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Randomized clinical trials with time-to-event outcomes have traditionallyused the log-rank test followed by the Cox proportional hazards (PH) model toestimate the hazard ratio between the treatment groups. These are valid underthe assumption that the right-censoring mechanism is non-informative, i.e.independent of the time-to-event of interest within each treatment group. Moregenerally, the censoring time might depend on additional covariates, andinverse probability of censoring weighting (IPCW) can be used to correct forthe bias resulting from the informative censoring. IPCW requires a correctlyspecified censoring time model conditional on the treatment and the covariates.Doubly robust inference in this setting has not been plausible previously dueto the non-collapsibility of the Cox model. However, with the recentdevelopment of data-adaptive machine learning methods we derive an augmentedIPCW (AIPCW) estimator that has the following doubly robust (DR) properties: itis model doubly robust, in that it is consistent and asymptotic normal (CAN),as long as one of the two models, one for the failure time and one for thecensoring time, is correctly specified; it is also rate doubly robust, in thatit is CAN as long as the product of the estimation error rates under these twomodels is faster than root-$n$. We investigate the AIPCW estimator usingextensive simulation in finite samples.

Doubly Robust Inference for Hazard Ratio under Informative Censoring with Machine Learning