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

arXiv: https://arxiv.org/abs/2406.14085 · HTML: https://mlsanity.com/paper/2406.14085/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 49 references that are in the map.
- First posted on arXiv 20 Jun 2024.

## Builds on (most cited first, 11 of 11)

- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Why do tree-based models still outperform deep learning on tabular data?](https://mlsanity.com/paper/2207.08815/) (2022)
- [Continuous and Discrete-Time Survival Prediction with Neural Networks](https://mlsanity.com/paper/1910.06724/) (2019)
- [Deep Survival Machines: Fully Parametric Survival Regression and Representation Learning for Censored Data with Competing Risks](https://mlsanity.com/paper/2003.01176/) (2020)
- [Survival Regression with Proper Scoring Rules and Monotonic Neural Networks](https://mlsanity.com/paper/2103.14755/) (2021)
- [SurvTRACE: Transformers for Survival Analysis with Competing Events](https://mlsanity.com/paper/2110.00855/) (2021)
- [The Brier Score under Administrative Censoring: Problems and Solutions](https://mlsanity.com/paper/1912.08581/) (2019)
- [Copula-Based Deep Survival Models for Dependent Censoring](https://mlsanity.com/paper/2306.11912/) (2023)
- [Inverse-Weighted Survival Games](https://mlsanity.com/paper/2111.08175/) (2021)
- [Deep Copula-Based Survival Analysis for Dependent Censoring with Identifiability Guarantees](https://mlsanity.com/paper/2312.15566/) (2023)
- [A review on competing risks methods for survival analysis](https://mlsanity.com/paper/2212.05157/) (2022)

## Abstract (arXiv)

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.