A Liberating Framework from Truncation and Censoring, with Application to Learning Treatment Effects

Time-to-event outcomes are often subject to left truncation and right censoring. While many survival analysis methods have been developed to handle truncation and censoring, majority of the past works require strong independence assumptions. We relax these stringent assumptions through leveraging covariate information together with orthogonal learning, and develop a liberating framework from left truncation and right censoring so that desirable properties like double robustness can be immediately transferred from settings without truncation or censoring. To illustrate its generality and ease to use, the framework is applied to estimation of the average treatment effect (ATE) and the conditional average treatment effect (CATE). For the ATE, we establish both model and rate double robustness under confounding, truncation and censoring; for the CATE, we show that the orthogonal and the doubly robust learners under these three sources of bias can achieve oracle rate of convergence. We study the estimators both theoretically and through extensive simulation, and apply them to analyzing the effect of mid-life heavy drinking on late life cognitive impairment free survival, using data from the Honolulu Asia Aging Study.