We study the variable selection problem in survival analysis to identify the most important factors affecting the survival time when the variables have prior knowledge that they have a mutual correlation through a graph structure. We consider the Cox proportional hazard model with a graph-based regularizer for variable selection. A computationally efficient algorithm is developed to solve the graph regularized maximum likelihood problem by connecting to group lasso. We provide theoretical guarantees about the recovery error and asymptotic distribution of the proposed estimators. The good performance and benefit of the proposed approach compared with existing methods are demonstrated in both synthetic and real data examples.
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