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, mean-ingful 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 algo-rithm and apply our method to a large data set of longitudinal patient records. The survival fil-ter gives good predictive performance when com-pared to two baselines and identifies clinically meaningful patterns of disease interaction.