| Spatial boundary analysis is an area that is currently underdeveloped for irregular areal (lattice) data, even though most publicly available human health data are of this type. In this dissertation, we begin by reviewing some existing boundary analysis methods and edge detection methods from the image processing literature. We also give a brief introduction to the conditional autoregressive (CAR) distribution, widely used to model local dependence in areal data. We then suggest a variety of hierarchical models for areal boundary analysis that hierarchically or jointly parameterize both the areas and the edge segments.;We apply these methods to hospice service area estimation, where we seek to determine the geographic service areas of two cancer hospice systems in northeastern Minnesota based only on death counts abstracted from Medicare billing records. The method offers conceptually appealing solutions for these data that remain computationally feasible. 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.;The dissertation then extends the proposed hierarchical boundary analysis models to the multivariate case. Utilizing recent developments in multivariate conditionally autoregressive (MCAR) distributions and spatial structural equation modeling, we suggest a variety of Bayesian hierarchical models for multivariate areal boundary analysis, including some that incorporate random neighborhood structure. Many of our models can be implemented via standard software, namely WinBUGS for posterior sampling and R for summarization and plotting. We illustrate our methods using Minnesota county-level esophagus, larynx, and lung cancer data, comparing models that account for both, only one, or neither of the aforementioned correlations. We identify both composite and cancer-specific boundaries, selecting the best statistical model using the DIC criterion. Our results indicate primary boundaries in both the composite and cancer-specific response surface separating the mining- and tourism-oriented northeast counties from the remainder of the state, as well as secondary (residual) boundaries in the Twin Cities metro area.;Finally, we discuss our results and mention possibilities for future research in this area. |
