# Time-to-Event Prediction with Neural Networks and Cox Regression

arXiv: https://arxiv.org/abs/1907.00825 · HTML: https://mlsanity.com/paper/1907.00825/

## Key facts

- Cited by 175 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2019.

## Built on by (most cited first, 30 of 175)

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- [Deep Cox Mixtures for Survival Regression](https://mlsanity.com/paper/2101.06536/) (2021)
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- [SurvSHAP(t): Time-dependent explanations of machine learning survival models](https://mlsanity.com/paper/2208.11080/) (2022)
- [Longitudinal Fairness with Censorship](https://mlsanity.com/paper/2203.16024/) (2022)
- [CoxKAN: Kolmogorov-Arnold Networks for Interpretable, High-Performance Survival Analysis](https://mlsanity.com/paper/2409.04290/) (2024)
- [SurvSet: An open-source time-to-event dataset repository](https://mlsanity.com/paper/2203.03094/) (2022)
- [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)
- [An Introduction to Deep Survival Analysis Models for Predicting Time-to-Event Outcomes](https://mlsanity.com/paper/2410.01086/) (2024)
- [Distributionally Robust Survival Analysis: A Novel Fairness Loss Without Demographics](https://mlsanity.com/paper/2211.10508/) (2022)
- [Fair Decision-making Under Uncertainty](https://mlsanity.com/paper/2301.12364/) (2023)
- [Fairness in Survival Analysis with Distributionally Robust Optimization](https://mlsanity.com/paper/2409.10538/) (2024)
- [Medical Imaging and Machine Learning](https://mlsanity.com/paper/2103.01938/) (2021)
- [DeepPAMM: Deep Piecewise Exponential Additive Mixed Models for Complex Hazard Structures in Survival Analysis](https://mlsanity.com/paper/2202.07423/) (2022)
- [Individual Fairness under Uncertainty](https://mlsanity.com/paper/2302.08015/) (2023)
- [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)
- [DySurv: dynamic deep learning model for survival analysis with conditional variational inference](https://mlsanity.com/paper/2310.18681/) (2023)
- [Tabular Foundation Models Can Do Survival Analysis](https://mlsanity.com/paper/2601.22259/) (2026)
- [T-SCI: A Two-Stage Conformal Inference Algorithm with Guaranteed Coverage for Cox-MLP](https://mlsanity.com/paper/2103.04556/) (2021)
- [The structure of online social networks modulates the rate of lexical change](https://mlsanity.com/paper/2104.05010/) (2021)
- [Inverse-Weighted Survival Games](https://mlsanity.com/paper/2111.08175/) (2021)
- [The Concordance Index decomposition: A measure for a deeper understanding of survival prediction models](https://mlsanity.com/paper/2203.00144/) (2022)
- [Federated Survival Forests](https://mlsanity.com/paper/2302.02807/) (2023)
- [MGCT: Mutual-Guided Cross-Modality Transformer for Survival Outcome Prediction using Integrative Histopathology-Genomic Features](https://mlsanity.com/paper/2311.11659/) (2023)

## Abstract (arXiv)

New methods for time-to-event prediction are proposed by extending the Cox proportional hazards model with neural networks. Building on methodology from nested case-control studies, we propose a loss function that scales well to large data sets, and enables fitting of both proportional and non-proportional extensions of the Cox model. Through simulation studies, the proposed loss function is verified to be a good approximation for the Cox partial log-likelihood. The proposed methodology is compared to existing methodologies on real-world data sets, and is found to be highly competitive, typically yielding the best performance in terms of Brier score and binomial log-likelihood. A python package for the proposed methods is available at https://github.com/havakv/pycox.