The Survival Filter: Joint Survival Analysis with a Latent Time Series

Abstract

Survival analysis is a core task in applied statistics, which models time-to-failure or time-to-event data. In the clinical domain, meaningful events can be the onset of different disease for a given patient. Because patients often have a wide range of diseases with complex interactions amongst them, it would be beneficial to model time to all diseases simultaneously. We propose and describe the survival filter model for this task, and apply it to a real-world, large dataset of longitudinal patient records. The model admits a scalable variational inference algorithm based on noisy gradients constructed from sampling the variational approximation. Experiments show that the survival filter model gives good predictive performance when compared to two baselines, and identifies clinically meaningful latent factors to represent diseases that co-occur in time.