# Beyond Cox Models: Assessing the Performance of Machine-Learning Methods in Non-Proportional Hazards and Non-Linear Survival Analysis

arXiv: https://arxiv.org/abs/2504.17568 · HTML: https://mlsanity.com/paper/2504.17568/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 30 references that are in the map.
- First posted on arXiv 24 Apr 2025.

## Builds on (most cited first, 7 of 7)

- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [Deep Survival Machines: Fully Parametric Survival Regression and Representation Learning for Censored Data with Competing Risks](https://mlsanity.com/paper/2003.01176/) (2020)
- [SurvTRACE: Transformers for Survival Analysis with Competing Events](https://mlsanity.com/paper/2110.00855/) (2021)
- [auton-survival: an Open-Source Package for Regression, Counterfactual Estimation, Evaluation and Phenotyping with Censored Time-to-Event Data](https://mlsanity.com/paper/2204.07276/) (2022)
- [FastCPH: Efficient Survival Analysis for Neural Networks](https://mlsanity.com/paper/2208.09793/) (2022)
- [SurvHive: a package to consistently access multiple survival-analysis packages](https://mlsanity.com/paper/2502.02223/) (2025)

## Built on by (most cited first, 3 of 3)

- [Position: Stop Chasing the C-index when Evaluating Survival Analysis Models](https://mlsanity.com/paper/2506.02075/) (2025)
- [Neural Diffusion Processes for Physically Interpretable Survival Prediction](https://mlsanity.com/paper/2510.00733/) (2025)
- [The C-index illusion: discrimination without calibration in published survival models](https://mlsanity.com/paper/2607.19526/) (2026)

## Abstract (arXiv)

Survival analysis often relies on Cox models, assuming both linearity and proportional hazards (PH). This study evaluates machine and deep learning methods that relax these constraints, comparing their performance with penalized Cox models on a benchmark of three synthetic and three real datasets. In total, eight different models were tested, including six non-linear models of which four were also non-PH. Although Cox regression often yielded satisfactory performance, we showed the conditions under which machine and deep learning models can perform better. Indeed, the performance of these methods has often been underestimated due to the improper use of Harrell's concordance index (C-index) instead of more appropriate scores such as Antolini's concordance index, which generalizes C-index in cases where the PH assumption does not hold. In addition, since occasionally high C-index models happen to be badly calibrated, combining Antolini's C-index with Brier's score is useful to assess the overall performance of a survival method. Results on our benchmark data showed that survival prediction should be approached by testing different methods to select the most appropriate one according to sample size, non-linearity and non-PH conditions. To allow an easy reproducibility of these tests on our benchmark data, code and documentation are freely available at https://github.com/compbiomed-unito/survhive.