Assessing Spatial Disparities: A Bayesian Linear Regression Approach

Epidemiological investigations of regionally aggregated spatial data often involve detecting spatial health disparities between neighboring regions on a map of disease mortality or incidence rates. Analyzing such data introduces spatial dependence among the health outcomes and seeks to report statistically significant spatial disparities by delineating boundaries that separate neighboring regions with widely disparate health outcomes. However, current statistical methods are often inadequate for appropriately defining what constitutes a spatial disparity and for constructing rankings of posterior probabilities that are robust under changes to such a definition. More specifically, non-parametric Bayesian approaches endow spatial effects with discrete probability distributions using Dirichlet processes, or generalizations thereof, and rely upon computationally intensive methods for inferring on weakly identified parameters. In this manuscript, we introduce a Bayesian linear regression framework to detect spatial health disparities. This enables us to exploit Bayesian conjugate posterior distributions in a more accessible manner and accelerate computation significantly over existing Bayesian non-parametric approaches. Simulation experiments conducted over a county map of the entire United States demonstrate the effectiveness of our method and we apply our method to a data set from the Institute of Health Metrics and Evaluation (IHME) on age-standardized US county-level estimates of mortality rates across tracheal, bronchus, and lung cancer.