Individual Participant Data Meta-Analysis - A Handbook for Healthcare Research

Description: Richard Riley is a Professor of Biostatistics at Keele University, having previous held posts at the Universities of Birmingham, Liverpool and Leicester. His role at Keele focuses on statistical and methodological research for prognosis and meta-analysis, whilst supporting clinical projects in these areas. He is a Statistics Editor for the BMJ, and a co-convenor of the Cochrane Prognosis Methods Group. Richard co-leads a summer school in Prognosis Research Methods, and leads a number of statistical training courses for risk prediction and IPD meta-analysis. Jayne Tierney is a Reader in Evidence Synthesis at the MRC Clinical Trials Unit at UCL, London and Deputy Director of the MRC London Hub for Trials Methodology Research. For around 20 years, she has been responsible for designing and conducting systematic reviews and meta-analyses based on IPD to rigorously evaluate the effectiveness of therapies for a range of cancers and other conditions; projects that have influenced practice guidelines and the treatment of patients worldwide. She has also provided training workshops and published guidance on their conduct, and recently led the development of a series of papers on the use and impact of IPD meta-analysis. Lesley Stewart is Professor of Evidence Synthesis and Director of the Centre for Reviews and Dissemination at the University of York, having previously held posts with the Medical Research Council. She was a founding member of the Cochrane Collaboration and has been co-convenor of the IPD Meta-analysis methods group since inception. She began working on IPD synthesis in 1988 and has completed many international collaborative IPD meta-analyses, mainly in cancer topics. She recently chaired the development of PRISMA-IPD and is Co-Editor in Chief of the journal Systematic Reviews. Methods. She is on the Editorial Board of Wiley journal Research Synthesis Methods and BMJ Open. She is past president of the Society for Research Synthesis Methodology. Acknowledgements xxiii 1 Individual Participant Data Meta-analysis for Healthcare Research 1 Richard D. Riley, Lesley A. Stewart, and Jayne F. Tierney 1.1 Introduction 1 1.2 What Is IPD and How Does It Differ from Aggregate Data? 1 1.3 IPD Meta-analysis: A New Era for Evidence Synthesis 2 1.4 Scope of This Book and Intended Audience 2 Part I Rationale, Planning, and Conduct 7 2 Rationale for Embarking on an IPD Meta-analysis Project 9 Jayne F. Tierney, Richard D. Riley, Catrin Tudur Smith, Mike Clarke, and Lesley A. Stewart 2.1 Introduction 9 2.2 How Does the Research Process Differ for IPD and Aggregate Data Meta-analysis Projects? 10 2.2.1 The Research Aims 10 2.2.2 The process and methods 10 2.3 What Are the Potential Advantages of an IPD Meta-analysis Project? 11 2.4 What Are the Potential Challenges of an IPD Meta-Analysis Project? 14 2.5 Empirical Evidence of Differences between Results of IPD and Aggregate Data Metaanalysis Projects 14 2.6 Guidance for Deciding When IPD Meta-analysis Projects Are Needed to Evaluate Treatment Effects from Randomised Trials 15 2.6.1 Are IPD Needed to Tackle the Research Question? 15 2.6.2 Are IPD Needed to Improve the Completeness and Uniformity of Outcomes and Participant-level Covariates? 17 2.6.3 Are IPD Needed to Improve the Information Size? 17 2.6.4 Are IPD Needed to Improve the Quality of Analysis? 