  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 MCMC 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 data set on respiratory cancer in Louisiana from the SEER
program.
