Multiple Imputation and its Application (Statistics in Practice)

✍ Scribed by James R. Carpenter, Jonathan W. Bartlett, Tim P. Morris, Angela M. Wood, Matteo Quartagno, Michael G. Kenward

• Publisher: Wiley
• Year: 2023
• Tongue: English
• Leaves: 467
• Edition: 2
• Category: Library

✦ Synopsis

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

Cover
Title Page
Copyright
Contents
Part I FOUNDATIONS
Chapter 1 Introduction
1.1 Reasons for missing data
1.2 Examples
1.3 Patterns of missing data
1.3.1 Consequences of missing data
1.4 Inferential framework and notation
1.4.1 Missing completely at random (MCAR)
1.4.2 Missing at random (MAR)
1.4.3 Missing not at random (MNAR)
1.4.4 Ignorability
1.5 Using observed data to inform assumptions about the missingness mechanism
1.6 Implications of missing data mechanisms for regression analyses
1.6.1 Partially observed response
1.6.2 Missing covariates
1.6.3 Missing covariates and response
1.6.4 Subtle issues I: the odds ratio
1.6.5 Implication for linear regression
1.6.6 Subtle issues II: sub‐sample ignorability
1.6.7 Summary: when restricting to complete records is valid
Summary
Exercises
Chapter 2 The multiple imputation procedure and its justification
2.1 Introduction
2.2 Intuitive outline of the MI procedure
2.3 The generic MI procedure
2.4 Bayesian justification of MI
2.5 Frequentist inference
2.5.1 Large number of imputations
2.5.2 Small number of imputations
2.5.3 Inference for vector &bfitbeta;
2.5.4 Combining likelihood ratio tests
2.6 Choosing the number of imputations
2.7 Some simple examples
2.7.1 Estimating the mean with σ2 known by the imputer and analyst
2.7.2 Estimating the mean with σ2 known only by the imputer
2.7.3 Estimating the mean with σ2 unknown
2.7.4 General linear regression with σ2 known
2.8 MI in more general settings
2.8.1 Proper imputation
2.8.2 Congenial imputation and substantive model
2.8.3 Uncongenial imputation and substantive models
2.8.4 Survey sample settings
2.9 Constructing congenial imputation models
Discussion
Exercises
Part II MULTIPLE IMPUTATION FOR SIMPLE DATA STRUCTURES
Chapter 3 Multiple imputation of quantitative data
3.1 Regression imputation with a monotone missingness pattern
3.1.1 MAR mechanisms consistent with a monotone pattern
3.1.2 Justification
3.2 Joint modelling
3.2.1 Fitting the imputation model
3.2.2 Adding covariates
3.3 Full conditional specification
3.3.1 Justification
3.4 Full conditional specification versus joint modelling
3.5 Software for multivariate normal imputation
3.6 Discussion
3.6 Exercises
Chapter 4 Multiple imputation of binary and ordinal data
4.1 Sequential imputation with monotone missingness pattern
4.2 Joint modelling with the multivariate normal distribution
4.3 Modelling binary data using latent normal variables
4.3.1 Latent normal model for ordinal data
4.4 General location model
4.5 Full conditional specification
4.5.1 Justification
4.6 Issues with over‐fitting
4.7 Pros and cons of the various approaches
4.8 Software
Discussion
Exercises
Chapter 5 Imputation of unordered categorical data
5.1 Monotone missing data
5.2 Multivariate normal imputation for categorical data
5.3 Maximum indicant model
5.3.1 Continuous and categorical variable
5.3.2 Imputing missing data
5.4 General location model
5.5 FCS with categorical data
5.6 Perfect prediction issues with categorical data
5.7 Software
Discussion
Exercises
Part III Multiple imputation in practice
Chapter 6 Non‐linear relationships, interactions, and other derived variables
6.1 Introduction
6.1.1 Interactions
6.1.2 Squares
6.1.3 Ratios
6.1.4 Sum scores
