This research endeavor delves into the nuanced complexities of estimating and inferring heterogeneous treatment effects in dynamic treatment settings, where the number of samples N and the dimensionality of the confounders d are high and disparate, i.e., d≫N. In contrast to one-time exposures, estimating the intermediate conditional outcomes becomes arduous when treatments are sequentially assigned across two exposure times. To address this challenge, we propose a novel doubly robust (DR) representation for such intermediate mean models. We combine this representation with a standard DR identification of the dynamic treatment effect (DTE) to devise a sequential doubly robust Lasso (S-DRL) estimator. The proposed estimator is consistent under the condition that at least one nuisance function is correctly parametrized for each exposure time and treatment path, representing a weaker requirement than existing low- and high-dimensional literature. Our findings underscore the significance of identifying and estimating the interposed conditional mean functions, as it can significantly impact the estimation quality. Multiple exposure times DR representations suggest performing sequential DR estimation backward in time irrespective of the parametric forms used for estimation purposes.

Bio: Yuqian Zhang is an assistant professor at the Institute of Statistics and Big Data, Renmin University. He obtained his Ph.D. at the University of California - San Diego in 2022 and his bachelor's degree at Wuhan University in 2016. His research focuses on theory and methodology in causal inference, missing data problems, semi-supervised inference, high-dimensional statistics, and machine learning. He received the Best Student Paper Award (Nonparametric Statistics Section) from the American Statistical Association in 2021.