# DeepPAMM: Deep Piecewise Exponential Additive Mixed Models for Complex Hazard Structures in Survival Analysis

arXiv: https://arxiv.org/abs/2202.07423 · HTML: https://mlsanity.com/paper/2202.07423/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 47 references that are in the map.
- First posted on arXiv 12 Feb 2022.

## Builds on (most cited first, 14 of 14)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [A Scalable Discrete-Time Survival Model for Neural Networks](https://mlsanity.com/paper/1805.00917/) (2018)
- [Continuous and Discrete-Time Survival Prediction with Neural Networks](https://mlsanity.com/paper/1910.06724/) (2019)
- [Deep Survival Analysis](https://mlsanity.com/paper/1608.02158/) (2016)
- [Semi-Structured Deep Piecewise Exponential Models](https://mlsanity.com/paper/2011.05824/) (2020)
- [deepregression: a Flexible Neural Network Framework for Semi-Structured Deep Distributional Regression](https://mlsanity.com/paper/2104.02705/) (2021)
- [A Wide and Deep Neural Network for Survival Analysis from Anatomical Shape and Tabular Clinical Data](https://mlsanity.com/paper/1909.03890/) (2019)
- [A General Machine Learning Framework for Survival Analysis](https://mlsanity.com/paper/2006.15442/) (2020)
- [Image-based Survival Analysis for Lung Cancer Patients using CNNs](https://mlsanity.com/paper/1808.09679/) (2018)
- [Towards modelling hazard factors in unstructured data spaces using gradient-based latent interpolation](https://mlsanity.com/paper/2110.11312/) (2021)

## Built on by (most cited first, 12 of 12)

- [Deep Learning for Survival Analysis: A Review](https://mlsanity.com/paper/2305.14961/) (2023)
- [A New PHO-rmula for Improved Performance of Semi-Structured Networks](https://mlsanity.com/paper/2306.00522/) (2023)
- [Survival In-Context: Amortized Bayesian Survival Analysis via Prior-Fitted Networks](https://mlsanity.com/paper/2603.29475/) (2026)
- [Interpretable Machine Learning for Survival Analysis](https://mlsanity.com/paper/2403.10250/) (2024)
- [Bayesian Semi-structured Subspace Inference](https://mlsanity.com/paper/2401.12950/) (2024)
- [How Inverse Conditional Flows Can Serve as a Substitute for Distributional Regression](https://mlsanity.com/paper/2405.05429/) (2024)
- [SurvDiff: A Diffusion Model for Generating Synthetic Data in Survival Analysis](https://mlsanity.com/paper/2509.22352/) (2025)
- [Semi-structured multi-state delinquency model for mortgage default](https://mlsanity.com/paper/2603.26309/) (2026)
- [Case-Base Neural Networks: survival analysis with time-varying, higher-order interactions](https://mlsanity.com/paper/2301.06535/) (2023)
- [A Functional Extension of Semi-Structured Networks](https://mlsanity.com/paper/2410.05430/) (2024)
- [dnamite: A Python Package for Neural Additive Models](https://mlsanity.com/paper/2503.07642/) (2025)
- [Deep Survival Analysis in Multimodal Medical Data: A Parametric and Probabilistic Approach with Competing Risks](https://mlsanity.com/paper/2507.07804/) (2025)

## Abstract (arXiv)

Survival analysis (SA) is an active field of research that is concerned with time-to-event outcomes and is prevalent in many domains, particularly biomedical applications. Despite its importance, SA remains challenging due to small-scale data sets and complex outcome distributions, concealed by truncation and censoring processes. The piecewise exponential additive mixed model (PAMM) is a model class addressing many of these challenges, yet PAMMs are not applicable in high-dimensional feature settings or in the case of unstructured or multimodal data. We unify existing approaches by proposing DeepPAMM, a versatile deep learning framework that is well-founded from a statistical point of view, yet with enough flexibility for modeling complex hazard structures. We illustrate that DeepPAMM is competitive with other machine learning approaches with respect to predictive performance while maintaining interpretability through benchmark experiments and an extended case study.