Spatial Semiparametric Proportional Hazards Models for Analyzing Infant Mortality Rates in Minnesota Counties

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. We analyze a set of spatially correlated infant mortality rates in the counties in Minnesota. In the absence of appropriate surrogates for standard of health in the different counties, epidemiologists and health professionals are particularly interested in discerning spatial patterns that might be present among the counties for pre- and post-natal care. We develop a Bayesian hierarchical framework to model these data that builds upon the usual Cox model by incorporating county-specific frailties that account for possible geographical clustering. We demonstrate that spatial frailties have a role to play not only in capturing spatial trends, but also in improving the performance of the models.