  We study the variable selection problem in survival analysis to identify the
most important factors affecting survival time. Our method incorporates prior
knowledge of mutual correlations among variables, represented through a graph.
We utilize the Cox proportional hazard model with a graph-based regularizer for
variable selection. We present a computationally efficient algorithm developed
to solve the graph regularized maximum likelihood problem by establishing
connections with the group lasso, and provide theoretical guarantees about the
recovery error and asymptotic distribution of the proposed estimators. The
improved performance of the proposed approach compared with existing methods
are demonstrated in both synthetic and real organ transplantation datasets.
