Statistical Inference for Data-adaptive Doubly Robust Estimators with Survival Outcomes

We present an inverse probability weighted estimator for survival analysis under informative right censoring. Our estimator has the novel property that it converges to a normal variable at $n^{1/2}$ rate for a large class of censoring probability estimators, including many data-adaptive (e.g., machine learning) prediction methods. We present the formula of the asymptotic variance of the estimator, which allows the computation of asymptotically correct confidence intervals and p-values under data-adaptive estimation of the censoring and treatment probabilities. We demonstrate the asymptotic properties of the estimator in simulation studies, and illustrate its use in a phase III clinical trial for estimating the effect of a novel therapy for the treatment of breast cancer.