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

A multi-event survival model predicts the time until an instance experiences each of several different events, given the instance's description. Unlike competing-event models, the events here are not mutually exclusive and often exhibit statistical dependencies. Existing approaches for multi-event survival analysis have generally been limited, most focusing on producing simple risk scores for each event, rather than the time-to-event itself. To overcome these issues, we introduce MENSA, a novel deep learning approach for multi-event survival analysis. MENSA jointly learns representations of the input features while capturing the complex dependence structure among events. In practice, it attempts to optimize the sum of the traditional negative log-likelihood across events and a novel trajectory-based likelihood, which encourages the model to learn the temporal order in which events occur. Experiments on real-world clinical datasets show that MENSA consistently gives good discrimination performances and accurate time-to-event predictions in single-event, competing-risk, and multi-event problems. Additionally, MENSA is more computationally-efficient, requiring fewer parameters and FLOPs than multiple state-of-the-art survival baselines when applied to large-dimensional datasets (more than 100 features).

@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 }
}