Doubly Robust Estimators for Heterogeneous Treatment Effects in Heteroskedastic Survival Data

Given the increasing interest focus on personalized medicine, a number of advanced statistical methods have been developed for estimating heterogeneous treatment effects (HTEs). However, methods for estimating HTEs in medical applications are limited, as they often involve potentially censored and heteroskedastic survival outcomes. Ignoring censoring and heteroskedasticity may introduce bias into HTEs. Therefore, in this study, we proposed two doubly robust (DR) methods for estimating HTEs based on nonparametric failure time (NFT) Bayesian additive regression trees (BART). Our contributions are as follows: (1) by using NFT BART as the prediction model, we avoid many restrictive assumptions, such as linearity, proportional hazards, and homoscedasticity; (2) we extend the DR-Learner to survival data, allowing it to handle the common issue of censoring and confounding in observational data; (3) we conduct a comprehensive simulation study of the present HTEs estimation strategies using several data generation processes in which we systematically vary the sample size of the training set, treatment-specific propensity score distribution, censoring rate, unbalanced treatment assignment, complexity of the model and bias function, and heteroskedastic or homoscedastic outcome. Through simulations, we demonstrate the effectiveness and robustness of the two proposed approaches in estimating HTEs. We also conduct a real data application of individualized hypertension management on observational data from the National Health and Nutrition Examination Survey (NHANES). Consequently, the proposed methods could yield robust estimates of HTE in observational survival data.