  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 DAGSurv. We illustrate the performance of 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 Cox Proportional Hazards, DeepSurv and Deephit,
which are oblivious to the underlying causal relationship between data
entities.
