Given an instance, a multi-event survival model predicts the time until that instance experiences each of several different events. These events are not mutually exclusive and there are often statistical dependencies between them. There are relatively few multi-event survival results, most focusing on producing a simple risk score, rather than the time-to-event itself. To overcome these issues, we introduce MENSA, a novel, deep learning approach for multi-event survival analysis that can jointly learn representations of the input covariates and the dependence structure between events. As a practical motivation for multi-event survival analysis, we consider the problem of predicting the time until a patient with amyotrophic lateral sclerosis (ALS) loses various physical functions, i.e., the ability to speak, swallow, write, or walk. When estimating when a patient is no longer able to swallow, our approach achieves an L1-Margin loss of 278.8 days, compared to 355.2 days when modeling each event separately. In addition, we also evaluate our approach in single-event and competing risk scenarios by modeling the censoring and event distributions as equal contributing factors in the optimization process, and show that our approach performs well across multiple benchmark datasets. The source code is available at: https://github.com/thecml/mensa
View on arXiv@article{lillelund2025_2409.06525,
title={ MENSA: A Multi-Event Network for Survival Analysis with Trajectory-based Likelihood Estimation },
author={ Christian Marius Lillelund and Ali Hossein Gharari Foomani and Weijie Sun and Shi-ang Qi and Russell Greiner },
journal={arXiv preprint arXiv:2409.06525},
year={ 2025 }
}