Continuous and Discrete-Time Survival Prediction with Neural Networks

Håvard Kvamme; Ørnulf Borgan

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arXiv · 1910.06724

Continuous and Discrete-Time Survival Prediction with Neural Networks

Håvard Kvamme·Ørnulf Borgan

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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.

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Håvard Kvamme, Ørnulf Borgan. 2019-10-15. Continuous and Discrete-Time Survival Prediction with Neural Networks. https://arxiv.org/abs/1910.06724

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