The survival filter: Joint survival analysis with a latent time series

Survival analysis is a core task in applied statistics, which models time-to-failure or time-to-event data. In the clinical domain, for example, meaningful events are defined as the onset of different diseases for a given patient. Survival analysis is limited, however, for analyzing modern electronic health records. Patients often have a wide range of diseases, and there are complex interactions among the relative risks of different events. To this end, we develop the survival filter model, a time-series model for joint survival analysis that models multiple patients and multiple diseases. We develop a scalable variational inference algorithm and apply our method to a large data set of longitudinal patient records. The survival filter gives good predictive performance when compared to two baselines and identifies clinically meaningful patterns of disease interaction.