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

Abstract

Randomized clinical trials with time-to-event outcomes have traditionally used the log-rank test followed by the Cox proportional hazards (PH) model to estimate the hazard ratio between the treatment groups. These are valid under the assumption that the right-censoring mechanism is non-informative, i.e. independent of the time-to-event of interest within each treatment group. More generally, the censoring time might depend on additional covariates, and inverse probability of censoring weighting (IPCW) can be used to correct for the bias resulting from the informative censoring. IPCW requires a correctly specified censoring time model conditional on the treatment and the covariates. Doubly robust inference in this setting has not been plausible previously due to the non-collapsibility of the Cox model. However, with the recent development of data-adaptive machine learning methods we derive an augmented IPCW (AIPCW) estimator that has the following doubly robust (DR) properties: it is 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 the censoring time, is correctly specified; it is also rate doubly robust, in that it is CAN as long as the product of the estimation error rates under these two models is faster than root-n. We investigate the AIPCW estimator using extensive simulation in finite samples.

A Cautionary Note on Doubly Robust Estimators Involving Continuous-time Structure

“…These are the two cases doubly robust estimators are usually considered. Luo and Xu (2022); Wang et al (2022); Ying (2022) have incorporated the idea of this paper into their proofs of asymptotics.…”