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Bayesian Spatial Boundary Analysis for Areal Health Outcome Data

Bradley P. Carlin, University of Minnesota

Wednesday, April 13, 2005, 4:00 p.m.

140 Bardeen, Coffee and Cookies at 3:30 p.m. in Room 4331 CSSC

ABSTRACT

In the analysis of spatially referenced data, interest often focuses not on prediction of the spatially indexed variable itself, but on boundary analysis, i.e., the determination of boundaries on the map that separate areas of higher and lower values. Existing boundary analysis methods are sometimes generically referred to as “wombling,” after a foundational paper by Womble (1951). In this paper we propose MCMC-driven hierarchical Bayesian methods for areal data (i.e., data which consist only of sums or averages over geopolitical regions). Such methods are valuable in determining boundaries for data sets that, perhaps due to confidentiality concerns, are available only in ecological (aggregated) format, or are only collected this way (e.g., delivery of health care or cost information). Our methods employ conditionally autoregressive (CAR) models in the usual way for capturing the similarity of rates in neighboring regions, as well as in a novel way to model the similarity of the likelihood that neighboring region-separating segments are part of the wombled boundary. For multivariate response data, multivariate CAR (MCAR) models also emerge as helpful. We illustrate our methods with an analysis of service areas of competing cancer hospice care systems measured at the zip code level in northeastern Minnesota.

NOTE: This work is joint with Haijun Ma of the Division of Biostatistics, University of Minnesota.

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