# Isotonic Survival Regression: Calibrated Survival Distributions from Deep Cox Models

arXiv: https://arxiv.org/abs/2605.16571 · HTML: https://mlsanity.com/paper/2605.16571/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 88 references that are in the map.
- First posted on arXiv 15 May 2026.

## Builds on (most cited first, 30 of 30)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Publicly Available Clinical BERT Embeddings](https://mlsanity.com/paper/1904.03323/) (2019)
- [Data Efficient and Weakly Supervised Computational Pathology on Whole Slide Images](https://mlsanity.com/paper/2004.09666/) (2020)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [Med-BERT: pre-trained contextualized embeddings on large-scale structured electronic health records for disease prediction](https://mlsanity.com/paper/2005.12833/) (2020)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks](https://mlsanity.com/paper/1905.11001/) (2019)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [Multimodal Whole Slide Foundation Model for Pathology](https://mlsanity.com/paper/2411.19666/) (2024)
- [Visual Language Pretrained Multiple Instance Zero-Shot Transfer for Histopathology Images](https://mlsanity.com/paper/2306.07831/) (2023)
- [Accelerating Data Processing and Benchmarking of AI Models for Pathology](https://mlsanity.com/paper/2502.06750/) (2025)
- [Molecular-driven Foundation Model for Oncologic Pathology](https://mlsanity.com/paper/2501.16652/) (2025)
- [Conformalized Survival Analysis](https://mlsanity.com/paper/2103.09763/) (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)
- [Isotonic Distributional Regression](https://mlsanity.com/paper/1909.03725/) (2019)
- [HEALNet: Multimodal Fusion for Heterogeneous Biomedical Data](https://mlsanity.com/paper/2311.09115/) (2023)
- [Conformalized survival analysis with adaptive cutoffs](https://mlsanity.com/paper/2211.01227/) (2022)
- [BERTSurv: BERT-Based Survival Models for Predicting Outcomes of Trauma Patients](https://mlsanity.com/paper/2103.10928/) (2021)
- [Conformalized Survival Distributions: A Generic Post-Process to Increase Calibration](https://mlsanity.com/paper/2405.07374/) (2024)
- [Monotone Least Squares and Isotonic Quantiles](https://mlsanity.com/paper/1901.02398/) (2019)
- [Distributional (Single) Index Models](https://mlsanity.com/paper/2006.09219/) (2020)
- [Interpretable Survival Analysis for Heart Failure Risk Prediction](https://mlsanity.com/paper/2310.15472/) (2023)
- [Toward Conditional Distribution Calibration in Survival Prediction](https://mlsanity.com/paper/2410.20579/) (2024)
- [Conformal Survival Bands for Risk Screening under Right-Censoring](https://mlsanity.com/paper/2505.04568/) (2025)
- [Doubly Robust and Efficient Calibration of Prediction Sets for Right-Censored Time-to-Event Outcomes](https://mlsanity.com/paper/2501.04615/) (2025)
- [Conformal predictive intervals in survival analysis: a re-sampling approach](https://mlsanity.com/paper/2408.06539/) (2024)
- [Two-sided conformalized survival analysis](https://mlsanity.com/paper/2410.24136/) (2024)
- [Training-Set Conditionally Valid Prediction Sets with Right-Censored Data](https://mlsanity.com/paper/2505.02213/) (2025)

## Abstract (arXiv)

Time-to-event data is widespread across the life sciences and engineering, but it is typically encountered together with censoring, which complicates the application of standard machine learning methods. Deep Cox models have emerged as a popular method for analyzing time-to-event data because they gracefully handle censoring and can be used with unstructured data such as clinical text reports, genomic sequences, and pathology images. However, their predicted survival probabilities are often poorly calibrated, thus limiting their practical utility. In this paper, we propose a novel post hoc calibration method for Deep Cox models that uses isotonic regression to refine predicted survival probabilities without affecting discriminative power. We establish favorable theoretical guarantees, including a double-robustness property and asymptotic calibration. Experiments on synthetic and real-world clinical data demonstrate the empirical effectiveness of our method.