A Marginalized Zero‐Inflated Negative Binomial Model for Spatial Data: Modeling COVID‐19 Deaths in Georgia

Abstract

ABSTRACTSpatial count data with an abundance of zeros arise commonly in disease mapping studies. Typically, these data are analyzed using zero‐inflated models, which comprise a mixture of a point mass at zero and an ordinary count distribution, such as the Poisson or negative binomial. However, due to their mixture representation, conventional zero‐inflated models are challenging to explain in practice because the parameter estimates have conditional latent‐class interpretations. As an alternative, several authors have proposed marginalized zero‐inflated models that simultaneously model the excess zeros and the marginal mean, leading to a parameterization that more closely aligns with ordinary count models. Motivated by a study examining predictors of COVID‐19 death rates, we develop a spatiotemporal marginalized zero‐inflated negative binomial model that directly models the marginal mean, thus extending marginalized zero‐inflated models to the spatial setting. To capture the spatiotemporal heterogeneity in the data, we introduce region‐level covariates, smooth temporal effects, and spatially correlated random effects to model both the excess zeros and the marginal mean. For estimation, we adopt a Bayesian approach that combines full‐conditional Gibbs sampling and Metropolis–Hastings steps. We investigate features of the model and use the model to identify key predictors of COVID‐19 deaths in the US state of Georgia during the 2021 calendar year.