Hierarchical multivariate CAR models for spatio-temporally correlated survival data

Survival models have a long history in the biomedical and biostatistical literattue, and are enormously popular in the analysis of time-to-event data. Very often these data will be grouped into strata, such as clinical sites, geographic regions, and so on. Such data will often be available over multiple time periods, and for multiple diseases. In this paper, we consider hierarchical spatial process models for multivariate survival data sets which are spatio-temporally arranged. Such models must account for correlations between survival Fates in neighboring spatial regions, adjacent time periods, and similar diseases (say, different forms of cancer). We investigate Cox semiparametric survival modeling approaches, adding spatial and temporal effects in a hierarchical structure. Due to data limitations and computational complexity issues, we avoid geostatistical (kriging) models, and instead handle spatial correlation by placing a particular multivariate generalization of the conditionally autoregressive (CAR) distribution on the region-specific frailties. Exemplification is provided using time-to-event data for various cancers from the National Cancer Institute's Surveillance, Epidemiology, and End Results (SEER) database.