18 2.7 Concluding Remarks 19 3 Planning and Initiating an IPD Meta-analysis Project 21 Lesley A. Stewart, Richard D. Riley, and Jayne F. Tierney 3.1 Introduction 22 3.2 Organisational Approach 22 3.2.1 Collaborative IPD Meta-analysis Project 22 3.2.2 IPD Meta-analysis Projects Using Data Repositories or Data-sharing Platforms 24 3.3 Developing a Project Scope 26 3.4 Assessing Feasibility and 'In Principle' Support and Collaboration 26 3.5 Establishing a Team with the Right Skills 29 3.6 Advisory and Governance Functions 30 3.7 Estimating How Long the Project Will Take 31 3.8 Estimating the Resources Required 33 3.9 Obtaining Funding 38 3.10 Obtaining Ethical Approval 39 3.11 Data-sharing Agreement 41 3.12 Additional Planning for Prospective Meta-analysis Projects 41 3.13 Concluding Remarks 43 4 Running an IPD Meta-analysis Project: From Developing the Protocol to Preparing Data for Meta-analysis 45 Jayne F. Tierney, Richard D. Riley, Larysa H.M. Rydzewska, and Lesley A. Stewart 4.1 Introduction 46 4.2 Preparing to Collect IPD 46 4.2.1 Defining the Objectives and Eligibility Criteria 46 4.2.2 Developing the Protocol for an IPD Meta-analysis Project 49 4.2.3 Identifying and Screening Potentially Eligible Trials 51 4.2.4 Deciding Which Information Is Needed to Summarise Trial Characteristics 51 4.2.5 Deciding How Much IPD Are Needed 52 4.2.6 Deciding Which Variables Are Needed in the IPD 52 4.2.7 Developing a Data Dictionary for the IPD 55 4.3 Initiating and Maintaining Collaboration 57 4.4 Obtaining IPD 59 4.4.1 Ensuring That IPD Are De-identified 59 4.4.2 Providing Data Transfer Guidance 60 4.4.3 Transferring trial IPD securely 61 4.4.4 Storing Trial IPD Securely 61 4.4.5 Making Best Use of IPD from Repositories 61 4.5 Checking and Harmonising Incoming IPD 62 4.5.1 The Process and Principles 63 4.5.2 Initial Checking of IPD for Each Trial 63 4.5.3 Harmonising IPD across Trials 64 4.5.4 Checking the Validity, Range and Consistency of Variables 65 4.6 Checking the IPD to Inform Risk of Bias Assessments 66 4.6.1 The Randomisation Process 68 4.6.2 Deviations from the Intended Interventions 71 4.6.3 Missing Outcome Data 73 4.6.4 Measurement of the Outcome 74 4.7 Assessing and Presenting the Overall Quality of a Trial 76 4.8 Verification of Finalised Trial IPD 77 4.9 Merging IPD Ready for Meta-analysis 77 4.10 Concluding Remarks 80 Part I References 81 Part II Fundamental Statistical Methods and Principles 87 5 The Two-stage Approach to IPD Meta-analysis 89 Richard D. Riley, Thomas P.A. Debray, Tim P. Morris, and Dan Jackson 5.1 Introduction 90 5.2 First Stage of a Two-stage IPD Meta-analysis 90 5.2.1 General Format of Regression Models to Use in the First Stage 92 5.2.2 Estimation of Regression Models Applied in the First Stage 92 5.2.3 Regression for Different Outcome Types 94 5.2.3.1 Continuous Outcomes 94 5.2.3.2 Binary Outcomes 98 5.2.3.3 Ordinal and Multinomial Outcomes 99 5.2.3.4 Count and Incidence Rate Outcomes 100 5.2.3.5 Time-to-Event Outcomes 101 5.2.4 Adjustment for Prognostic Factors 102 5.2.5 Dealing with Other Trial Designs and Missing Data 103 5.3 Second Stage of a Two-stage IPD Meta-analysis 106 5.3.1 Meta-analysis Assuming a Common Treatment Effect 106 5.3.2 Meta-analysis Assuming Random Treatment Effects 107 5.3.3 Forest Plots and Percentage Trial Weights 110 5.3.4 Heterogeneity Measures and Statistics 110 5.3.5 Alternative Weighting Schemes 112 5.3.6 Frequentist Estimation of the Between-Trial Variance of Treatment Effect 113 5.3.7 Deriving Confidence Intervals for the Summary Treatment Effect 113 5.3.8 Bayesian Estimation Approaches 115 5.3.8.1 An Introduction to Bayes' Theorem and Bayesian Inference 115 5.3.8.2 Using a Bayesian Meta-Analysis Model in the Second Stage 115 5.3.8.3 Applied Example 117 5.3.9 Interpretation of Summary Effects from Meta-analysis 118 5.3.10 Prediction Interval for the Treatment Effect in a New Trial 118 5.4 Meta-regression and Subgroup Analyses 120 5.5 The