Hierarchical and joint site-edge methods for medicare hospice service region boundary analysis

Hospice service offers a convenient and ethically preferable health-care option for terminally ill patients. However, this option is unavailable to patients in remote areas not served by any hospice system. In this article, we seek to determine the service areas of two particular cancer hospice systems in northeastern Minnesota based only on death counts abstracted from Medicare billing records. The problem is one of spatial boundary analysis, a field that appears statistically underdeveloped for irregular areal (lattice) data, even though most publicly available human health data are of this type. In this article, we suggest a variety of hierarchical models for areal boundary analysis that hierarchically or jointly parameterize both the areas and the edge segments. This leads to conceptually appealing solutions for our data that remain computationally feasible. While our approaches parallel similar developments in statistical image restoration using Markov random fields, important differences arise due to the irregular nature of our lattices, the sparseness and high variability of our data, the existence of important covariate information, and most importantly, our desire for full posterior inference on the boundary. Our results successfully delineate service areas for our two Minnesota hospice systems that sometimes conflict with the hospices' self-reported service areas. We also obtain boundaries for the spatial residuals from our fits, separating regions that differ for reasons yet unaccounted for by our model.