IDNetwork: A deep illness-death network based on multi-state event history process for disease prognostication.

Multi-state models can capture the different patterns of disease evolution. In particular, the illness-death model is used to follow disease progression from a healthy state to an intermediate state of the disease and to a death-related final state. We aim to use those models in order to adapt treatment decisions according to the evolution of the disease. In state-of-the art methods, the risks of transition between the states are modeled via (semi-) Markov processes and transition-specific Cox proportional hazard (P.H.) models. The Cox P.H. model assumes that each variable makes a linear contribution to the model, but the relationship between covariates and risks can be more complex in clinical situations. To address this challenge, we propose a neural network architecture called illness-death network (IDNetwork) that relaxes the linear Cox P.H. assumption within an illness-death process. IDNetwork employs a multi-task architecture and uses a set of fully connected subnetworks in order to learn the probabilities of transition. Through simulations, we explore different configurations of the architecture and demonstrate the added value of our model. IDNetwork significantly improves the predictive performance compared to state-of-the-art methods on a simulated data set, on two clinical trials for patients with colon cancer and on a real-world data set in breast cancer.