Statistical Inference for Machine Learning Inverse Probability Weighting with Survival Outcomes
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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.
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