DAGSurv: Directed Ayclic Graph Based Survival Analysis Using Deep Neural Networks

Causal structures for observational survival data provide crucial information regarding the relationships between covariates and time-to-event. We derive motivation from the information theoretic source coding argument, and show that incorporating the knowledge of the directed acyclic graph (DAG) can be beneficial if suitable source encoders are employed. As a possible source encoder in this context, we derive a variational inference based conditional variational autoencoder for causal structured survival prediction, which we refer to as \texttt{DAGSurv}. We illustrate the performance of \texttt{DAGSurv} on low and high-dimensional synthetic datasets, and real-world datasets such as METABRIC and GBSG. We demonstrate that the proposed method outperforms other survival analysis baselines such as \texttt{Cox} Proportional Hazards, \texttt{DeepSurv} and \texttt{Deephit}, which are oblivious to the underlying causal relationship between data entities.