Deep Multi-task Gaussian Processes for Survival Analysis with Competing Risks

Designing optimal treatment plans for patients with comorbidities requires accurate cause-specific mortality prognosis. Motivated by the recent availability of linked electronic health records, we develop a nonparametric Bayesian model for survival analysis with competing risks, which can be used for jointly assessing a patient's risk of multiple (competing) adverse outcomes. The model views a patient's survival times with respect to the competing risks as the outputs of a deep multi-task Gaussian process (DMGP), the inputs to which are the patients' covari-ates. Unlike parametric survival analysis methods based on Cox and Weibull models, our model uses DMGPs to capture complex non-linear interactions between the patients' covariates and cause-specific survival times, thereby learning flexible patient-specific and cause-specific survival curves, all in a data-driven fashion without explicit parametric assumptions on the hazard rates. We propose a varia-tional inference algorithm that is capable of learning the model parameters from time-to-event data while handling right censoring. Experiments on synthetic and real data show that our model outperforms the state-of-the-art survival models.