Calibrated Deep Nonparametric Survival Analysis
Fahad Kamran, Jenna Wiens
Abstract: In survival analysis, deep learning approaches have recently been proposed for estimating an individual's probability of survival over some time horizon. Such approaches can capture complex non-linear relationships, without relying on restrictive assumptions regarding the specific form of the relationship between an individual's characteristics and their underlying survival process. To date, however, these methods have focused primarily on optimizing discriminative performance, and have ignored model calibration. Well-calibrated survival curves present realistic and meaningful probabilistic estimates of the true underlying survival process for an individual. However, due to the lack of ground-truth regarding the underlying stochastic process of survival for an individual, optimizing for and measuring calibration in survival analysis is an inherently difficult task. In this work, we i) propose a new loss function, for training deep nonparametric survival analysis models, that maximizes discriminative performance, subject to good calibration, and ii) present a calibration metric for survival analysis that facilitates model comparison. Through experiments on two publicly available clinical datasets, we show that our proposed approach achieves the same discriminative performance as state-of-the-art methods, while leading to over a 60% reduction in calibration error.