ipdmetan Software Package 121 5.6 Combining IPD with Aggregate Data from non-IPD Trials 124 5.7 Concluding Remarks 125 6 The One-stage Approach to IPD Meta-analysis 127 Richard D. Riley and Thomas P.A. Debray 127 6.1 Introduction 128 6.2 One-stage IPD Meta-analysis Models Using Generalised Linear Mixed Models 129 6.2.1 Basic Statistical Framework of One-stage Models Using GLMMs 129 6.2.1.1 Continuous Outcomes 130 6.2.1.2 Binary Outcomes 130 6.2.1.3 Ordinal and Multinomial Outcomes 135 6.2.1.4 Count and Incidence Rate Outcomes 136 6.2.2 Specifying Parameters as Either Common, Stratified, or Random 136 6.2.3 Accounting for Clustering of Participants within Trials 139 6.2.3.1 Examples 141 6.2.4 Choice of Stratified Intercept or Random Intercepts 141 6.2.4.1 Findings from Simulation Studies 142 6.2.4.2 Our Preference for Using a Stratified Intercept 142 6.2.4.3 Allowing for Correlation between Random Effects on Intercept and Treatment Effect 143 6.2.5 Stratified or Common Residual Variances 144 6.2.6 Adjustment for Prognostic Factors 145 6.2.7 Inclusion of Trial-level Covariates 145 6.2.8 Estimation of One-stage IPD Meta-analysis Models Using GLMMs 146 6.2.8.1 Software for Fitting One-stage Models 146 6.2.8.2 ML Estimation and Downward Bias in Between-trial Variance Estimates 146 6.2.8.3 Trial-specific Centering of Variables to Improve ML Estimation of One-stage Models with a Stratified Intercept 147 6.2.8.4 REML Estimation 147 6.2.8.5 Deriving Confidence Intervals for ParametersPpost-estimation 149 6.2.8.6 Prediction Intervals 151 6.2.8.7 Derivation of Percentage Trial Weights 151 6.2.8.8 Bayesian Estimation for One-stage Models 151 6.2.9 A Summary of Recommendations 152 6.3 One-stage Models for Time-to-event Outcomes 152 6.3.1 Cox Proportional Hazard Framework 152 6.3.1.1 Stratifying Using Proportional Baseline Hazards and Frailty Models 152 6.3.1.2 Stratifying Baseline Hazards without Assuming Proportionality 154 6.3.1.3 Comparison of Approaches 154 6.3.1.4 Estimation Methods 154 6.3.1.5 Example 156 6.3.2 Fully Parametric Approaches 157 6.3.3 Extension to Time-varying Hazard Ratios and Joint Models 157 6.4 One-stage Models Combining Different Sources of Evidence 159 6.4.1 Combining IPD Trials with Partially Reconstructed IPD from Non-IPD Trials 159 6.4.2 Combining IPD and Aggregate Data Using Hierarchical Related Regression 160 6.4.3 Combining IPD from Parallel Group, Cluster and Cross-over Trials 161 6.5 Reporting of One-stage Models in Protocols and Publications 162 6.6 Concluding Remarks 162 7 Using IPD Meta-analysis to Examine Interactions between Treatment Effect and Participant-level Covariates 163 Richard D. Riley and David J. Fisher 7.1 Introduction 164 7.2 Meta-regression and Its Limitations 166 7.2.1 Meta-regression of Aggregated Participant-level Covariates 166 7.2.2 Low Power and Aggregation Bias 166 7.2.3 Empirical Evidence of the Difference Between Using Across-trial and Within-trial Information to Estimate Treatment-covariate Interactions 167 7.3 Two-stage IPD Meta-analysis to Estimate Treatment-covariate Interactions 168 7.3.1 The Two-stage Approach 168 7.3.2 Applied Example: Is the Effect of Anti-hypertensive Treatment Different for Males and Females? 170 7.3.3 Do Not Quantify Interactions by Comparing Meta-analysis Results for Subgroups 171 7.4 The One-stage Approach 174 7.4.1 Merging Within-trial and Across-trial Information 174 7.4.2 Separating Within-trial and Across-trial Information 175 7.4.2.1 Approach (i) for a One-stage Survival Model: Center the Covariate and Include the Covariate Mean 175 7.4.2.2 Approach (ii) for a One-stage Survival Model: Stratify All Nuisance Parameters by Trial 176 7.4.2.3 Approaches (i) and (ii) for Continuous and Binary Outcomes 176 7.4.2.4 Comparison of Approaches (i) and (ii) 177 7.4.3 Applied Examples 177 7.4.3.1 Is Age an Effect Modifier for Epilepsy Treatment? 