# Proper Scoring Rules for Survival Analysis

arXiv: https://arxiv.org/abs/2305.00621 · HTML: https://mlsanity.com/paper/2305.00621/

## Key facts

- Cited by 9 papers in the map (data through 7 Oct 2026).
- Builds on 14 of its 45 references that are in the map.
- First posted on arXiv 1 May 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [Machine Learning for Survival Analysis: A Survey](https://mlsanity.com/paper/1708.04649/) (2017)
- [Continuous and Discrete-Time Survival Prediction with Neural Networks](https://mlsanity.com/paper/1910.06724/) (2019)
- [Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation](https://mlsanity.com/paper/2203.06102/) (2022)
- [Effective Ways to Build and Evaluate Individual Survival Distributions](https://mlsanity.com/paper/1811.11347/) (2018)
- [Deep Recurrent Survival Analysis](https://mlsanity.com/paper/1809.02403/) (2018)
- [Survival Regression with Proper Scoring Rules and Monotonic Neural Networks](https://mlsanity.com/paper/2103.14755/) (2021)
- [Countdown Regression: Sharp and Calibrated Survival Predictions](https://mlsanity.com/paper/1806.08324/) (2018)
- [X-CAL: Explicit Calibration for Survival Analysis](https://mlsanity.com/paper/2101.05346/) (2021)
- [Inverse-Weighted Survival Games](https://mlsanity.com/paper/2111.08175/) (2021)
- [SAFE: A Neural Survival Analysis Model for Fraud Early Detection](https://mlsanity.com/paper/1809.04683/) (2018)
- [Avoiding C-hacking when evaluating survival distribution predictions with discrimination measures](https://mlsanity.com/paper/2112.04828/) (2021)
- [Censored Quantile Regression Neural Networks for Distribution-Free Survival Analysis](https://mlsanity.com/paper/2205.13496/) (2022)

## Built on by (most cited first, 9 of 9)

- [Proper scoring rules for estimation and forecast evaluation](https://mlsanity.com/paper/2504.01781/) (2025)
- [Conformalized Survival Distributions: A Generic Post-Process to Increase Calibration](https://mlsanity.com/paper/2405.07374/) (2024)
- [Truthful Elicitation of Imprecise Forecasts](https://mlsanity.com/paper/2503.16395/) (2025)
- [NeuralSurv: Deep Survival Analysis with Bayesian Uncertainty Quantification](https://mlsanity.com/paper/2505.11054/) (2025)
- [On Training Survival Models with Scoring Rules](https://mlsanity.com/paper/2403.13150/) (2024)
- [SoC-DT: Standard-of-Care Aligned Digital Twins for Patient-Specific Tumor Dynamics](https://mlsanity.com/paper/2510.03287/) (2025)
- [Subgroup Discovery with the Cox Model](https://mlsanity.com/paper/2512.20762/) (2025)
- [Proper Scoring Rules for Agentic Uncertainty Quantification](https://mlsanity.com/paper/2605.24756/) (2026)
- [Proper Scoring Rules for Right-Censored Survival Data](https://mlsanity.com/paper/2606.06393/) (2026)

## Abstract (arXiv)

Survival analysis is the problem of estimating probability distributions for future event times, which can be seen as a problem in uncertainty quantification. Although there are fundamental theories on strictly proper scoring rules for uncertainty quantification, little is known about those for survival analysis. In this paper, we investigate extensions of four major strictly proper scoring rules for survival analysis and we prove that these extensions are proper under certain conditions, which arise from the discretization of the estimation of probability distributions. We also compare the estimation performances of these extended scoring rules by using real datasets, and the extensions of the logarithmic score and the Brier score performed the best.