Spatial confounding in multivariate areal data analysis.

We investigate spatial confounding in the presence of multivariate disease dependence. Although multiple methods have been proposed for adjusting statistical models to mitigate spatial confounding in estimating regression coefficients, the results on interactions between spatial confounding and multivariate dependence are very limited. We contribute to this domain by investigating spatial confounding from the "analysis" and "data generation" perspectives in a Bayesian coregionalized areal regression model. We derive novel results that show that under spatial confounding, posterior variance inflation is limited in multivariate areal models and spatial point estimators of fixed effects retain higher precision compared to their non-spatial counterparts. We demonstrate the favorable performance of spatial analysis compared to a non-spatial model in our simulation experiments, even in the presence of spatial confounding and a misspecified spatial structure. In this regard, we align with recommendations from several authors in preferring hierarchical spatial models. We analyze county-level data from the US on obesity/diabetes prevalence and diabetes-related cancer mortality, comparing the results with and without spatial random effects.