177 7.4.3.2 Is the Effect of an Early Support Hospital Discharge Modified by Having a Carer Present? 178 7.4.4 Coding of the Treatment Covariate and Adjustment for Other Covariates 178 7.4.4.1 Example 180 7.4.5 Estimating the Aggregation Bias Directly 180 7.4.6 Reporting Summary Treatment Effects for Subgroups after Adjusting for Aggregation Bias 180 7.5 Combining IPD and non-IPD Trials 181 7.5.1 Can We Recover Interaction Estimates from non-IPD Trials? 181 7.5.2 How to Incorporate Interaction Estimates from non-IPD Trials in an IPD Metaanalysis 182 7.6 Handling of Continuous Covariates 184 7.6.1 Do Not Categorise Continuous Covariates 184 7.6.2 Interactions May Be Non-linear 185 7.6.2.1 Rationale and an Example 185 7.6.2.2 Two-stage Multivariate IPD Meta-analysis for Summarising Non-linear Interactions 186 7.6.2.3 One-stage IPD Meta-analysis for Summarising Non-linear Interactions 190 7.7 Handling of Categorical or Ordinal Covariates 191 7.8 Misconceptions and Cautions 191 7.8.1 Genuine Treatment-covariate Interactions Are Rare 191 7.8.2 Interactions May Depend on the Scale of Analysis 192 7.8.3 Measurement Error May Impact Treatment-covariate Interactions 193 7.8.4 Even without Treatment-covariate Interactions, the Treatment Effect on Absolute Risk May Differ across Participants 193 7.8.5 Between-trial Heterogeneity in Treatment Effect Should Not Be Used to Guide Whether Treatment-covariate Interactions Exist at the Participant Level 194 7.9 Is My Identified Treatment-covariate Interaction Genuine? 195 7.10 Reporting of Analyses of Treatment-covariate Interactions 196 7.11 Can We Predict a New Patient's Treatment Effect? 196 7.11.1 Linking Predictions to Clinical Decision Making 198 7.12 Concluding Remarks 198 8 One-stage versus Two-stage Approach to IPD Meta-analysis: Differences and Recommendations 199 Richard D. Riley, Danielle L. Burke, and Tim Morris 8.1 Introduction 200 8.2 One-stage and Two-stage Approaches Usually Give Similar Results 200 8.2.1 Evidence to Support Similarity of One-stage and Two-stage IPD Meta-analysis Results 200 8.2.2 Examples 202 8.2.3 Some Claims in Favour of the One-stage Approach Are Misleading 203 8.3 Ten Key Reasons Why One-stage and Two-stage Approaches May Give Different Results 203 8.3.1 Reason I: Exact One-stage Likelihood When Most Trials Are Small 204 8.3.2 Reason II: How Clustering of Participants Within Trials Is Modelled 207 8.3.3 Reason III: Coding of the Treatment Variable in One-stage Models Fitting with ML Estimation 208 8.3.4 Reason IV: Different Estimation Methods for tau2 210 8.3.5 Reason V: Specification of Prognostic Factor and Adjustment Terms 210 8.3.6 Reason VI: Specification of the Residual Variances 212 8.3.7 Reason VI: Choice of Common Effect or Random Effects for the Parameter of Interest 213 8.3.8 Reason VIII: Derivation of Confidence Intervals 213 8.3.9 Reason IX: Accounting for Correlation Amongst Multiple Outcomes or Time-points 214 8.3.10 Reason X: Aggregation Bias for Treatment Covariate Interactions 215 8.3.11 Other Potential Causes 215 8.4 Recommendations and Guidance 216 8.5 Concluding Remarks 217 Part II References 219 Part III Critical Appraisal and Dissemination 237 9 Examining the Potential for Bias in IPD Meta-analysis Results 239 Richard D. Riley, Jayne F. Tierney, and Lesley A. Stewart 9.1 Introduction 240 9.2 Publication and Reporting Biases of Trials 240 9.2.1 Impact on IPD Meta-analysis Results 240 9.2.2 Examining Small-study Effects Using Funnel Plots 241 9.2.3 Small-study Effects May