Transformation-Invariant Learning of Optimal Individualized Decision Rules with Time-to-Event Outcomes

In many important applications of precision medicine, the outcome of interest is time to an event (e.g., death, relapse of disease) and the primary goal is to identify the optimal individualized decision rule (IDR) to prolong survival time. Existing work in this area have been mostly focused on estimating the optimal IDR to maximize the restricted mean survival time in the population. We propose a new robust framework for estimating an optimal static or dynamic IDR with time-to-event outcomes based on an easy-to-interpret quantile criterion. The new method does not need to specify an outcome regression model and is robust for heavy-tailed distribution. The estimation problem corresponds to a nonregular M-estimation problem with both finite and infinite-dimensional nuisance parameters. Employing advanced empirical process techniques, we establish the statistical theory of the estimated parameter indexing the optimal IDR. Furthermore, we prove a novel result that the proposed approach can consistently estimate the optimal value function under mild conditions even when the optimal IDR is nonunique, which happens in the challenging setting of exceptional laws. We also propose a smoothed resampling procedure for inference. The proposed methods are implemented in the R-package QTOCen. We demonstrate the performance of the proposed new methods via extensive Monte Carlo studies and a real data application. Supplementary materials for this article are available online.