The Cox regression model is a commonly used model in survival analysis. In public health studies, clinical data are often collected from medical service providers of different locations. There are large geographical variations in the covariate effects on survival rates from particular diseases. In this paper, we focus on the variable selection issue for the Cox regression model with spatially varying coefficients. We propose a Bayesian hierarchical model which incorporates a horseshoe prior for sparsity and a point mass mixture prior to determine whether a regression coefficient is spatially varying. An efficient two-stage computational method is used for posterior inference and variable selection. It essentially applies the existing method for maximizing the partial likelihood for the Cox model by site independently first and then applying an Markov chain Monte Carlo algorithm for variable selection based on results of the first stage. Extensive simulation studies are carried out to examine the empirical performance of the proposed method. Finally, we apply the proposed methodology to analyzing a real dataset on respiratory cancer in Louisiana from the Surveillance, Epidemiology, and End Results (SEER) program.

中文翻译：

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具有空间变化系数的 Cox 回归模型的贝叶斯变量选择与路易斯安那州呼吸道癌数据的应用

Cox回归模型是生存分析中常用的模型。在公共卫生研究中，临床数据通常是从不同地点的医疗服务提供者那里收集的。协变量对特定疾病存活率的影响存在很大的地理差异。在本文中，我们关注具有空间变化系数的 Cox 回归模型的变量选择问题。我们提出了一个贝叶斯层次模型，该模型在确定回归系数是否在空间上变化之前结合了稀疏性的马蹄形先验和点质量混合。一种有效的两阶段计算方法用于后验推断和变量选择。它本质上是先独立地应用现有的方法来最大化 Cox 模型的部分似然度，然后根据第一阶段的结果应用马尔可夫链蒙特卡罗算法进行变量选择。进行了广泛的模拟研究以检查所提出方法的经验性能。最后，我们应用所提出的方法来分析来自监测、流行病学和最终结果 (SEER) 计划的路易斯安那州呼吸道癌的真实数据集。