DPWTE: A Deep Learning Approach to Survival Analysis Using a Parsimonious Mixture of Weibull Distributions

Survival analysis is widely used in medicine, engineering, finance, and many other areas. The fundamental problem considered in this branch of statistics is to capture the relationship between the covariates and the event time distribution. In this paper, we propose a novel network-based approach to survival analysis, called DPWTE, that uses a neural network to learn the distribution of the event times. DPWTE makes an assumption that (individual) event time distribution follows a finite mixture of Weibull distribution whose parameters are functions of the covariates. In addition, given a fixed upper bound of the mixture size, the model finds the optimal combination of Weibull distributions to model the underlying distribution. For this purpose, we introduce the Sparse Weibull Mixture layer, in the network, that selects through its weights, the Weibull distributions composing the mixture, whose mixing parameters are significant. To stimulate this selection, we apply a sparse regularization on this layer by adding a penalty term to the loss function that takes into account both observed and censored events, i.e. events that are not observed before the end of the period study. We conduct experiments on real-world datasets showing that the proposed model provides a performance improvement over the state-of-the-art models.