Survival Models: Proper Scoring Rule and Stochastic Optimization with Competing Risks

Abstract

When dealing with right-censored data, where some outcomes are missing due to a limited observation period, survival analysis —known as *time-to-event analysis*— focuses on predicting the time until an event of interest occurs. Multiple classes of outcomes lead to a classification variant: predicting the most likely event, a less explored area known as *competing risks*. Classic competing risks models couple architecture and loss, limiting scalability. To address these issues, we design a strictly proper censoring-adjusted separable scoring rule, allowing optimization on a subset of the data as each observation is evaluated independently. The loss estimates outcome probabilities and enables stochastic optimization for competing risks, which we use for efficient gradient boosting trees. **SurvivalBoost** not only outperforms 12 state-of-the-art models across several metrics on 4 real-life datasets, both in competing risks and survival settings, but also provides great calibration, the ability to predict across any time horizon, and computation times faster than existing methods.