🤖 AI Summary
This paper addresses spatial confounding under multivariate disease dependence, characterizing its dual interference mechanisms: from the modeling perspective, spatial random effects inflate posterior variances of fixed effects; from the data-generating perspective, correlations between covariates and unobserved spatial confounders induce biased inference. We innovatively distinguish variance inflation due to spatial confounding from that caused by multicollinearity, and propose the first diagnostic framework for spatial confounding in multivariate areal data. We theoretically prove—and empirically verify via large-scale simulation and U.S. county-level obesity, diabetes, and cancer mortality data—that incorporating spatial effects improves estimation efficiency even under spatial confounding and model misspecification. Leveraging Bayesian coregionalization, posterior variance decomposition, and hierarchical spatial modeling, our work establishes theoretical foundations and empirical evidence for the robustness of multivariate spatial models in complex, dependent disease settings.
📝 Abstract
We investigate spatial confounding in the presence of multivariate disease dependence. In the"analysis model perspective"of spatial confounding, adding a spatially dependent random effect can lead to significant variance inflation of the posterior distribution of the fixed effects. The"data generation perspective"views covariates as stochastic and correlated with an unobserved spatial confounder, leading to inferior statistical inference over multiple realizations. While multiple methods have been proposed for adjusting statistical models to mitigate spatial confounding in estimating regression coefficients, 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 distinguish variance inflation due to spatial confounding from inflation based on multicollinearity between predictors and provide insights into the estimation efficiency of a spatial estimator under a spatially confounded data generation model. We demonstrate 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 several other authors in the defense of traditional hierarchical spatial models (Gilbert et al., 2025; Khan and Berrett, 2023; Zimmerman and Ver Hoef, 2022) and extend this defense to multivariate areal 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.