Flexible and Interpretable Models for Survival Data

As datasets continue to increase in size, there is growing interest in methods for prediction that are both Received January 2018 flexible and interpretable. A flurry of recent work on this topic has focused on additive modeling in the Revised February 2019 regression setting, and in particular, on the use of data-adaptive nonlinear functions that can be used to flexibly model each covariate's effect, conditional on the other features in the model. In this article, we extend this recent line of work to the survival setting. We develop an additive Cox proportional hazards model, in which each additive function is obtained by trend filtering, so that the fitted functions are piece-wise polynomial with adaptively chosen knots. An efficient proximal gradient descent algorithm is used to fit the model. We demonstrate its performance in simulations and in application to a primary biliary cirrhosis data set, as well as a dataset consisting of time to publication for clinical trials in the biomedical literature. Supplementary materials for this article are available online.