# Fairness in Survival Analysis with Distributionally Robust Optimization

arXiv: https://arxiv.org/abs/2409.10538 · HTML: https://mlsanity.com/paper/2409.10538/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 45 references that are in the map.
- First posted on arXiv 31 Aug 2024.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [An Intersectional Definition of Fairness](https://mlsanity.com/paper/1807.08362/) (2018)
- [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)
- [Effective Ways to Build and Evaluate Individual Survival Distributions](https://mlsanity.com/paper/1811.11347/) (2018)
- [Distributionally Robust Losses for Latent Covariate Mixtures](https://mlsanity.com/paper/2007.13982/) (2020)
- [X-CAL: Explicit Calibration for Survival Analysis](https://mlsanity.com/paper/2101.05346/) (2021)
- [Learning by Minimizing the Sum of Ranked Range](https://mlsanity.com/paper/2010.01741/) (2020)
- [SODEN: A Scalable Continuous-Time Survival Model through Ordinary Differential Equation Networks](https://mlsanity.com/paper/2008.08637/) (2020)
- [TkML-AP: Adversarial Attacks to Top-k Multi-Label Learning](https://mlsanity.com/paper/2108.00146/) (2021)
- [Rank-based Decomposable Losses in Machine Learning: A Survey](https://mlsanity.com/paper/2207.08768/) (2022)
- [Sum of Ranked Range Loss for Supervised Learning](https://mlsanity.com/paper/2106.03300/) (2021)
- [Longitudinal Fairness with Censorship](https://mlsanity.com/paper/2203.16024/) (2022)
- [Distributionally Robust Survival Analysis: A Novel Fairness Loss Without Demographics](https://mlsanity.com/paper/2211.10508/) (2022)
- [SurvLatent ODE : A Neural ODE based time-to-event model with competing risks for longitudinal data improves cancer-associated Venous Thromboembolism (VTE) prediction](https://mlsanity.com/paper/2204.09633/) (2022)
- [Deep Kernel Survival Analysis and Subject-Specific Survival Time Prediction Intervals](https://mlsanity.com/paper/2007.12975/) (2020)
- [Survival Analysis via Ordinary Differential Equations](https://mlsanity.com/paper/2009.03449/) (2020)
- [Uncertainty-Aware Time-to-Event Prediction using Deep Kernel Accelerated Failure Time Models](https://mlsanity.com/paper/2107.12250/) (2021)
- [Evaluating Model Performance Under Worst-case Subpopulations](https://mlsanity.com/paper/2407.01316/) (2024)
- [Flexible Group Fairness Metrics for Survival Analysis](https://mlsanity.com/paper/2206.03256/) (2022)

## Built on by (most cited first, 14 of 14)

- [LLM-MedQA: Enhancing Medical Question Answering through Case Studies in Large Language Models](https://mlsanity.com/paper/2501.05464/) (2024)
- [An Introduction to Deep Survival Analysis Models for Predicting Time-to-Event Outcomes](https://mlsanity.com/paper/2410.01086/) (2024)
- [Position: Stop Chasing the C-index when Evaluating Survival Analysis Models](https://mlsanity.com/paper/2506.02075/) (2025)
- [Improving Generalization of Medical Image Registration Foundation Model](https://mlsanity.com/paper/2505.06527/) (2025)
- [Preserving AUC Fairness in Learning with Noisy Protected Groups](https://mlsanity.com/paper/2505.18532/) (2025)
- [Robust AI-Generated Face Detection with Imbalanced Data](https://mlsanity.com/paper/2505.02182/) (2025)
- [Robust Fairness Vision-Language Learning for Medical Image Analysis](https://mlsanity.com/paper/2505.03153/) (2025)
- [Distributionally Robust Learning in Survival Analysis](https://mlsanity.com/paper/2506.01348/) (2025)
- [From Fragile to Certified: Wasserstein Audits of Group Fairness Under Distribution Shift](https://mlsanity.com/paper/2509.26241/) (2025)
- [Synthetic Survival Control: Extending Synthetic Controls for "When-If" Decision](https://mlsanity.com/paper/2511.14133/) (2025)
- [Robust Multi-Source Covid-19 Detection in CT Images](https://mlsanity.com/paper/2604.03320/) (2026)
- [Robust Fair Disease Diagnosis in CT Images](https://mlsanity.com/paper/2604.09710/) (2026)
- [Causal Fairness for Survival Analysis](https://mlsanity.com/paper/2605.11362/) (2026)
- [Distributionally Robust Survival Models under Subpopulation Shift and Outlier Contamination](https://mlsanity.com/paper/2610.02868/) (2026)

## Abstract (arXiv)

We propose a general approach for encouraging fairness in survival analysis models based on minimizing a worst-case error across all subpopulations that occur with at least a user-specified probability. This approach can be used to convert many existing survival analysis models into ones that simultaneously encourage fairness, without requiring the user to specify which attributes or features to treat as sensitive in the training loss function. From a technical standpoint, our approach applies recent developments of distributionally robust optimization (DRO) to survival analysis. The complication is that existing DRO theory uses a training loss function that decomposes across contributions of individual data points, i.e., any term that shows up in the loss function depends only on a single training point. This decomposition does not hold for commonly used survival loss functions, including for the Cox proportional hazards model, its deep neural network variants, and many other recently developed models that use loss functions involving ranking or similarity score calculations. We address this technical hurdle using a sample splitting strategy. We demonstrate our sample splitting DRO approach by using it to create fair versions of a diverse set of existing survival analysis models including the Cox model (and its deep variant DeepSurv), the discrete-time model DeepHit, and the neural ODE model SODEN. We also establish a finite-sample theoretical guarantee to show what our sample splitting DRO loss converges to. For the Cox model, we further derive an exact DRO approach that does not use sample splitting. For all the models that we convert into DRO variants, we show that the DRO variants often score better on recently established fairness metrics (without incurring a significant drop in accuracy) compared to existing survival analysis fairness regularization techniques.