Learning treatment effects under covariate dependent left truncation and right censoring

In observational studies with delayed entry, causal inference for time-to-event outcomes can be challenging. The challenges arise because, in addition to the potential confounding bias from observational data, the collected data often also suffers from the selection bias due to left truncation, where only subjects with time-to-event (such as death) greater than the enrollment times are included, as well as bias from informative right censoring. To estimate the treatment effects on time-to-event outcomes in such settings, inverse probability weighting (IPW) is often employed. However, IPW is sensitive to model misspecifications, which makes it vulnerable, especially when faced with three sources of biases. Moreover, IPW is inefficient. To address these challenges, we propose a doubly robust framework to handle covariate dependent left truncation and right censoring that can be applied to a wide range of estimation problems, including estimating average treatment effect (ATE) and conditional average treatment effect (CATE). For average treatment effect, we develop estimators that enjoy model double robustness and rate double robustness. For conditional average treatment effect, we develop orthogonal and doubly robust learners that can achieve oracle rate of convergence. Our framework represents the first attempt to construct doubly robust estimators and orthogonal learners for treatment effects that account for all three sources of biases: confounding, selection from covariate-induced dependent left truncation, and informative right censoring. We apply the proposed methods to analyze the effect of midlife alcohol consumption on late-life cognitive impairment, using data from Honolulu Asia Aging Study.