Arise Due to the Factors Causing Heterogeneity 243 9.3 Biased Availability of the IPD from Trials 244 9.3.1 Examining the Impact of Availability Bias 245 9.3.2 Example: IPD Meta-analysis Examining High-dose Chemotherapy for the Treatment of Non-Hodgkin Lymphoma 246 9.4 Trial Quality (risk of bias) 247 9.5 Other Potential Biases Affecting IPD Meta-analysis Results 248 9.5.1 Trial Selection Bias 248 9.5.2 Selective Outcome Availability 250 9.5.3 Use of Inappropriate Methods by the IPD Meta-analysis Research Team 250 9.6 Concluding Remarks 251 10 Reporting and Dissemination of IPD Meta-analyses 253 Lesley A. Stewart, Richard D. Riley, and Jayne F. Tierney 10.1 Introduction 253 10.2 Reporting IPD Meta-analysis Projects in Academic Reports 254 10.2.1 PRISMA-IPD Title and Abstract Sections 255 10.2.2 PRISMA-IPD Introduction Section 259 10.2.3 PRISMA-IPD Methods Section 259 10.2.4 PRISMA-IPD Results Section 262 10.2.5 PRISMA-IPD Discussion and Funding Sections 266 10.3 Additional Means of Disseminating Findings 266 10.3.1 Key Audiences 267 10.3.1.1 The IPD Collaborative Group 267 10.3.1.2 Patient and Public Audiences 267 10.3.1.3 Guideline Developers 268 10.3.2 Communication Channels 268 10.3.2.1 Evidence Summaries and Policy Briefings 268 10.3.2.2 Press Releases 268 10.3.2.3 Social Media 270 10.4 Concluding Remarks 270 11 A Tool for the Critical Appraisal of IPD Meta-analysis Projects (CheckMAP) 271 Jayne F. Tierney, Lesley A. Stewart, Claire L. Vale, and Richard D. Riley 11.1 Introduction 271 11.2 The CheckMAP Tool 272 11.3 Was the IPD Meta-analysis Project Done within a Systematic Review Framework? 272 11.4 Were the IPD Meta-analysis Project Methods Pre-specified in a Publicly Available Protocol? 274 11.5 Did the IPD Meta-analysis Project Have a Clear Research Question Qualified by Explicit Eligibility Criteria? 276 11.6 Did the IPD Meta-analysis Project Have a Systematic and Comprehensive Search Strategy? 276 11.7 Was the Approach to Data Collection Consistent and Thorough? 277 11.8 Were IPD Obtained from Most Eligible Trials and Their Participants? 277 11.9 Was the Validity of the IPD Checked for Each Trial? 278 11.10 Was the Risk of Bias Assessed for Each Trial and Its Associated IPD? 27811.10.1 Was the Randomisation Process Checked Based on IPD? 278 11.10.2 Were the IPD Checked to Ensure That All (or Most) Randomised Participants Were Included? 279 11.10.3 Were All Important Outcomes Included in the IPD? 279 11.10.4 Were the Outcomes Measured/Defined Appropriately? 279 11.10.5 Was the Quality of Outcome Data Checked? 280 11.11 Were the Methods of Meta-analysis Appropriate? 280 11.11.1 Were the Analyses Pre-specified in Detail and the Key Estimands Defined? 280 11.11.2 Were the Methods of Summarising the Overall Effects of Treatments Appropriate? 281 11.11.3 Were the Methods of Assessing whether Effects of Treatments Varied by Trial-level Characteristics Appropriate? 281 11.11.4 Were the Methods of Assessing whether Effects of Treatments Varied by Participant-level Characteristics Appropriate? 282 11.11.5 Was the Robustness of Conclusions Checked Using Relevant Sensitivity or Other Analyses? 282 11.11.6 Did the IPD Meta-analysis Project's Report Cover the Items Described in PRISMAIPD? 282 11.12 Concluding Remarks 283 Part III References 285 Part IV Special Topics in Statistics 291 12 Power Calculations for Planning an IPD Meta-analysis 293 Richard D. Riley and Joie Ensor 12.1 Introduction 294 12.1.1 Rationale for Power Calculations in an IPD Meta-analysis 294 12.1.2 Premise for This Chapter 294 12.2 Motivating Example: Power of a Planned IPD Meta-analysis of Trials of Interventions to Reduce Weight Gain in Pregnant Women 295 12.2.1 Background 295 12.2.2 What Is the Power to Detect a Treatment-BMI Interaction? 