  Disease maps are an important tool in cancer epidemiology used for the
analysis of geographical variations in disease rates and the investigation of
environmental risk factors underlying spatial patterns. Cancer maps help
epidemiologists highlight geographic areas with high and low prevalence,
incidence, or mortality rates of cancers, and the variability of such rates
over a spatial domain. When more than one cancer is of interest, the models
must also capture the inherent or endemic association between the diseases in
addition to the spatial association. This article develops interpretable and
easily implementable spatial autocorrelation models for two or more cancers.
The article builds upon recent developments in univariate disease mapping that
have shown the use of mathematical structures such as directed acyclic graphs
to capture spatial association for a single cancer, estimating inherent or
endemic association for two cancers in addition to the association over space
(clustering) for each of the cancers. The method builds a Bayesian hierarchical
model where the spatial effects are introduced as latent random effects for
each cancer. We analyze the relationship between incidence rates of esophagus
and lung cancer extracted from the Surveillance, Epidemiology, and End Results
(SEER) Program. Our analysis shows statistically significant association
between the county-wise incidence rates of lung and esophagus cancer across
California. The bivariate directed acyclic graphical model performs better than
competing bivariate spatial models in the existing literature.
