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.

翻译：我们研究生存分析中的变量选择问题,以确定影响生存时间的最重要因素,当变量事先知道它们通过图形结构具有相互关系时,这些变量会影响生存时间。我们考虑Cox比例风险模型,该模型带有基于图表的变量选择常规化器。我们开发了一种计算高效的算法,通过连接群列,解决图形标准化的最大可能性问题。我们从理论上保证了拟议测算器的回收错误和无药可治分布。与现有方法相比,拟议方法的良好性能和效益在合成和真实数据实例中都得到了证明。