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 \emph{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 \emph{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. \textbf{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.