Continuous and Discrete-Time Survival Prediction with Neural Networks

TL;DR

This paper introduces a novel continuous-time survival prediction method using neural networks, improving accuracy through discretization, interpolation, and a piecewise constant hazard rate approach, outperforming existing methods.

Contribution

It proposes a new continuous-time survival prediction method, PC-Hazard, based on neural networks and piecewise constant hazard rates, enhancing existing discretization and interpolation techniques.

Findings

Discretization by quantiles outperforms equidistant schemes for small datasets.

Interpolation schemes improve survival estimate accuracy.

PC-Hazard method performs competitively with state-of-the-art survival prediction techniques.

Abstract

Application of discrete-time survival methods for continuous-time survival prediction is considered. For this purpose, a scheme for discretization of continuous-time data is proposed by considering the quantiles of the estimated event-time distribution, and, for smaller data sets, it is found to be preferable over the commonly used equidistant scheme. Furthermore, two interpolation schemes for continuous-time survival estimates are explored, both of which are shown to yield improved performance compared to the discrete-time estimates. The survival methods considered are based on the likelihood for right-censored survival data, and parameterize either the probability mass function (PMF) or the discrete-time hazard rate, both with neural networks. Through simulations and study of real-world data, the hazard rate parametrization is found to perform slightly better than the parametrization of the PMF. Inspired by these investigations, a continuous-time method is proposed by assuming that the continuous-time hazard rate is piecewise constant. The method, named PC-Hazard, is found to be highly competitive with the aforementioned methods in addition to other methods for survival prediction found in the literature.