Teaching Models To Survive: Proper Scoring Rule and Stochastic Optimization with Competing Risks
This work addresses a less-studied classification variant in survival analysis for applications like healthcare or reliability engineering, offering a practical improvement with faster and more accurate predictions.
The paper tackles the problem of predicting outcome probabilities in survival analysis with competing risks, where data are right-censored, by introducing a strictly proper censoring-adjusted scoring rule that enables stochastic optimization. The result is a model called MultiIncidence, which outperforms 11 state-of-the-art models in probability estimation, can predict at any time horizon, and is much faster than alternatives.
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.