6.1.5 Composite endpoints
6.2 No missing data in derived variables
6.3 Simple methods
6.3.1 Impute then transform
6.3.2 Transform then impute/just another variable
6.3.3 Adapting standard imputation models and passive imputation
6.3.4 Predictive mean matching
6.3.5 Imputation separately by groups for interactions
6.4 Substantive‐model‐compatible imputation
6.4.1 The basic idea
6.4.2 Latent‐normal joint model SMC imputation
6.4.3 Factorised conditional model SMC imputation
6.4.4 Substantive model compatible fully conditional specification
6.4.5 Auxiliary variables
6.4.6 Missing outcome values
6.4.7 Congeniality versus compatibility
6.4.8 Discussion of SMC imputation
6.5 Returning to the problems
6.5.1 Ratios
6.5.2 Splines
6.5.3 Fractional polynomials
6.5.4 Multiple imputation with conditional questions or ‘skips’
Exercises
Chapter 7 Survival data
7.1 Missing covariates in time‐to‐event data
7.1.1 Approximately compatible approaches
7.1.2 Substantive model compatible approaches
7.2 Imputing censored event times
7.3 Non‐parametric, or ‘hot deck’ imputation
7.3.1 Non‐parametric imputation for time‐to‐event data
7.4 Case–cohort designs
7.4.1 Standard analysis of case–cohort studies
7.4.2 Multiple imputation for case–cohort studies
7.4.3 Full cohort
7.4.4 Intermediate approaches
7.4.5 Sub‐study approach
Discussion
Exercises
Chapter 8 Prognostic models, missing data, and multiple imputation
8.1 Introduction
8.2 Motivating example
8.3 Missing data at model implementation
8.4 Multiple imputation for prognostic modelling
8.5 Model building
8.5.1 Model building with missing data
8.5.2 Imputing predictors when model building is to be performed
8.6 Model performance
8.6.1 How should we pool MI results for estimation of performance?
8.6.2 Calibration
8.6.3 Discrimination
8.6.4 Model performance measures with clinical interpretability
8.7 Model validation
8.7.1 Internal model validation
8.7.2 External model validation
8.8 Incomplete data at implementation
8.8.1 MI for incomplete data at implementation
8.8.2 Alternatives to multiple imputation
Exercises
Chapter 9 Multi‐level multiple imputation
9.1 Multi‐level imputation model
9.1.1 Imputation of level‐1 variables
9.1.2 Imputation of level 2 variables
9.1.3 Accommodating the substantive model
9.2 MCMC algorithm for imputation model
9.2.1 Ordered and unordered categorical data
9.2.2 Imputing missing values
9.2.3 Substantive model compatible imputation
9.2.4 Checking model convergence
9.3 Extensions
9.3.1 Cross‐classification and three‐level data
9.3.2 Random level 1 covariance matrices
9.3.3 Model fit
9.4 Other imputation methods
9.4.1 One‐step and two‐step FCS
9.4.2 Substantive model compatible imputation
9.4.3 Non‐parametric methods
9.4.4 Comparisons of different methods
9.5 Individual participant data meta‐analysis
9.5.1 Different measurement scales
9.5.2 When to apply Rubin's rules
9.5.3 Homoscedastic versus heteroscedastic imputation model
9.6 Software
Discussion
Exercises
Chapter 10 Sensitivity analysis: MI unleashed
10.1 Review of MNAR modelling
10.2 Framing sensitivity analysis: estimands
10.2.1 Definition of the estimand
10.2.2 Two common estimands
10.3 Pattern mixture modelling with MI
10.3.1 Missing covariates
10.3.2 Sensitivity with multiple variables: the NAR FCS procedure
10.3.3 Application to survival analysis
10.4 Pattern mixture approach with longitudinal data via MI
10.4.1 Change in slope post‐deviation
10.5 Reference based imputation
10.5.1 Constructing joint distributions of pre‐ and post‐intercurrent event data
10.5.2 Technical details
10.5.3 Software
10.5.4 Information anchoring