295 12.2.3 Power of an IPD Meta-analysis to Detect a Treatment-covariate Interaction for a Continuous Outcome 295 12.2.4 Closed-form Solutions 296 12.2.4.1 Application to the i-WIP Example 298 12.2.5 Simulation-based Power Calculations for a Two-stage IPD Meta-analysis 299 12.2.5.1 Application to the i-WIP Example 300 12.2.6 Power Results Naively Assuming the IPD All Come from a Single Trial 301 12.3 The Contribution of Individual Trials Toward Power 301 12.3.1 Contribution According to Sample Size 301 12.3.2 Contribution According to Covariate and Outcome Variability 302 12.4 The Impact of Model Assumptions on Power 302 12.4.1 Impact of Allowing for Heterogeneity in the Interaction 302 12.4.2 Impact of Wrongly Modelling BMI as a Binary Variable 304 12.4.3 Impact of Adjusting for Additional Covariates 304 12.5 Extensions 305 12.5.1 Power Calculations for Binary and Time-to-event Outcomes 305 12.5.2 Simulation Using a One-stage IPD Meta-analysis Approach 306 12.5.3 Examining the Potential Precision of IPD Meta-analysis Results 307 12.5.4 Estimating the Power of a New Trial Conditional on IPD Meta-analysis Results 307 12.6 Concluding Remarks 309 13 Multivariate Meta-analysis Using IPD 311 Richard D. Riley, Dan Jackson, and Ian R. White 13.1 Introduction 312 13.2 General Two-stage Approach for Multivariate IPD Meta-analysis 314 13.2.1 First-stage Analyses 315 13.2.1.1 Obtaining Treatment Effect Estimates and Their Variances for Continuous Outcomes 315 13.2.1.2 Obtaining Within-trial Correlations Directly or via Bootstrapping for Continuous Outcomes 316 13.2.1.3 Extension to Binary, Time-to-event and Mixed Outcomes 317 13.2.2 Second-stage Analysis: Multivariate Meta-analysis Model 319 13.2.2.1 Multivariate Model Structure 320 13.2.2.2 Dealing with Missing Outcomes 320 13.2.2.3 Frequentist Estimation of the Multivariate Model 321 13.2.2.4 Bayesian Estimation of the Multivariate Model 322 13.2.2.5 Joint Inferences and Predictions 322 13.2.2.6 Alternative Specifications for the Between-trial Variance Matrix with Missing Outcomes 323 13.2.2.7 Combining IPD and non-IPD Trials 323 13.2.3 Useful Measures to Accompany Multivariate Meta-analysis Results 324 13.2.3.1 Heterogeneity Measures 324 13.2.3.2 Percentage Trial Weights 325 13.2.3.3 The Efficiency (E) and Borrowing of Strength (BoS) Statistics 325 13.2.4 Understanding the Impact of Correlation and Borrowing of Strength 326 13.2.4.1 Anticipating the Value of BoS When Assuming Common Treatment Effects 326 13.2.4.2 BoS When Assuming Random Treatment Effects 327 13.2.4.3 How the Borrowing of Strength Impacts upon the Summary Meta-analysis Estimates 327 13.2.4.4 How the Correlation Impacts upon Joint Inferences across Outcomes 328 13.2.5 Software 328 13.3 Application to an IPD Meta-analysis of Anti-hypertensive Trials 329 13.3.1 Bivariate Meta-analysis of SBP and DBP 329 13.3.1.1 First-stage Results 329 13.3.1.2 Second-stage Results 329 13.3.1.3 Predictive Inferences 331 13.3.2 Bivariate Meta-analysis of CVD and Stroke 332 13.3.3 Multivariate Meta-analysis of SBP, DBP, CVD and Stroke 332 13.4 Extension to Multivariate Meta-regression 333 13.5 Potential Limitations of Multivariate Meta-analysis 334 13.5.1 The Benefits of a Multivariate Meta-analysis for Each Outcome Are Often Small 335 13.5.2 Model Specification and Estimation Is Non-trivial 335 13.5.3 Benefits Arise under Assumptions 335 13.6 One-stage Multivariate IPD Meta-analysis Applications 337 13.6.1 Summary Treatment Effects 337 13.6.1.1 Applied Example 337 13.6.2 Multiple Treatment-covariate Interactions 337 13.6.2.1 Applied Example 339 13.6.3 Multinomial Outcomes 339 13.7 