Teaching Models To Survive: Proper Scoring Rule and Stochastic Optimization with Competing Risks

TL;DR

This paper introduces a new loss function for competing risks survival analysis that enables efficient stochastic optimization, improving prediction accuracy and speed over existing models.

Contribution

The authors propose a censoring-adjusted scoring rule for competing risks, allowing stochastic training of gradient boosting trees and outperforming state-of-the-art methods.

Findings

MultiIncidence outperforms 11 existing models in probability estimation.

The new method is faster and more flexible in predicting at various time horizons.

It effectively handles right-censored data in competing risks scenarios.

Abstract

When data are right-censored, i.e. some outcomes are missing due to a limited period of observation, survival analysis can compute the "time to event". Multiple classes of outcomes lead to a classification variant: predicting the most likely event, known as competing risks, which has been less studied. To build a loss that estimates outcome probabilities for such settings, we introduce a strictly proper censoring-adjusted separable scoring rule that can be optimized on a subpart of the data because the evaluation is made independently of observations. It enables stochastic optimization for competing risks which we use to train gradient boosting trees. Compared to 11 state-of-the-art models, this model, MultiIncidence, performs best in estimating the probability of outcomes in survival and competing risks. It can predict at any time horizon and is much faster than existing alternatives.