Estimating Calibrated Individualized Survival Curves with Deep Learning

In survival analysis, deep learning approaches have 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 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 and measuring calibration in survival analysis is an inherently difficult task. In this work, we i) highlight the shortcomings of existing approaches in terms of calibration and ii) propose a new training scheme for optimizing deep survival analysis models that maximizes discriminative performance, subject to good calibration. Compared to state-of-the-art approaches across two publicly available datasets, our proposed training scheme leads to significant improvements in calibration, while maintaining good discriminative performance.