Bayesian two-part spatial models for semicontinuous data with application to emergency department expenditures

In health services research, it is common to encounter semicontinuous data characterized by a point mass at zero and a continuous distribution of positive values. Examples include medical expenditures, in which the zeros represent patients who do not use health services, while the continuous distribution describes the level of expenditures among users. Semicontinuous data are customarily analyzed using two-part mixture models. In the spatial analysis of semicontinuous data, two-part models are especially appealing because they provide a joint picture of how health services utilization and associated expenditures vary across geographic regions. However, when applying these models, careful attention must be paid to distributional choices, as model misspecification can lead to biased and imprecise inferences. This paper introduces a broad class of Bayesian two-part models for the spatial analysis of semicontinuous data. Specific models considered include two-part lognormal, log skew-elliptical, and Bayesian non-parametric models. Multivariate conditionally autoregressive priors are used to link model components and provide spatial smoothing across neighboring regions, resulting in a joint spatial modeling framework for health utilization and expenditures. We develop a fully conjugate Gibbs sampling scheme, leading to efficient posterior computation. We illustrate the approach using data from a recent study of emergency department expenditures.