Incorporating temporal and spatial variation could potentially enhance
information gathered from survival data. This paper proposes a Bayesian semi-
parametric model for capturing spatio{temporal heterogeneity within the propor-
tional hazards framework. The spatial correlation is introduced in the form of
county{level frailties. The temporal e®ect is introduced by considering the strati-
¯cation of the proportional hazards model, where the time{dependent hazards are
indirectly modeled using a probability model for related probability distributions.
With this aim, an autoregressive dependent tailfree process is introduced. The
full Kullback{Leibler support of the proposed process is provided. The approach
is illustrated using simulated data and data from the Surveillance Epidemiology
and End Results database of the National Cancer Institute on patients in Iowa
diagnosed with breast cancer.