Time-to-Event Prediction with Neural Networks and Cox Regression

TL;DR

This paper introduces neural network extensions to the Cox proportional hazards model for improved time-to-event prediction, demonstrating competitive performance on real data and providing an accessible Python package.

Contribution

It presents a scalable loss function for neural network-based Cox models, enabling both proportional and non-proportional hazard modeling, validated through simulations and real data comparisons.

Findings

The proposed loss function closely approximates Cox partial log-likelihood.

The method outperforms existing approaches in Brier score and log-likelihood.

A Python package implementation is provided for practical use.

Abstract

New methods for time-to-event prediction are proposed by extending the Cox proportional hazards model with neural networks. Building on methodology from nested case-control studies, we propose a loss function that scales well to large data sets, and enables fitting of both proportional and non-proportional extensions of the Cox model. Through simulation studies, the proposed loss function is verified to be a good approximation for the Cox partial log-likelihood. The proposed methodology is compared to existing methodologies on real-world data sets, and is found to be highly competitive, typically yielding the best performance in terms of Brier score and binomial log-likelihood. A python package for the proposed methods is available at https://github.com/havakv/pycox.