# Conformalized Survival Analysis

arXiv: https://arxiv.org/abs/2103.09763 · HTML: https://mlsanity.com/paper/2103.09763/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 105 references that are in the map.
- First posted on arXiv 17 Mar 2021.

## Builds on (most cited first, 18 of 18)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [A comparison of some conformal quantile regression methods](https://mlsanity.com/paper/1909.05433/) (2019)
- [With Malice Towards None: Assessing Uncertainty via Equalized Coverage](https://mlsanity.com/paper/1908.05428/) (2019)
- [Conformal prediction with localization](https://mlsanity.com/paper/1908.08558/) (2019)
- [Knowing what you know: valid and validated confidence sets in multiclass and multilabel prediction](https://mlsanity.com/paper/2004.10181/) (2020)
- [Censored Quantile Regression Forest](https://mlsanity.com/paper/2001.03458/) (2020)
- [Contrast Trees and Distribution Boosting](https://mlsanity.com/paper/1912.03785/) (2019)
- [Program Evaluation with Right-Censored Data](https://mlsanity.com/paper/1604.02642/) (2016)

## Built on by (most cited first, 30 of 53)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [Selection by Prediction with Conformal p-values](https://mlsanity.com/paper/2210.01408/) (2022)
- [PAC Prediction Sets Under Covariate Shift](https://mlsanity.com/paper/2106.09848/) (2021)
- [Predictive Inference with Feature Conformal Prediction](https://mlsanity.com/paper/2210.00173/) (2022)
- [Adaptive conformal classification with noisy labels](https://mlsanity.com/paper/2309.05092/) (2023)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Split Localized Conformal Prediction](https://mlsanity.com/paper/2206.13092/) (2022)
- [An Information Theoretic Perspective on Conformal Prediction](https://mlsanity.com/paper/2405.02140/) (2024)
- [Conformal Off-policy Prediction](https://mlsanity.com/paper/2206.06711/) (2022)
- [Conformal Prediction for Network-Assisted Regression](https://mlsanity.com/paper/2302.10095/) (2023)
- [Recommendation Systems with Distribution-Free Reliability Guarantees](https://mlsanity.com/paper/2207.01609/) (2022)
- [Bellman Conformal Inference: Calibrating Prediction Intervals For Time Series](https://mlsanity.com/paper/2402.05203/) (2024)
- [Conformal Prediction Intervals for Markov Decision Process Trajectories](https://mlsanity.com/paper/2206.04860/) (2022)
- [Wasserstein Generative Regression](https://mlsanity.com/paper/2306.15163/) (2023)
- [Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations](https://mlsanity.com/paper/2502.14105/) (2025)
- [Conformal Methods for Quantifying Uncertainty in Spatiotemporal Data: A Survey](https://mlsanity.com/paper/2209.03580/) (2022)
- [Weighted Aggregation of Conformity Scores for Classification](https://mlsanity.com/paper/2407.10230/) (2024)
- [Conformal Frequency Estimation using Discrete Sketched Data with Coverage for Distinct Queries](https://mlsanity.com/paper/2211.04612/) (2022)
- [Conformalized Survival Distributions: A Generic Post-Process to Increase Calibration](https://mlsanity.com/paper/2405.07374/) (2024)
- [SymmPI: Predictive Inference for Data with Group Symmetries](https://mlsanity.com/paper/2312.16160/) (2023)
- [Conformal Tail Risk Control for Large Language Model Alignment](https://mlsanity.com/paper/2502.20285/) (2025)
- [Distribution-Free Conformal Joint Prediction Regions for Neural Marked Temporal Point Processes](https://mlsanity.com/paper/2401.04612/) (2024)
- [Post-selection Inference for Conformal Prediction: Trading off Coverage for Precision](https://mlsanity.com/paper/2304.06158/) (2023)
- [Distribution-Free Matrix Prediction Under Arbitrary Missing Pattern](https://mlsanity.com/paper/2305.11640/) (2023)
- [Toward Conditional Distribution Calibration in Survival Prediction](https://mlsanity.com/paper/2410.20579/) (2024)

## Abstract (arXiv)

Existing survival analysis techniques heavily rely on strong modelling assumptions and are, therefore, prone to model misspecification errors. In this paper, we develop an inferential method based on ideas from conformal prediction, which can wrap around any survival prediction algorithm to produce calibrated, covariate-dependent lower predictive bounds on survival times. In the Type I right-censoring setting, when the censoring times are completely exogenous, the lower predictive bounds have guaranteed coverage in finite samples without any assumptions other than that of operating on independent and identically distributed data points. Under a more general conditionally independent censoring assumption, the bounds satisfy a doubly robust property which states the following: marginal coverage is approximately guaranteed if either the censoring mechanism or the conditional survival function is estimated well. Further, we demonstrate that the lower predictive bounds remain valid and informative for other types of censoring. The validity and efficiency of our procedure are demonstrated on synthetic data and real COVID-19 data from the UK Biobank.