  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 types of the priors for spatially varying
coefficients. A model selection criterion, logarithm of the pseudo-marginal
likelihood (LPML), is developed to assess the fit of 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 data.
