Generative estimation of conditional survival function

We propose a deep generative approach to nonparametric estimation of conditional survival and hazard functions with censored data. The key idea of the proposed method is to first learn a conditional generator for the joint conditional distribution of the observed time and censoring indicator given covariates, and then construct the Kaplan-Meier and Nelson-Aalen estimators based on this conditional generator for conditional hazard and survival functions. Our method combines ideas from the recently developed deep generative learning and classical nonparametric estimation in survival analysis. We establish the convergence properties of the generative nonparametric estimators. Our numerical studies validate the proposed method.