# Deep Learning of Semi-Competing Risk Data via a New Neural Expectation-Maximization Algorithm

arXiv: https://arxiv.org/abs/2212.12028 · HTML: https://mlsanity.com/paper/2212.12028/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 66 references that are in the map.
- First posted on arXiv 22 Dec 2022.

## Builds on (most cited first, 8 of 8)

- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review](https://mlsanity.com/paper/1611.00740/) (2016)
- [Deep Survival Analysis](https://mlsanity.com/paper/1608.02158/) (2016)
- [High-Dimensional Survival Analysis: Methods and Applications](https://mlsanity.com/paper/2205.02948/) (2022)
- [Penalized Estimation of Frailty-Based Illness-Death Models for Semi-Competing Risks](https://mlsanity.com/paper/2202.00618/) (2022)
- [Marginalized Frailty-Based Illness-Death Model: Application to the UK-Biobank Survival Data](https://mlsanity.com/paper/1906.03187/) (2019)
- [An Accelerated Failure Time Regression Model for Illness-Death Data: A Frailty Approach](https://mlsanity.com/paper/2205.03954/) (2022)

## Abstract (arXiv)

Prognostication for lung cancer, a leading cause of mortality, remains a complex task, as it needs to quantify the associations of risk factors and health events spanning a patient's entire life. One challenge is that an individual's disease course involves non-terminal (e.g., disease progression) and terminal (e.g., death) events, which form semi-competing relationships. Our motivation comes from the Boston Lung Cancer Study, a large lung cancer survival cohort, which investigates how risk factors influence a patient's disease trajectory. Following developments in the prediction of time-to-event outcomes with neural networks, deep learning has become a focal area for the development of risk prediction methods in survival analysis. However, limited work has been done to predict multi-state or semi-competing risk outcomes, where a patient may experience adverse events such as disease progression prior to death. We propose a novel neural expectation-maximization algorithm to bridge the gap between classical statistical approaches and machine learning. Our algorithm enables estimation of the non-parametric baseline hazards of each state transition, risk functions of predictors, and the degree of dependence among different transitions, via a multi-task deep neural network with transition-specific sub-architectures. We apply our method to the Boston Lung Cancer Study and investigate the impact of clinical and genetic predictors on disease progression and mortality.