Semiparametric spatio-temporal frailty modeling

Recent developments in GIS have encouraged health science databases to incorporate geographical information about the subjects under study. Such databases have in turn generated interest among statisticians to develop and analyze models that account for spatial clustering and variation. In this article we develop a semiparametric (Cox) hierarchical Bayesian frailty model for capturing spatio-temporal heterogeneity in the survival patterns of women diagnosed with breast cancer in Iowa. In the absence of appropriate surrogates for standards of treatments and health care for cancer patients in the different counties, epidemiologists and health-care professionals are interested in discerning spatial patterns in survival from breast cancer that might be present among the counties. In addition, it is naturally of interest to see if the counties show discernible temporal trends over the years. The SEER (Surveillance Epidemiology and End Results) database from the National Cancer Institute (NCI) provides data on a cohort of breast cancer patients observed progressively through time, spanning 26 years. We implement our hierarchical spatio-temporal models on data extracted from the database for the 99 counties of Iowa. Our results suggest log-relative hazards that are generally flat initially, but steadily decrease for more recent years.