# Countdown Regression: Sharp and Calibrated Survival Predictions

arXiv: https://arxiv.org/abs/1806.08324 · HTML: https://mlsanity.com/paper/1806.08324/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2018.

## Built on by (most cited first, 30 of 31)

- [MOTOR: A Time-To-Event Foundation Model For Structured Medical Records](https://mlsanity.com/paper/2301.03150/) (2023)
- [Deep Learning for Survival Analysis: A Review](https://mlsanity.com/paper/2305.14961/) (2023)
- [Survival Regression with Proper Scoring Rules and Monotonic Neural Networks](https://mlsanity.com/paper/2103.14755/) (2021)
- [X-CAL: Explicit Calibration for Survival Analysis](https://mlsanity.com/paper/2101.05346/) (2021)
- [SurvITE: Learning Heterogeneous Treatment Effects from Time-to-Event Data](https://mlsanity.com/paper/2110.14001/) (2021)
- [Proper scoring rules for estimation and forecast evaluation](https://mlsanity.com/paper/2504.01781/) (2025)
- [An Introduction to Deep Survival Analysis Models for Predicting Time-to-Event Outcomes](https://mlsanity.com/paper/2410.01086/) (2024)
- [An Effective Meaningful Way to Evaluate Survival Models](https://mlsanity.com/paper/2306.01196/) (2023)
- [Conformalized Survival Distributions: A Generic Post-Process to Increase Calibration](https://mlsanity.com/paper/2405.07374/) (2024)
- [Survival Mixture Density Networks](https://mlsanity.com/paper/2208.10759/) (2022)
- [Proper Scoring Rules for Survival Analysis](https://mlsanity.com/paper/2305.00621/) (2023)
- [Inverse-Weighted Survival Games](https://mlsanity.com/paper/2111.08175/) (2021)
- [Avoiding C-hacking when evaluating survival distribution predictions with discrimination measures](https://mlsanity.com/paper/2112.04828/) (2021)
- [A Large-Scale Neutral Comparison Study of Survival Models on Low-Dimensional Data](https://mlsanity.com/paper/2406.04098/) (2024)
- [Toward Conditional Distribution Calibration in Survival Prediction](https://mlsanity.com/paper/2410.20579/) (2024)
- [Individual Survival Curves with Conditional Normalizing Flows](https://mlsanity.com/paper/2107.12825/) (2021)
- [Flexible Group Fairness Metrics for Survival Analysis](https://mlsanity.com/paper/2206.03256/) (2022)
- [Toward a Well-Calibrated Discrimination via Survival Outcome-Aware Contrastive Learning](https://mlsanity.com/paper/2410.11340/) (2024)
- [Deep conditional transformation models for survival analysis](https://mlsanity.com/paper/2210.11366/) (2022)
- [Censored Quantile Regression Neural Networks for Distribution-Free Survival Analysis](https://mlsanity.com/paper/2205.13496/) (2022)
- [Interpretable Prediction and Feature Selection for Survival Analysis](https://mlsanity.com/paper/2404.14689/) (2024)
- [Towards Flexible Time-to-event Modeling: Optimizing Neural Networks via Rank Regression](https://mlsanity.com/paper/2307.08044/) (2023)
- [DNAMite: Interpretable Calibrated Survival Analysis with Discretized Additive Models](https://mlsanity.com/paper/2411.05923/) (2024)
- [On Training Survival Models with Scoring Rules](https://mlsanity.com/paper/2403.13150/) (2024)
- [Scoring rule nets: beyond mean target prediction in multivariate regression](https://mlsanity.com/paper/2409.14456/) (2024)
- [Self-Consistent Equation-guided Neural Networks for Censored Time-to-Event Data](https://mlsanity.com/paper/2503.09097/) (2025)
- [CRAFT: Time Series Forecasting with Cross-Future Behavior Awareness](https://mlsanity.com/paper/2505.13896/) (2025)
- [A Scalable Nonparametric Continuous-Time Survival Model through Numerical Quadrature](https://mlsanity.com/paper/2605.16208/) (2026)
- [Isotonic Survival Regression: Calibrated Survival Distributions from Deep Cox Models](https://mlsanity.com/paper/2605.16571/) (2026)
- [Proper Scoring Rules for Right-Censored Survival Data](https://mlsanity.com/paper/2606.06393/) (2026)

## Abstract (arXiv)

Probabilistic survival predictions from models trained with Maximum Likelihood Estimation (MLE) can have high, and sometimes unacceptably high variance. The field of meteorology, where the paradigm of maximizing sharpness subject to calibration is popular, has addressed this problem by using scoring rules beyond MLE, such as the Continuous Ranked Probability Score (CRPS). In this paper we present the Survival-CRPS, a generalization of the CRPS to the survival prediction setting, with right-censored and interval-censored variants. We evaluate our ideas on the mortality prediction task using two different Electronic Health Record (EHR) data sets (STARR and MIMIC-III) covering millions of patients, with suitable deep neural network architectures: a Recurrent Neural Network (RNN) for STARR and a Fully Connected Network (FCN) for MIMIC-III. We compare results between the two scoring rules while keeping the network architecture and data fixed, and show that models trained with Survival-CRPS result in sharper predictive distributions compared to those trained by MLE, while still maintaining calibration.