In this study, we explore the competing risks framework in survival analysis, where the goal is not only to predict the time until an event occurs but also to account for the possibility of multiple outcomes. Traditional survival analysis models focus on a single event, but competing risks present a classification challenge, which has been less explored. A key limitation of classic competing risks models lies in the coupling of architecture and loss, affecting scalability. As an example, the well-known Fine&Gray linear model has a computational cost that grows quadratically, making it impossible to use for analyzing large observational cohorts, which are increasingly common today.

We have designed a strictly censoring-adjusted separable scoring rule to address these issues. This loss incorporates the Inverse Propensity Censoring Weighting (IPCW) scheme, a well-established method to adjust for the censoring distribution. Thus, this scoring rule allows optimization on a subset of the data because the evaluation of the loss is conducted independently for each observation during training. Our new loss estimates outcome probabilities and enables stochastic optimization for competing risks. Although our loss function can be used with any stochastic optimization algorithm, we opted for a novel gradient-boosting method specifically designed for survival analysis and competing risks settings: SuvivalBoost. Using gradient-boosted trees, this method naturally handles missing values, making it well-suited for real-world datasets.

We first establish the theoretical properties of our strictly proper scoring rule in the context of competing risks. Then, we demonstrate the abilities of SurvivalBoost. Indeed, SurvivalBoost outperforms 12 state-of-the-art models across several metrics on 4 real-life datasets, both in competing risks and survival settings. Among those models, we compared SurvivalBoost with marginal models depending on the setting -Aalen-Johansen or Kaplan-Meier-, with linear models -Cox or Fine&Gray-, machine learning methods using trees -Random Forests or Gradient Boosting methods- and deep-learning methods e.g. DeepHit. Regarding the different datasets, we considered SEER, one large real-life competing risks dataset with 500k datapoints with 60% of censored events, and three survival analysis datasets of varying sizes (METABRIC with 1k datapoints, SUPPORT with 8k datapoints, and KKBOX with 2M datapoints). We found that SurvivalBoost obtains the best results on several metrics, but also provides excellent calibration, the ability to predict across any time horizon, and faster computation times compared to existing methods, and prove that most of them do not scale to datasets like SEER or KKBOX even with GPUs.

This work is detailed in an article available on Arxiv (https://arxiv.org/pdf/2410.16765) and we provide an open-source with the Python library hazardous (https://soda-inria.github.io/hazardous/), which is compatible with Scikit-learn. The library also includes several competing risks metrics - the adapted C-index and the Integrated Brier Score in the competing risks setting, and the accuracy in time, a metric to assess the most predicted event and the observed event for a given patient - and practical examples for applying SurvivalBoost in both survival and competing risks scenarios.