Novel data-adaptive statistical methods for observational and experimental studies with applications to HIV/AIDS research

Abstract

Data-adaptive statistical methods can often be used to improve different attributes of estimators, such as their asymptotic variance, calibration, and predictive accuracy. In this dissertation, we (i) describe how careful estimation of the propensity score can be used to improve the efficiency of a matching estimator; (ii) propose and examine the asymptotic properties of isotonic calibration in the context of conditional average treatment effect estimation; and (iii) implement and assess a SuperLearner for HIV risk prediction that can be used to improve the precision of treatment effect estimators in HIV prevention trials. Matching adjusts for confounding by comparing individuals with similar propensity score; however, it often results in an inefficient estimator. In Chapter 2, we propose mitigating this inefficiency by including an optimal covariate ---estimated via data adaptive methods--- in the propensity score model. Chapter 3 describes how isotonic calibration, paired with flexible estimation of the pseudo-outcomes, can be used to calibrate a given CATE estimator. We provide rates of convergence of our method's calibration and predictive performance. Finally, in Chapter 4, we propose using flexible data adaptive methods to implement a Super Learner for HIV prediction and assess its performance when predicting HIV risk based on different combinations of baseline covariates and varying risk time windows.