Deep Survival Analysis: Nonparametrics and Missingness

Clinical care requires understanding the time to medical events. Medical events include the time to a disease like chronic kidney disease progressing or the time to a complication as in stroke for high blood pressure. Models for event times live in the framework provided by survival analysis. We expand on deep survival analysis (Ranganath et al., 2016a), a deep generative model for survival analysis in the presence of missing data, where the survival times are modeled using Weibull distributions. We develop methods to relax the distributional assumptions in deep survival analysis using survival distributions that can approximate any true survival function. We show that the model structure mimics the information-optimal procedure in the presence of missing data. Our experiments demonstrate that moving to flexible survival functions yields better likelihoods and concordances for coronary heart disease prediction from electronic health records.