36512.5.1 Theoretical Treatment of Validity of Network Meta?-Analysis 36512.5.2 GRADE Assessment of Quality of Evidence from a Network Meta?-Analyses 36612.5.3 Reliability of Recommendations Versus Quality of Evidence: The Role of Sensitivity Analysis 36812.6 Summary and Further Reading 36912.7 Exercises 373Solutions to Exercises 375Appendices 401References 409Index 447