Special Applications of Multivariate Meta-analysis 340 13.7.1 Longitudinal Data and Multiple Time-points 340 13.7.1.1 Applied Example 341 13.7.1.2 Extensions 342 13.7.2 Surrogate Outcomes 342 13.7.3 Development of Multi-parameter Models for Dose Response and Prediction 344 13.7.4 Test Accuracy 345 13.7.5 Treatment-covariate Interactions 345 13.7.5.1 Non-linear Trends 345 13.7.5.2 Multiple Treatment-covariate Interactions 345 13.8 Concluding Remarks 346 14 Network Meta-analysis Using IPD 347 Richard D. Riley, David M. Phillippo, and Sofia Dias 14.1 Introduction 348 14.2 Rationale and Assumptions for Network Meta-analysis 348 14.3 Network Meta-analysis Models Assuming Consistency 350 14.3.1 A Two-stage Approach 350 14.3.2 A One-stage Approach 351 14.3.3 Summary Results after a Network Meta-analysis 352 14.3.4 Example: Comparison of Eight Thrombolytic Treatments after Acute Myocardial Infarction 352 14.3.4.1 Two-stage Approach 353 14.3.4.2 One-stage Approach 357 14.4 Ranking Treatments 357 14.5 How Do We Examine Inconsistency between Direct and Indirect Evidence? 359 14.6 Benefits of IPD for Network Meta-analysis 361 14.6.1 Benefit 1: Examining and Plotting Distributions of Covariates across Trials Providing Different Comparisons 361 14.6.2 Benefit 2: Adjusting for Prognostic Factors to Improve Consistency and Reduce Heterogeneity 361 14.6.3 Benefit 3: Including Treatment-covariate Interactions 362 14.6.4 Benefit 4: Multiple Outcomes 365 14.7 Combining IPD and Aggregate Data in Network Meta-analysis 365 14.7.1 Multilevel Network Meta-regression 367 14.7.2 Example: Treatments to Reduce Plaque Psoriasis 369 14.8 Further Topics 370 14.8.1 Accounting for Dose and Class 370 14.8.2 Inclusion of 'Real-world' Evidence 372 14.8.3 Cumulative Network Meta-analysis 372 14.8.4 Quality Assessment and Reporting 372 14.9 Concluding Remarks 372 Part IV References 375 Part V Diagnosis, Prognosis and Prediction 387 15 IPD Meta-analysis for Test Accuracy Research 389 Richard D. Riley, Brooke Levis, and Yemisi Takwoingi 389 15.1 Introduction 390 15.1.1 Meta-analysis of Test Accuracy Studies 390 15.1.2 The Need for IPD 391 15.1.3 Scope of This Chapter 394 15.2 Motivating Example: Diagnosis of Fever in Children Using Ear Temperature 394 15.3 Key Steps Involved in an IPD Meta-analysis of Test Accuracy Studies 397 15.3.1 Defining the Research Objectives 397 15.3.2 Searching for Studies with Eligible IPD 397 15.3.3 Extracting Key Study Characteristics and Information 398 15.3.4 Evaluating Risk of Bias of Eligible Studies 398 15.3.5 Obtaining, Cleaning and Harmonising IPD 401 15.3.6 Undertaking IPD Meta-analysis to Summarise Test Accuracy at a Particular Threshold 401 15.3.6.1 Bivariate IPD Meta-analysis to Summarise Sensitivity and Specificity 401 15.3.6.2 Examining and Summarising Heterogeneity 402 15.3.6.3 Combining IPD and non-IPD Studies 403 15.3.6.4 Application to the Fever Example 403 15.3.6.5 Bivariate Meta-analysis of PPV and NPV 404 15.3.7 Examining Accuracy-covariate Associations 406 15.3.7.1 Model Specification Using IPD Studies 407 15.3.7.2 Combining IPD and Aggregate Data 408 15.3.7.3 Application to the Fever Example 408 15.3.8 Performing Sensitivity Analyses and Examining Small-study Effects 409 15.3.9 Reporting and Interpreting Results 409 15.4 IPD Meta-analysis of Test Accuracy at Multiple Thresholds 410 15.4.1 Separate Meta-analysis at Each Threshold 410 15.4.2 Joint Meta-analysis of All Thresholds 410 15.4.2.1 Modelling Using the Multinomial Distribution 411 15.4.2.2 Modelling the Underlying Distribution of the Continuous Test Values 412 15.5 IPD Meta-analysis for Examining a Test's Clinical Utility 414 15.5.1 Net Benefit and Decision Curves 415 15.5.2 