Statistical Inference for Machine Learning Inverse Probability Weighting with Survival Outcomes

Inverse probability weighting (IPW) is an important estimation technique for studies with missing outcome data, and for causal inference from observational studies. In survival analysis under right censoring, inverse weighting by the probability of censoring conditional on covariates (henceforth referred to as censoring mechanism) can be used to adjust for informative censoring. Since the censoring mechanism is often unknown, it must be estimated from data. Asymptotic properties of the IPW estimator such as consistency and its large sample distribution thus depend on the large sample behavior of the estimator of the censoring mechanism. In low dimensional problems with categorical covariates, the nonparametric maximum likelihood estimator (NPMLE) may be employed. In moderate to high dimensions or with continuous covariates, the curse of dimensionality precludes the use of the NPMLE, making it necessary to use smoothing techniques.