In this paper, we develop a variable selection framework with the spike-and-slab prior distribution via the hazard function of the Cox model. Specifically, we consider the transformation of the score and information functions for the partial likelihood function evaluated at the given data from the parameter space into the space generated by the logarithm of the hazard ratio. Thereby, we reduce the nonlinear complexity of the estimation equation for the Cox model and allow the utilization of a wider variety of stable variable selection methods. Then, we use a stochastic variable search Gibbs sampling approach via the spike-and-slab prior distribution to obtain the sparsity structure of the covariates associated with the survival outcome. Additionally, we conduct numerical simulations to evaluate the finite-sample performance of our proposed method. Finally, we apply this novel framework on lung adenocarcinoma data to find important genes associated with decreased survival in subjects with the disease.

在本文中，我们通过 Cox 模型的风险函数开发了一个具有尖峰和平板先验分布的变量选择框架。具体来说，我们考虑将在给定数据处评估的部分似然函数的分数和信息函数从参数空间转换为由风险比的对数生成的空间。因此，我们降低了 Cox 模型估计方程的非线性复杂性，并允许使用更广泛的稳定变量选择方法。然后，我们通过spike-and-slab先验分布使用随机变量搜索Gibbs抽样方法来获得与生存结果相关的协变量的稀疏结构。此外，我们进行数值模拟来评估我们提出的方法的有限样本性能。