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

arXiv: https://arxiv.org/abs/2410.16765 · HTML: https://mlsanity.com/paper/2410.16765/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 59 references that are in the map.
- First posted on arXiv 22 Oct 2024.

## Builds on (most cited first, 12 of 12)

- [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)
- [Effective Ways to Build and Evaluate Individual Survival Distributions](https://mlsanity.com/paper/1811.11347/) (2018)
- [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)

## Built on by (most cited first, 6 of 6)

- [Position: Stop Chasing the C-index when Evaluating Survival Analysis Models](https://mlsanity.com/paper/2506.02075/) (2025)
- [Stepwise Fine and Gray: Subject-Specific Variable Selection Shows When Hemodynamic Data Improves Prognostication of Comatose Post-Cardiac Arrest Patients](https://mlsanity.com/paper/2508.06023/) (2025)
- [On the calibration of survival models with competing risks](https://mlsanity.com/paper/2602.00194/) (2026)
- [Deep Survival Analysis of Longitudinal EHR Data for Joint Prediction of Hospitalization and Death in COPD Patients](https://mlsanity.com/paper/2511.05960/) (2025)
- [Deep Kernel Aalen-Johansen Estimator: An Interpretable and Flexible Neural Net Framework for Competing Risks](https://mlsanity.com/paper/2512.08063/) (2025)
- [Proper Scoring Rules for Right-Censored Survival Data](https://mlsanity.com/paper/2606.06393/) (2026)

## Abstract (arXiv)

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.