Multiple Imputation and its Application

JAMES R. CARPENTER is Professor of Medical Statistics at the London School of Hygiene & Tropical Medicine and Programme Leader in Methodology at the MRC Clinical Trials Unit at UCL, UK. JONATHAN W. BARTLETT is a Professor of Medical Statistics at the London School of Hygiene & Tropical Medicine, UK. TIM P. MORRIS is Principal Research Fellow in Medical Statistics at the MRC Clinical Trials Unit at UCL, UK. ANGELA M. WOOD is Professor of Health Data Science in the Department of Public Health and Primary Care, University of Cambridge, UK. MATTEO QUARTAGNO is Senior Research Fellow in Medical Statistics at the MRC Clinical Trials Unit at UCL, UK. MICHAEL G. KENWARD retired in 2016 after sixteen years as GlaxoSmithKline Professor of Biostatistics at the London School of Hygiene & Tropical Medicine, UK.

• Preface to the second edition xiiiData acknowledgements xvAcknowledgements xviiGlossary xixPart I Foundations 11 Introduction 31.1 Reasons for missing data 51.2 Examples 61.3 Patterns of missing data 71.4 Inferential framework and notation 101.5 Using observed data to inform assumptions about the missingness mechanism 211.6 Implications of missing data mechanisms for regression analyses 241.7 Summary 342 The Multiple Imputation Procedure and Its Justification 392.1 Introduction 392.2 Intuitive outline of the MI procedure 402.3 The generic MI procedure 452.4 Bayesian justification of mi 482.5 Frequentist inference 502.6 Choosing the number of imputations 552.7 Some simple examples 562.8 mi in more general settings 642.9 Constructing congenial imputation models 722.10 Discussion 73Part II Multiple Imputation for Simple Data Structures 793 Multiple Imputation of Quantitative Data 813.1 Regression imputation with a monotone missingness pattern 813.2 Joint modelling 853.3 Full conditional specification 903.4 Full conditional specification versus joint modelling 923.5 Software for multivariate normal imputation 933.6 Discussion 934 Multiple Imputation of Binary and Ordinal Data 964.1 Sequential imputation with monotone missingness pattern 964.2 Joint modelling with the multivariate normal distribution 984.3 Modelling binary data using latent normal variables 1004.4 General location model 1084.5 Full conditional specification 1084.6 Issues with over-fitting 1104.7 Pros and cons of the various approaches 1144.8 Software 1164.9 Discussion 1165 Imputation of Unordered Categorical Data 1195.1 Monotone missing data 1195.2 Multivariate normal imputation for categorical data 1215.3 Maximum indicant model 1215.4 General location model 1255.5 FCS with categorical data 1285.6 Perfect prediction issues with categorical data 1305.7 Software 1305.8 Discussion 130Part III Multiple Imputation in Practice 1336 Non-linear Relationships, Interactions, and Other Derived Variables 1356.1 Introduction 1356.2 No missing data in derived variables 1416.3 Simple methods 1436.4 Substantive-model-compatible imputation 1526.5 Returning to the problems 1657 Survival Data 1757.1 Missing covariates in time-to-event data 1757.2 Imputing censored event times 1867.3 Non-parametric, or 'hot deck' imputation 1887.4 Case–cohort designs 1917.5 Discussion 1978 Prognostic Models, Missing Data, and Multiple Imputation 2008.1 Introduction 2008.2 Motivating example 2018.3 Missing data at model implementation 2018.4 Multiple imputation for prognostic modelling 2028.5 Model building 2028.6 Model performance 2048.7 Model validation 2068.8 Incomplete data at implementation 2089 Multi-level Multiple Imputation 2139.1 Multi-level imputation model 2139.2 MCMC algorithm for imputation model 2249.3 Extensions 2319.4 Other imputation methods 2349.5 Individual participant data meta-analysis 2379.6 Software 2419.7 Discussion 24110 Sensitivity Analysis: MI Unleashed 24510.1 Review of MNAR modelling 24610.2 Framing sensitivity analysis: estimands 24910.3 Pattern mixture modelling with mi 25110.4 Pattern mixture approach with longitudinal data via mi 26310.5 Reference based imputation 26710.6 Approximating a selection model by importance weighting 27910.7 Discussion 28911 Multiple Imputation for Measurement Error and Misclassification 29411.1 Introduction 29411.2 Multiple imputation with validation data 29611.3 Multiple imputation with replication data 30111.4 External information on the measurement process 30711.5 Discussion 30812 Multiple Imputation with Weights 31212.1 Using model-based predictions in strata 31312.2 Bias in the MI variance estimator 31412.3 MI with weights 31712.4 A multi-level approach 32012.5 Further topics 32812.6 Discussion 32913 Multiple Imputation for Causal Inference 33313.1 Multiple imputation for causal inference in point exposure studies 33313.2 Multiple imputation and propensity scores 33813.3 Principal stratification via multiple imputation 34313.4 Multiple imputation for IV analysis 34613.5 Discussion 35014 Using Multiple Imputation in Practice 35514.1 A general approach 35514.2 Objections to multiple imputation 35914.3 Reporting of analyses with incomplete data 36314.4 Presenting incomplete baseline data 36414.5 Model diagnostics 36514.6 How many imputations? 36614.7 Multiple imputation for each substantive model, project, or dataset? 36914.8 Large datasets 37014.9 Multiple imputation and record linkage 37514.10 Setting random number seeds for multiple imputation analyses 37714.11 Simulation studies including multiple imputation 37714.12 Discussion 381Appendix A Markov Chain Monte Carlo 384A.1 Metropolis Hastings sampler 385A.2 Gibbs sampler 386A.3 Missing data 387Appendix B Probability Distributions 388B.1 Posterior for the multivariate normal distribution 391Appendix C Overview of Multiple Imputation in R, Stata 394C.1 Basic multiple imputation using R 394C.2 Basic MI using Stata 395References 398Author Index 419Index of Examples 429Subject Index 431