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A Spatiotemporal Quantile Regression Model for Emergency Department Expenditures

Brian Neelon, Medical University of South Carolina 
*Fan Li, Duke University 
Lane Burgette, RAND Corporation 
Sara Neelon, Duke University 

Keywords: asymmetric Laplace distribution, Bayesian inference, conditionally autoregressive prior, medical expenditures, quantile regression, spatiotemporal model

Motivated by a recent study of geographic and temporal trends in emergency department care, we developed a spatiotemporal quantile regression model for the analysis of emergency department-related medical expenditures. The model yields distinct spatial patterns across time for each quantile of the response distribution, which is important in the spatial analysis of expenditures, as there is often little spatiotemporal variation in mean expenditures, but more pronounced variation in the extremes. The model has a hierarchical structure incorporating patient-level and region-level predictors as well as spatiotemporal random effects. We model the random effects via intrinsic conditionally autoregressive priors, improving small-area estimation through maximum spatiotemporal smoothing. We adopt a Bayesian modeling approach based on an asymmetric Laplace distribution and develop an efficient posterior sampling scheme that relies solely on conjugate full conditionals. We apply our model to data from the Duke support repository, a large georeferenced database containing health and financial data for Duke Health System patients residing in Durham County, North Carolina.