Parametric models for spatially correlated survival data for individuals with multiple cancers.

Incorporating spatial variation could potentially enhance information coming from survival data. In addition, simultaneous (joint) modeling of time-to-event data from different diseases, such as cancers, from the same patient could provide useful insights as to how these diseases behave together. This paper proposes Bayesian hierarchical survival models for capturing spatial correlations within the proportional hazards (PH) and proportional odds (PO) frameworks. Parametric (Weibull for the PH and log-logistic for the PO) models were used for the baseline distribution while spatial correlation is introduced in the form of county-cancer-level frailties. We illustrate with data from the Surveillance Epidemiology and End Results database of the National Cancer Institute on patients in Iowa diagnosed with multiple gastrointestinal cancers. Model checking and comparison among competing models were performed and some implementation issues were presented. We recommend the use of the spatial PH model for this data set.