Multiple Imputation For Marginal And Mixed Models In Longitudinal Data With Informative Missingness
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Multiple Imputation for Marginal and Mixed Models in Longitudinal Data with Informative Missingness
Abstract: The method of multiple imputation by Rubin (1978) calls for imputing draws from a predictive distribution and incorporates the sampling variability due to the missing values. If data are missing at random in the sense of Rubin (1976), it is well known that multiple imputation based on the correct missing data model, when used along with maximum likelihood, yields consistent estimators and valid inference. However, multiple imputation for longitudinal data, and in the case where missingness is not at random, has not been well studied. In this thesis, I consider longitudinal data with informative missingness, where the missing data process depends on the individual random effects. I propose a multiple imputation method based on a conditional linear mixed-effects model with summary measures for missing data as additional fixed effects, and implement this method using Markov Chain Monte Carlo. Furthermore, when the complete data is to be analyzed using a marginal model, another major approach for the analysis of longitudinal data, imputation can be performed based on a corresponding mixed-effects model. In this setting, it is of interest to study the validity of the inference since the imputation and analysis models differ. I conduct a simulation study to compare the performance of estimators under a variety of circumstances. Results show that the proposed multiple imputation approach corrects bias caused by ignoring the missing data mechanism, and the inference is fairly robust to the imputation model.
Missing Data in Longitudinal Studies
Drawing from the authors' own work and from the most recent developments in the field, Missing Data in Longitudinal Studies: Strategies for Bayesian Modeling and Sensitivity Analysis describes a comprehensive Bayesian approach for drawing inference from incomplete data in longitudinal studies. To illustrate these methods, the authors employ
Longitudinal Data Analysis
Although many books currently available describe statistical models and methods for analyzing longitudinal data, they do not highlight connections between various research threads in the statistical literature. Responding to this void, Longitudinal Data Analysis provides a clear, comprehensive, and unified overview of state-of-the-art theory