Considerable recent interest has focused on doubly robust estimatorsfor a population mean response in the presence of incomplete data,which involve models for both the propensity score and the regressionof outcome on covariates.The ``usual" doubly robust estimator mayyield severely biased inferences if neither of these models iscorrectly specified and can exhibit nonnegligible bias if theestimated propensity score is close to zero for some observations.In part oneof this dissertation, wepropose alternative doubly robust estimators that achieve comparableor improved performance relative to existing methods, even with someestimated propensity scores close to zero.The second part of this dissertation focuses on drawing inference on parametersin general models in the presence of monotonely coarsened data, which can beviewed as a generalization of longitudinal data with a monotone missingness pattern, as isthe case when subjects drop out of a study. Estimators for parameters of interest includeboth inverse probability weighted estimators and doubly robust estimators.As a generalization of methods in part one, we propose alternative doubly robust estimatorsthat achieve comparable or improved performance relative to existing methods.We apply the proposed method to data from an AIDS clinical trial.
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Improving Efficiency and Robustness of Doubly Robust Estimators in the Presence of Coarsened Data