# Neural Fine-Gray: Monotonic neural networks for competing risks

arXiv: https://arxiv.org/abs/2305.06703 · HTML: https://mlsanity.com/paper/2305.06703/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 57 references that are in the map.
- First posted on arXiv 11 May 2023.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [Machine Learning for Survival Analysis: A Survey](https://mlsanity.com/paper/1708.04649/) (2017)
- [Deep Survival Machines: Fully Parametric Survival Regression and Representation Learning for Censored Data with Competing Risks](https://mlsanity.com/paper/2003.01176/) (2020)
- [Deep Cox Mixtures for Survival Regression](https://mlsanity.com/paper/2101.06536/) (2021)
- [Survival Regression with Proper Scoring Rules and Monotonic Neural Networks](https://mlsanity.com/paper/2103.14755/) (2021)
- [Neural Likelihoods via Cumulative Distribution Functions](https://mlsanity.com/paper/1811.00974/) (2018)
- [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)
- [Counterfactual Phenotyping with Censored Time-to-Events](https://mlsanity.com/paper/2202.11089/) (2022)
- [A review on competing risks methods for survival analysis](https://mlsanity.com/paper/2212.05157/) (2022)

## Built on by (most cited first, 20 of 20)

- [An Introduction to Deep Survival Analysis Models for Predicting Time-to-Event Outcomes](https://mlsanity.com/paper/2410.01086/) (2024)
- [Advancing Constrained Monotonic Neural Networks: Achieving Universal Approximation Beyond Bounded Activations](https://mlsanity.com/paper/2505.02537/) (2025)
- [HACSurv: A Hierarchical Copula-Based Approach for Survival Analysis with Dependent Competing Risks](https://mlsanity.com/paper/2410.15180/) (2024)
- [Survival In-Context: Amortized Bayesian Survival Analysis via Prior-Fitted Networks](https://mlsanity.com/paper/2603.29475/) (2026)
- [One Loss to Rule Them All: Marked Time-to-Event for Structured EHR Foundation Models](https://mlsanity.com/paper/2602.00541/) (2026)
- [MENSA: A Multi-Event Network for Survival Analysis with Trajectory-based Likelihood Estimation](https://mlsanity.com/paper/2409.06525/) (2024)
- [Competing Risks: Impact on Risk Estimation and Algorithmic Fairness](https://mlsanity.com/paper/2508.05435/) (2025)
- [Prediction of Survival Outcomes under Clinical Presence Shift: A Joint Neural Network Architecture](https://mlsanity.com/paper/2508.05472/) (2025)
- [Whole-body Representation Learning For Competing Preclinical Disease Risk Assessment](https://mlsanity.com/paper/2508.02307/) (2025)
- [Stepwise Fine and Gray: Subject-Specific Variable Selection Shows When Hemodynamic Data Improves Prognostication of Comatose Post-Cardiac Arrest Patients](https://mlsanity.com/paper/2508.06023/) (2025)
- [OPSurv: Orthogonal Polynomials Quadrature Algorithm for Survival Analysis](https://mlsanity.com/paper/2402.01955/) (2024)
- [Identifying treatment response subgroups in observational time-to-event data](https://mlsanity.com/paper/2408.03463/) (2024)
- [Wave-LSTM: Multi-scale analysis of somatic whole genome copy number profiles](https://mlsanity.com/paper/2408.12636/) (2024)
- [CRISP-NAM: Competing Risks Interpretable Survival Prediction with Neural Additive Models](https://mlsanity.com/paper/2505.21360/) (2025)
- [Deep Survival Analysis in Multimodal Medical Data: A Parametric and Probabilistic Approach with Competing Risks](https://mlsanity.com/paper/2507.07804/) (2025)
- [ADHAM: Additive Deep Hazard Analysis Mixtures for Interpretable Survival Regression](https://mlsanity.com/paper/2509.07108/) (2025)
- [Interpretable Fine-Gray Deep Survival Model for Competing Risks: Predicting Post-Discharge Foot Complications for Diabetic Patients in Ontario](https://mlsanity.com/paper/2511.12409/) (2025)
- [Deep Kernel Aalen-Johansen Estimator: An Interpretable and Flexible Neural Net Framework for Competing Risks](https://mlsanity.com/paper/2512.08063/) (2025)
- [SSH-Net: A Deep Neural Network for Predicting Failure Time Distribution Functions under Competing Risks with Application to GPU Data](https://mlsanity.com/paper/2606.20451/) (2026)
- [NOAH: Learning the Full Patient Journey. A Longitudinal Multimodal Time-Aware Model for Representation and Forecasting](https://mlsanity.com/paper/2609.09140/) (2026)

## Abstract (arXiv)

Time-to-event modelling, known as survival analysis, differs from standard regression as it addresses censoring in patients who do not experience the event of interest. Despite competitive performances in tackling this problem, machine learning methods often ignore other competing risks that preclude the event of interest. This practice biases the survival estimation. Extensions to address this challenge often rely on parametric assumptions or numerical estimations leading to sub-optimal survival approximations. This paper leverages constrained monotonic neural networks to model each competing survival distribution. This modelling choice ensures the exact likelihood maximisation at a reduced computational cost by using automatic differentiation. The effectiveness of the solution is demonstrated on one synthetic and three medical datasets. Finally, we discuss the implications of considering competing risks when developing risk scores for medical practice.