IPD Meta-analysis Models for Summarising Clinical Utility of a Test 416 15.5.3 Application to the Fever Example 417 15.6 Comparing Tests 418 15.6.1 Comparative Test Accuracy Meta-analysis Models 419 15.6.2 Applied Example 420 15.7 Concluding Remarks 420 16 IPD Meta-analysis for Prognostic Factor Research 421 Richard D. Riley, Karel G.M. Moons, and Thomas P.A. Debray 16.1 Introduction 422 16.1.1 Problems with Meta-analyses Based on Published Aggregate Data 422 16.1.2 Scope of This Chapter 424 16.2 Potential Advantages of an IPD Meta-analysis 424 16.2.1 Standardise Inclusion Criteria and Definitions 424 16.2.2 Standardise Statistical Analyses 425 16.2.3 Advanced Statistical Modelling 426 16.3 Key Steps Involved in an IPD Meta-analysis of Prognostic Factor Studies 427 16.3.1 Defining the Research Question 427 16.3.1.1 Unadjusted or Adjusted Prognostic Factor Effects? 429 16.3.2 Searching and Selecting Eligible Studies and Datasets 430 16.3.3 Extracting Key Study Characteristics and Information 433 16.3.4 Evaluating Risk of Bias of Eligible Studies 433 16.3.5 Obtaining, Cleaning and Harmonising IPD 433 16.3.6 Undertaking IPD Meta-analysis to Summarise Prognostic Effects 434 16.3.6.1 A Two-stage Approach Assuming a Linear Prognostic Trend 434 16.3.6.2 A Two-stage Approach with Non-linear Trends Using Splines or Polynomials 435 16.3.6.3 Incorporating Measurement Error 438 16.3.6.4 A One-stage Approach 440 16.3.6.5 Checking the Proportional Hazards Assumption 441 16.3.6.6 Dealing with Missing Data and Adjustment Factors 441 16.3.7 Examining Heterogeneity and Performing Sensitivity Analyses 442 16.3.8 Examining Small-study Effects 442 16.3.9 Reporting and Interpreting Results 443 16.4 Software 444 16.5 Concluding Remarks 444 17 IPD Meta-analysis for Clinical Prediction Model Research 447 Richard D. Riley, Kym I.E. Snell, Laure Wynants, Valentijn M.T. de Jong, Karel G.M. Moons, and Thomas P.A. Debray 17.1 Introduction 448 17.2 IPD Meta-analysis for Prediction Model Research 448 17.2.1 Types of Prediction Model Research 448 17.2.2 Why IPD Meta-analyses Are Needed 450 17.2.3 Key Steps Involved in an IPD Meta-analysis for Prediction Model Research 452 17.2.3.1 Define the Research Question and PICOTS System 452 17.2.3.2 Identify Relevant Existing Studies and Datasets 452 17.2.3.3 Examine Eligibility and Risk of Bias of IPD 452 17.2.3.4 Obtain, Harmonise and Summarise IPD 454 17.2.3.5 Undertake Meta-analysis and Quantify Heterogeneity 455 17.3 External Validation of an Existing Prediction Model Using IPD Meta-analysis 455 17.3.1 Measures of Predictive Performance in a Single Study 456 17.3.1.1 Overall Measures of Model Fit 456 17.3.1.2 Calibration Plots and Measures 456 17.3.1.3 Discrimination Measures 456 17.3.2 Potential for Heterogeneity in a Model's Predictive Performance 459 17.3.2.1 Causes of Heterogeneity in Model Performance 460 17.3.2.2 Disentangling Sources of Heterogeneity 461 17.3.3 Statistical Methods for IPD Meta-analysis of Predictive Performance 461 17.3.3.1 Two-stage IPD Meta-analysis 461 17.3.3.2 Example 1: Validation of Prediction Models for Cardiovascular Disease 463 17.3.3.3 Example 2: Meta-analysis of Case-mix Standardised Estimates of Model Performance 466 17.3.3.4 Example 3: Examining Predictive Performance of QRISK2 across Multiple Practices 468 17.3.3.5 One-stage IPD Meta-analysis 469 17.4 Updating and Tailoring of a Prediction Model Using IPD Meta-analysis 470 17.4.1 Example 1: Updating of the Baseline Hazard in a Prognostic Prediction Model 470 17.4.2 Example 2: Multivariate IPD Meta-analysis to Compare Different Model Updating Strategies 471 17.5 Comparison of Multiple Exi

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