Doubly Robust and Efficient Calibration of Prediction Sets for Censored Time-to-Event Outcomes

Abstract: Our objective is to construct well-calibrated prediction sets for a time-to-event outcome subject to right-censoring with guaranteed coverage. Our approach is inspired by modern conformal inference literature in that, unlike classical frameworks, we obviate the need for a well-specified parametric or semiparametric survival model to accomplish our goal. In contrast to existing conformal prediction methods for survival data, which restrict censoring to be of Type I, whereby potential censoring times are assumed to be fully observed on all units in both training and validation samples, we consider the more common right-censoring setting in which either only the censoring time or only the event time of primary interest is directly observed, whichever comes first. Under a standard conditional independence assumption between the potential survival and censoring times given covariates, we propose and analyze two methods to construct valid and efficient lower predictive bounds for the survival time of a future observation. The proposed methods build upon modern semiparametric efficiency theory for censored data, in that the first approach incorporates inverse-probability-of-censoring weighting to account for censoring, while the second approach is based on augmenting this method with an additional correction term. For both methods, we formally establish asymptotic coverage guarantees and demonstrate, both theoretically and through empirical experiments, that the augmented approach substantially improves efficiency over the inverse-probability-of-censoring weighting method. Specifically, its coverage error bound is of second-order mixed bias type, that is doubly robust, and therefore guaranteed to be asymptotically negligible relative to the coverage error of the non-augmented method.