Bayesian Variable Selection for Cox Regression Model with Spatially Varying Coefficients with Applications to Louisiana Respiratory Cancer Data

TL;DR

This paper introduces a Bayesian hierarchical model with spatially varying coefficients for Cox regression, enabling variable selection and accounting for geographical variations in survival analysis, demonstrated on Louisiana respiratory cancer data.

Contribution

It develops a novel Bayesian approach with a horseshoe prior and a two-stage computational method for spatially varying Cox models, addressing variable selection in geographically diverse data.

Findings

Effective variable selection in spatial Cox models.

Improved model performance demonstrated through simulations.

Insights into geographical effects on respiratory cancer survival.

Abstract

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.