Multiple Imputation and its Application

Multiple Imputation and its Application The most up-to-date edition of a bestselling guide to analyzing partially observed data In this comprehensively revised Second Edition of Multiple Imputation and its Application, a team of distinguished statisticians delivers an overview of the issues raised by missing data, the rationale for multiple imputation as a solution, and the practicalities of applying it in a multitude of settings. With an accessible and carefully structured presentation aimed at quantitative researchers, Multiple Imputation and its Application is illustrated with a range of examples and offers key mathematical details. The book includes a wide range of theoretical and computer-based exercises, tested in the classroom, which are especially useful for users of R or Stata. Readers will find: A comprehensive overview of one of the most effective and popular methodologies for dealing with incomplete data sets Careful discussion of key concepts A range of examples illustrating the key ideas Practical advice on using multiple imputation Exercises and examples designed for use in the classroom and/or private study Written for applied researchers looking to use multiple imputation with confidence, and for methods researchers seeking an accessible overview of the topic, Multiple Imputation and its Application will also earn a place in the libraries of graduate students undertaking quantitative analyses.

Table of Contents:
Preface to the second edition xiii Data acknowledgements xv Acknowledgements xvii Glossary xix Part I Foundations 1 1 Introduction 3 1.1 Reasons for missing data 5 1.2 Examples 6 1.3 Patterns of missing data 7 1.4 Inferential framework and notation 10 1.5 Using observed data to inform assumptions about the missingness mechanism 21 1.6 Implications of missing data mechanisms for regression analyses 24 1.7 Summary 34 2 The Multiple Imputation Procedure and Its Justification 39 2.1 Introduction 39 2.2 Intuitive outline of the MI procedure 40 2.3 The generic MI procedure 45 2.4 Bayesian justification of mi 48 2.5 Frequentist inference 50 2.6 Choosing the number of imputations 55 2.7 Some simple examples 56 2.8 mi in more general settings 64 2.9 Constructing congenial imputation models 72 2.10 Discussion 73 Part II Multiple Imputation for Simple Data Structures 79 3 Multiple Imputation of Quantitative Data 81 3.1 Regression imputation with a monotone missingness pattern 81 3.2 Joint modelling 85 3.3 Full conditional specification 90 3.4 Full conditional specification versus joint modelling 92 3.5 Software for multivariate normal imputation 93 3.6 Discussion 93 4 Multiple Imputation of Binary and Ordinal Data 96 4.1 Sequential imputation with monotone missingness pattern 96 4.2 Joint modelling with the multivariate normal distribution 98 4.3 Modelling binary data using latent normal variables 100 4.4 General location model 108 4.5 Full conditional specification 108 4.6 Issues with over-fitting 110 4.7 Pros and cons of the various approaches 114 4.8 Software 116 4.9 Discussion 116 5 Imputation of Unordered Categorical Data 119 5.1 Monotone missing data 119 5.2 Multivariate normal imputation for categorical data 121 5.3 Maximum indicant model 121 5.4 General location model 125 5.5 FCS with categorical data 128 5.6 Perfect prediction issues with categorical data 130 5.7 Software 130 5.8 Discussion 130 Part III Multiple Imputation in Practice 133 6 Non-linear Relationships, Interactions, and Other Derived Variables 135 6.1 Introduction 135 6.2 No missing data in derived variables 141 6.3 Simple methods 143 6.4 Substantive-model-compatible imputation 152 6.5 Returning to the problems 165 7 Survival Data 175 7.1 Missing covariates in time-to-event data 175 7.2 Imputing censored event times 186 7.3 Non-parametric, or 'hot deck' imputation 188 7.4 Case–cohort designs 191 7.5 Discussion 197 8 Prognostic Models, Missing Data, and Multiple Imputation 200 8.1 Introduction 200 8.2 Motivating example 201 8.3 Missing data at model implementation 201 8.4 Multiple imputation for prognostic modelling 202 8.5 Model building 202 8.6 Model performance 204 8.7 Model validation 206 8.8 Incomplete data at implementation 208 9 Multi-level Multiple Imputation 213 9.1 Multi-level imputation model 213 9.2 MCMC algorithm for imputation model 224 9.3 Extensions 231 9.4 Other imputation methods 234 9.5 Individual participant data meta-analysis 237 9.6 Software 241 9.7 Discussion 241 10 Sensitivity Analysis: MI Unleashed 245 10.1 Review of MNAR modelling 246 10.2 Framing sensitivity analysis: estimands 249 10.3 Pattern mixture modelling with mi 251 10.4 Pattern mixture approach with longitudinal data via mi 263 10.5 Reference based imputation 267 10.6 Approximating a selection model by importance weighting 279 10.7 Discussion 289 11 Multiple Imputation for Measurement Error and Misclassification 294 11.1 Introduction 294 11.2 Multiple imputation with validation data 296 11.3 Multiple imputation with replication data 301 11.4 External information on the measurement process 307 11.5 Discussion 308 12 Multiple Imputation with Weights 312 12.1 Using model-based predictions in strata 313 12.2 Bias in the MI variance estimator 314 12.3 MI with weights 317 12.4 A multi-level approach 320 12.5 Further topics 328 12.6 Discussion 329 13 Multiple Imputation for Causal Inference 333 13.1 Multiple imputation for causal inference in point exposure studies 333 13.2 Multiple imputation and propensity scores 338 13.3 Principal stratification via multiple imputation 343 13.4 Multiple imputation for IV analysis 346 13.5 Discussion 350 14 Using Multiple Imputation in Practice 355 14.1 A general approach 355 14.2 Objections to multiple imputation 359 14.3 Reporting of analyses with incomplete data 363 14.4 Presenting incomplete baseline data 364 14.5 Model diagnostics 365 14.6 How many imputations? 366 14.7 Multiple imputation for each substantive model, project, or dataset? 369 14.8 Large datasets 370 14.9 Multiple imputation and record linkage 375 14.10 Setting random number seeds for multiple imputation analyses 377 14.11 Simulation studies including multiple imputation 377 14.12 Discussion 381 Appendix A Markov Chain Monte Carlo 384 A.1 Metropolis Hastings sampler 385 A.2 Gibbs sampler 386 A.3 Missing data 387 Appendix B Probability Distributions 388 B.1 Posterior for the multivariate normal distribution 391 Appendix C Overview of Multiple Imputation in R, Stata 394 C.1 Basic multiple imputation using R 394 C.2 Basic MI using Stata 395 References 398 Author Index 419 Index of Examples 429 Subject Index 431