A Comparison of Bayesian Accelerated Failure Time Models with Spatially Varying Coefficients

The accelerated failure time (AFT) model is a commonly used tool in analyzing survival data. In public health studies, data is often collected from medical service providers in different locations. Survival rates from different locations often present geographically varying patterns. In this paper, we focus on the accelerated failure time model with spatially varying coefficients. We compare three different types of priors for spatially varying coefficients. A model selection criterion, logarithm of the pseudo-marginal likelihood (LPML), is employed to assess the fit of the AFT model with different priors. Extensive simulation studies are carried out to examine the empirical performance of the proposed methods. Finally, we apply our model to SEER data on prostate cancer in Louisiana and demonstrate the existence of spatially varying effects on survival rates from prostate cancer.