Deep Generative Survival Analysis: Nonparametric Estimation of Conditional Survival Function

We propose a deep generative approach to nonparametric estimation of conditional survival and hazard functions with right-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 the covariates, and then construct the Kaplan-Meier and Nelson-Aalen estimators based on this conditional generator for the conditional hazard and survival functions. Our method combines ideas from the recently developed deep generative learning and classical nonparametric estimation in survival analysis. We analyze the convergence properties of the proposed method and establish the consistency of the generative nonparametric estimators of the conditional survival and hazard functions. Our numerical experiments validate the proposed method and demonstrate its superior performance in a range of simulated models. We also illustrate the applications of the proposed method in constructing prediction intervals for survival times with the PBC (Primary Biliary Cholangitis) and SUPPORT (Study to Understand Prognoses and Preferences for Outcomes and Risks of Treatments) datasets.