Deep Cox Mixtures for Survival Regression

TL;DR

This paper introduces Deep Cox Mixtures, a novel survival regression model that combines mixture modeling with deep neural networks to improve survival predictions, especially for minority groups, outperforming existing methods in accuracy and calibration.

Contribution

The paper proposes a new mixture-based Cox regression approach with an efficient EM algorithm and deep hazard modeling, enhancing survival analysis accuracy and fairness.

Findings

Outperforms classical and modern survival models in predictive accuracy.

Achieves better calibration in healthcare survival predictions.

Shows significant improvements for minority demographic groups.

Abstract

Survival analysis is a challenging variation of regression modeling because of the presence of censoring, where the outcome measurement is only partially known, due to, for example, loss to follow up. Such problems come up frequently in medical applications, making survival analysis a key endeavor in biostatistics and machine learning for healthcare, with Cox regression models being amongst the most commonly employed models. We describe a new approach for survival analysis regression models, based on learning mixtures of Cox regressions to model individual survival distributions. We propose an approximation to the Expectation Maximization algorithm for this model that does hard assignments to mixture groups to make optimization efficient. In each group assignment, we fit the hazard ratios within each group using deep neural networks, and the baseline hazard for each mixture component non-parametrically. We perform experiments on multiple real world datasets, and look at the mortality rates of patients across ethnicity and gender. We emphasize the importance of calibration in healthcare settings and demonstrate that our approach outperforms classical and modern survival analysis baselines, both in terms of discriminative performance and calibration, with large gains in performance on the minority demographics.