Improving Efficiency and Robustness of Doubly Robust Estimators in the Presence of Coarsened Data

Abstract

Considerable recent interest has focused on doubly robust estimators for a population mean response in the presence of incomplete data, which involve models for both the propensity score and the regression of outcome on covariates. The ``usual" doubly robust estimator may yield severely biased inferences if neither of these models is correctly specified and can exhibit nonnegligible bias if the estimated propensity score is close to zero for some observations. In part one of this dissertation, we propose alternative doubly robust estimators that achieve comparable or improved performance relative to existing methods, even with some estimated propensity scores close to zero.

The second part of this dissertation focuses on drawing inference on parameters in general models in the presence of monotonely coarsened data, which can be viewed as a generalization of longitudinal data with a monotone missingness pattern, as is the case when subjects drop out of a study. Estimators for parameters of interest include both inverse probability weighted estimators and doubly robust estimators. As a generalization of methods in part one, we propose alternative doubly robust estimators that achieve comparable or improved performance relative to existing methods. We apply the proposed method to data from an AIDS clinical trial.