Non-linear survival analysis using neural networks

Abstract

We describe models for survival analysis which are based on a multi-layer perceptron, a type of neural network. These relax the assumptions of the traditional regression models, while including them as particular cases. They allow non-linear predictors to be fitted implicitly and the effect of the covariates to vary over time. The flexibility is included in the model only when it is beneficial, as judged by cross-validation. Such models can be used to guide a search for extra regressors, by comparing their predictive accuracy with that of linear models. Most also allow the estimation of the hazard function, of which a great variety can be modelled. In this paper we describe seven different neural network survival models and illustrate their use by comparing their performance in predicting the time to relapse for breast cancer patients.