10.6 Approximating a selection model by importance weighting
10.6.1 Weighting the imputations
10.6.2 Stacking the imputations and applying the weights
Discussion
Exercises
Chapter 11 Multiple imputation for measurement error and misclassification
11.1 Introduction
11.2 Multiple imputation with validation data
11.2.1 Measurement error
11.2.2 Misclassification
11.2.3 Imputing assuming error is non‐differential
11.2.4 Non‐linear outcome models
11.3 Multiple imputation with replication data
11.3.1 Measurement error
11.3.2 Misclassification
11.4 External information on the measurement process
Discussion
Exercises
Chapter 12 Multiple imputation with weights
12.1 Using model‐based predictions in strata
12.2 Bias in the MI variance estimator
12.3 MI with weights
12.3.1 Conditions for the consistency of &bfittheta;&wHat;MI
12.3.2 Conditions for the consistency of V&wHat;MI
12.4 A multi‐level approach
12.4.1 Evaluation of the multi‐level multiple imputation approach for handling survey weights
12.4.2 Results
12.5 Further topics
12.5.1 Estimation in domains
12.5.2 Two‐stage analysis
12.5.3 Missing values in the weight model
Discussion
Exercises
Chapter 13 Multiple imputation for causal inference
13.1 Multiple imputation for causal inference in point exposure studies
13.1.1 Randomised trials
13.1.2 Observational studies
13.2 Multiple imputation and propensity scores
13.2.1 Propensity scores for confounder adjustment
13.2.2 Multiple imputation of confounders
13.2.3 Imputation model specification
13.3 Principal stratification via multiple imputation
13.3.1 Principal strata effects
13.3.2 Estimation
13.4 Multiple imputation for IV analysis
13.4.1 Instrumental variable analysis for non‐adherence
13.4.2 Instrumental variable analysis via multiple imputation
Discussion
Exercises
Chapter 14 Using multiple imputation in practice
14.1 A general approach
14.1.1 Explore the proportions and patterns of missing data
14.1.2 Consider plausible missing data mechanisms
14.1.3 Consider whether missing at random is plausible
14.1.4 Choose the variables for the imputation model
14.1.5 Choose an appropriate imputation strategy and model/s
14.1.6 Set and record the seed of the pseudo‐random number generator
14.1.7 Fit the imputation model
14.1.8 Iterate and revise the imputation model if necessary
14.1.9 Estimate monte carlo error
14.1.10 Sensitivity analysis
14.2 Objections to multiple imputation
14.3 Reporting of analyses with incomplete data
14.4 Presenting incomplete baseline data
14.5 Model diagnostics
14.6 How many imputations?
14.6.1 Using the jack‐knife estimate of the Monte‐Carlo standard error
14.7 Multiple imputation for each substantive model, project, or dataset?
14.8 Large datasets
14.8.1 Large datasets and joint modelling
14.8.2 Shrinkage by constraining parameters
14.8.3 Comparison of the two approaches
14.9 Multiple imputation and record linkage
14.10 Setting random number seeds for multiple imputation analyses
14.11 Simulation studies including multiple imputation
14.11.1 Random number seeds for simulation studies including multiple imputation
14.11.2 Repeated simulation of all data or only the missingness mechanism?
14.11.3 How many imputations for simulation studies?
14.11.4 Multiple imputation for data simulation
Discussion
Exercises
A Markov Chain Monte Carlo
A.1 Metropolis Hastings sampler
A.2 Gibbs sampler
A.3 Missing data
B Probability distributions
B.1 Posterior for the multivariate normal distribution
C Overview of multiple imputation in R, Stata
C.1 Basic multiple imputation using R
C.2 Basic MI using Stata
Author Index
Index of Examples
Subject Index
EULA