deepAFT: A nonlinear accelerated failure time model with artificial neural network

The Cox regression model or accelerated failure time regression models are often used for describing the relationship between survival outcomes and potential explanatory variables. These models assume the studied covariates are connected to the survival time or its distribution or their transformations through a function of a linear regression form. In this article, we propose nonparametric, nonlinear algorithms (deepAFT methods) based on deep artificial neural networks to model survival outcome data in the broad distribution family of accelerated failure time models. The proposed methods predict survival outcomes directly and tackle the problem of censoring via an imputation algorithm as well as re-weighting and transformation techniques based on the inverse probabilities of censoring. Through extensive simulation studies, we confirm that the proposed deepAFT methods achieve accurate predictions. They outperform the existing regression models in prediction accuracy, while being flexible and robust in modeling covariate effects of various nonlinear forms. Their prediction performance is comparable to other established deep learning methods such as deepSurv and random survival forest methods. Even though the direct output is the expected survival time, the proposed AFT methods also provide predictions for distributional functions such as the cumulative hazard and survival functions without additional learning efforts. For situations where the popular Cox regression model may not be appropriate, the deepAFT methods provide useful and effective alternatives, as shown in simulations, and demonstrated in applications to a lymphoma clinical trial study.