Bradley P. Carlin, Ph.D.
Professor, Division of Biostatistics
School of Public Health
University of Minnesota
Minneapolis, Minnesota U.S.A.

Survival models have a long history in the biomedical and biostatistical literature, 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 talk we will consider spatial survival models from two general points of view: {\em geostatistical approaches}, where we use the exact geographic locations (e.g., latitude and longitude) of the strata, and {\em lattice approaches}, where we use only the positions of the strata relative to each other (e.g., which counties neighbor which others).  We will compare these approaches in the context of a data set on infant mortality in Minnesota counties between 1992 and 1996.

We will then consider hierarchical spatial process models for multivariate survival data sets which are spatio-temporally arranged. Such models must account for correlations between survival rates in neighboring spatial regions, adjacent time periods, and similar diseases (say, different forms of cancer).  We will investigate Cox semiparametric survival modeling approaches, adding spatial and temporal effects in a hierarchical structure.  Here, a multivariate lattice model for the region-specific frailties is most convenient. Exemplification will be provided using time-to-event data for various cancers from the National Cancer Institute’s Surveillance, Epidemiology, and End Results (SEER) database.