Wasserstein GAN-based estimation for conditional distribution function with current status data

Current status data are commonly encountered in modern medicine, econometrics and social science. Its unique characteristics pose significant challenges to the analysis of such data and the existing methods often suffer grave consequences when the underlying model is misspecified. To address these difficulties, we propose a model-free two-stage generative approach for estimating the conditional cumulative distribution function given predictors. We first learn a conditional generator nonparametrically for the joint conditional distribution of observation times and event status, and then construct the nonparametric maximum likelihood estimators of conditional distribution functions based on samples from the conditional generator. Subsequently, we study the convergence properties of the proposed estimator and establish its consistency. Simulation studies under various settings show the superior performance of the deep conditional generative approach over the classical modeling approaches and an application to Parvovirus B19 seroprevalence data yields reasonable predictions.