# X-CAL: Explicit Calibration for Survival Analysis

arXiv: https://arxiv.org/abs/2101.05346 · HTML: https://mlsanity.com/paper/2101.05346/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 53 references that are in the map.
- First posted on arXiv 13 Jan 2021.

## Builds on (most cited first, 9 of 9)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Multitask learning and benchmarking with clinical time series data](https://mlsanity.com/paper/1703.07771/) (2017)
- [Distribution Calibration for Regression](https://mlsanity.com/paper/1905.06023/) (2019)
- [Effective Ways to Build and Evaluate Individual Survival Distributions](https://mlsanity.com/paper/1811.11347/) (2018)
- [Deep Survival Analysis](https://mlsanity.com/paper/1608.02158/) (2016)
- [Deep Recurrent Survival Analysis](https://mlsanity.com/paper/1809.02403/) (2018)
- [Countdown Regression: Sharp and Calibrated Survival Predictions](https://mlsanity.com/paper/1806.08324/) (2018)
- [The Brier Score under Administrative Censoring: Problems and Solutions](https://mlsanity.com/paper/1912.08581/) (2019)

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

- [Survival Regression with Proper Scoring Rules and Monotonic Neural Networks](https://mlsanity.com/paper/2103.14755/) (2021)
- [Out-of-distribution Generalization in the Presence of Nuisance-Induced Spurious Correlations](https://mlsanity.com/paper/2107.00520/) (2021)
- [A Deep Variational Approach to Clustering Survival Data](https://mlsanity.com/paper/2106.05763/) (2021)
- [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)
- [Deep Probability Estimation](https://mlsanity.com/paper/2111.10734/) (2021)
- [Fairness in Survival Analysis with Distributionally Robust Optimization](https://mlsanity.com/paper/2409.10538/) (2024)
- [Counterfactual Phenotyping with Censored Time-to-Events](https://mlsanity.com/paper/2202.11089/) (2022)
- [Conformalized Survival Distributions: A Generic Post-Process to Increase Calibration](https://mlsanity.com/paper/2405.07374/) (2024)
- [Survival Kernets: Scalable and Interpretable Deep Kernel Survival Analysis with an Accuracy Guarantee](https://mlsanity.com/paper/2206.10477/) (2022)
- [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)
- [Survival In-Context: Amortized Bayesian Survival Analysis via Prior-Fitted Networks](https://mlsanity.com/paper/2603.29475/) (2026)
- [Toward Conditional Distribution Calibration in Survival Prediction](https://mlsanity.com/paper/2410.20579/) (2024)
- [Toward a Well-Calibrated Discrimination via Survival Outcome-Aware Contrastive Learning](https://mlsanity.com/paper/2410.11340/) (2024)
- [Explanations that reveal all through the definition of encoding](https://mlsanity.com/paper/2411.02664/) (2024)
- [Censored Quantile Regression Neural Networks for Distribution-Free Survival Analysis](https://mlsanity.com/paper/2205.13496/) (2022)
- [Explainable Censored Learning: Finding Critical Features with Long Term Prognostic Values for Survival Prediction](https://mlsanity.com/paper/2209.15450/) (2022)
- [A General Framework for Visualizing Embedding Spaces of Neural Survival Analysis Models Based on Angular Information](https://mlsanity.com/paper/2305.06862/) (2023)
- [Bayesian Active Learning for Censored Regression](https://mlsanity.com/paper/2402.11973/) (2024)
- [Learning Survival Distributions with the Asymmetric Laplace Distribution](https://mlsanity.com/paper/2505.03712/) (2025)
- [Good Rankings, Wrong Probabilities: A Calibration Audit of Multimodal Cancer Survival Models](https://mlsanity.com/paper/2604.04239/) (2026)
- [Hazard Gradient Penalty for Survival Analysis](https://mlsanity.com/paper/2205.13717/) (2022)
- [Weakly Supervised AI for Efficient Analysis of 3D Pathology Samples](https://mlsanity.com/paper/2307.14907/) (2023)
- [Survival Analysis with Adversarial Regularization](https://mlsanity.com/paper/2312.16019/) (2023)
- [TripleSurv: Triplet Time-adaptive Coordinate Loss for Survival Analysis](https://mlsanity.com/paper/2401.02708/) (2024)
- [Deep Neural Networks for Predicting Recurrence and Survival in Patients with Esophageal Cancer After Surgery](https://mlsanity.com/paper/2409.00163/) (2024)
- [Isotonic Survival Regression: Calibrated Survival Distributions from Deep Cox Models](https://mlsanity.com/paper/2605.16571/) (2026)
- [ChronoSurv: A Clinical Pathway-Guided Graph Framework for Multimodal Survival Analysis](https://mlsanity.com/paper/2606.19140/) (2026)

## Abstract (arXiv)

Survival analysis models the distribution of time until an event of interest, such as discharge from the hospital or admission to the ICU. When a model's predicted number of events within any time interval is similar to the observed number, it is called well-calibrated. A survival model's calibration can be measured using, for instance, distributional calibration (D-CALIBRATION) [Haider et al., 2020] which computes the squared difference between the observed and predicted number of events within different time intervals. Classically, calibration is addressed in post-training analysis. We develop explicit calibration (X-CAL), which turns D-CALIBRATION into a differentiable objective that can be used in survival modeling alongside maximum likelihood estimation and other objectives. X-CAL allows practitioners to directly optimize calibration and strike a desired balance between predictive power and calibration. In our experiments, we fit a variety of shallow and deep models on simulated data, a survival dataset based on MNIST, on length-of-stay prediction using MIMIC-III data, and on brain cancer data from The Cancer Genome Atlas. We show that the models we study can be miscalibrated. We give experimental evidence on these datasets that X-CAL improves D-CALIBRATION without a large decrease in concordance or likelihood.