Semiparametric bayesian modeling of spatio-survival data under cure fraction

We propose the use of Bayesian spatial modeling with cure rates to model colon cancer survival times for patients diagnosed in the state of Connecticut between 1973-2004, and with follow up time until 2007. This research is motivated by the SEER data base, but the proposed work offers useful contributions to general statistical theory and methodology in survival analysis, spatial statistics and cure rates modeling. In recent times, spatial variability components, cure possibilities, and the changes over time of the survival curve have been of paramount interest to researchers and public health decision makers. There has been research addressing each of these factors independently, but there is a need for a richer class of models to enable a comprehensive analysis of time to event data. We assume semi-parametric baseline hazard functions with a grid defined by join-point parameters similar to the ones used in join-point regression models. The hazard model is set up under the generalized proportional hazard framework in which we also include a covariance function. We integrate into the analysis the spatial correlation structure, in the form of county cancer level frailties and the cure rates. Finally, we compare across a broad collection of high-dimensional hierarchical models using the log of the pseudo-marginal likelihood. This paper uses a Bayesian hierarchical model for capturing spatial heterogeneity and cure rates for right censored time to event data under a semiparametric proportional hazard framework. We obtain the usual posterior estimates, smoothed by counties level maps of spatial frailties and cure rates.