Multiple Imputation and its Application (Statistics in Practice)

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