# ADHAM: Additive Deep Hazard Analysis Mixtures for Interpretable Survival Regression

arXiv: https://arxiv.org/abs/2509.07108 · HTML: https://mlsanity.com/paper/2509.07108/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 72 references that are in the map.
- First posted on arXiv 8 Sep 2025.

## Builds on (most cited first, 23 of 23)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [What Clinicians Want: Contextualizing Explainable Machine Learning for Clinical End Use](https://mlsanity.com/paper/1905.05134/) (2019)
- [Neural Photo Editing with Introspective Adversarial Networks](https://mlsanity.com/paper/1609.07093/) (2016)
- [Deep Survival Machines: Fully Parametric Survival Regression and Representation Learning for Censored Data with Competing Risks](https://mlsanity.com/paper/2003.01176/) (2020)
- [Effective Ways to Build and Evaluate Individual Survival Distributions](https://mlsanity.com/paper/1811.11347/) (2018)
- [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)
- [SurvTRACE: Transformers for Survival Analysis with Competing Events](https://mlsanity.com/paper/2110.00855/) (2021)
- [SurvLIME: A method for explaining machine learning survival models](https://mlsanity.com/paper/2003.08371/) (2020)
- [Neural Fine-Gray: Monotonic neural networks for competing risks](https://mlsanity.com/paper/2305.06703/) (2023)
- [SurvNAM: The machine learning survival model explanation](https://mlsanity.com/paper/2104.08903/) (2021)
- [An Effective Meaningful Way to Evaluate Survival Models](https://mlsanity.com/paper/2306.01196/) (2023)
- [Counterfactual Phenotyping with Censored Time-to-Events](https://mlsanity.com/paper/2202.11089/) (2022)
- [All Points Matter: Entropy-Regularized Distribution Alignment for Weakly-supervised 3D Segmentation](https://mlsanity.com/paper/2305.15832/) (2023)
- [Curve Your Enthusiasm: Concurvity Regularization in Differentiable Generalized Additive Models](https://mlsanity.com/paper/2305.11475/) (2023)
- [Survival Mixture Density Networks](https://mlsanity.com/paper/2208.10759/) (2022)
- [Extending the Neural Additive Model for Survival Analysis with EHR Data](https://mlsanity.com/paper/2211.07814/) (2022)
- [Competing Risks: Impact on Risk Estimation and Algorithmic Fairness](https://mlsanity.com/paper/2508.05435/) (2025)
- [Maximum Likelihood Estimation of Flexible Survival Densities with Importance Sampling](https://mlsanity.com/paper/2311.01660/) (2023)

## Abstract (arXiv)

Survival analysis is a fundamental tool for modeling time-to-event outcomes in healthcare. Recent advances have introduced flexible neural network approaches for improved predictive performance. However, most of these models do not provide interpretable insights into the association between exposures and the modeled outcomes, a critical requirement for decision-making in clinical practice. To address this limitation, we propose Additive Deep Hazard Analysis Mixtures (ADHAM), an interpretable additive survival model. ADHAM assumes a conditional latent structure that defines subgroups, each characterized by a combination of covariate-specific hazard functions. To select the number of subgroups, we introduce a post-training refinement that reduces the number of equivalent latent subgroups by merging similar groups. We perform comprehensive studies to demonstrate ADHAM's interpretability at the population, subgroup, and individual levels. Extensive experiments on real-world datasets show that ADHAM provides novel insights into the association between exposures and outcomes. Further, ADHAM remains on par with existing state-of-the-art survival baselines in terms of predictive performance, offering a scalable and interpretable approach to time-to-event prediction in healthcare.