Continuous and Discrete-Time Survival Prediction with Neural Networks

2019/10/15 by Håvard Kvamme, Kvamme, Håvard, Ørnulf Borgan +1 · 15 citations
Computer Science · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Methodology (stat.ME) #cs.LG #stat.ME #stat.ML

paper · pdf · doi:10.48550/arxiv.1910.06724

arxiv created 2019/10/15 · arxiv updated 2019/10/16

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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