Spatial modeling for correlated cancers using bivariate directed graphs

Abstract

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.