  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.
