# MENSA: A Multi-Event Network for Survival Analysis with Trajectory-based Likelihood Estimation

arXiv: https://arxiv.org/abs/2409.06525 · HTML: https://mlsanity.com/paper/2409.06525/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 73 references that are in the map.
- First posted on arXiv 10 Sep 2024.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (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)
- [SurvTRACE: Transformers for Survival Analysis with Competing Events](https://mlsanity.com/paper/2110.00855/) (2021)
- [An Extensive Data Processing Pipeline for MIMIC-IV](https://mlsanity.com/paper/2204.13841/) (2022)
- [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)
- [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 Effective Meaningful Way to Evaluate Survival Models](https://mlsanity.com/paper/2306.01196/) (2023)
- [SurvLatent ODE : A Neural ODE based time-to-event model with competing risks for longitudinal data improves cancer-associated Venous Thromboembolism (VTE) prediction](https://mlsanity.com/paper/2204.09633/) (2022)
- [Copula-Based Deep Survival Models for Dependent Censoring](https://mlsanity.com/paper/2306.11912/) (2023)
- [Deep Copula-Based Survival Analysis for Dependent Censoring with Identifiability Guarantees](https://mlsanity.com/paper/2312.15566/) (2023)
- [Deep-CR MTLR: a Multi-Modal Approach for Cancer Survival Prediction with Competing Risks](https://mlsanity.com/paper/2012.05765/) (2020)
- [Efficient Training of Probabilistic Neural Networks for Survival Analysis](https://mlsanity.com/paper/2404.06421/) (2024)

## 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)
- [Overcoming Dependent Censoring in the Evaluation of Survival Models](https://mlsanity.com/paper/2502.19460/) (2025)
- [A meaningful prediction of functional decline in amyotrophic lateral sclerosis based on multi-event survival analysis](https://mlsanity.com/paper/2506.02076/) (2025)

## Abstract (arXiv)

Most existing time-to-event methods focus on either single-event or competing-risks settings, leaving multi-event scenarios relatively underexplored. In many healthcare applications, for example, a patient may experience multiple clinical events, that can be non-exclusive and semi-competing. A common workaround is to train independent single-event models for such multi-event problems, but this approach fails to exploit dependencies and shared structures across events. To overcome these limitations, we propose MENSA (Multi-Event Network for Survival Analysis), a deep learning model that jointly learns flexible time-to-event distributions for multiple events, whether competing or co-occurring. In addition, we introduce a novel trajectory-based likelihood term that captures the temporal ordering between events. Across four multi-event datasets, MENSA improves predictive performance over many state-of-the-art baselines. Source code is available at https://github.com/thecml/mensa.