  Regional aggregates of health outcomes over delineated administrative units
(e.g., states, counties, zip codes), or areal units, are widely used by
epidemiologists to map mortality or incidence rates and capture geographic
variation. To capture health disparities over regions, we seek "difference
boundaries" that separate neighboring regions with significantly different
spatial effects. Matters are more challenging with multiple outcomes over each
unit, where we capture dependence among diseases as well as across the areal
units. Here, we address multivariate difference boundary detection for
correlated diseases. We formulate the problem in terms of Bayesian pairwise
multiple comparisons and seek the posterior probabilities of neighboring
spatial effects being different. To achieve this, we endow the spatial random
effects with a discrete probability law using a class of multivariate
areally-referenced Dirichlet process (MARDP) models that accommodate spatial
and inter-disease dependence. We evaluate our method through simulation studies
and detect difference boundaries for multiple cancers using data from the
Surveillance, Epidemiology, and End Results (SEER) Program of the National
Cancer Institute.
