BSTZINB: A Bayesian Framework for Negative-Binomial Modeling of Spatio-Temporal Zero-Inflated Count Data in Epidemiology

Modern Bayesian hierarchical methodologies allow us to leverage spatio-temporal dependencies between observations, enhancing both health effect estimation and map visualization in efficient and flexible ways. However, the necessary levels of statistical software are often unavailable or difficult to access. We have recently examined Bayesian spatio-temporal models to estimate the association between COVID-19 death counts and various social and environmental risk factors, including ambient air pollution exposure. Typically, it is very common that in an infection disease mapping problem with count data, we have excessive zeros, and it is usually for over-dispersed count outcome variables. Furthermore, the theory suggests that the excess zeros are generated by a separate process from the count values and that the excess zeros need to be modeled independently. Our proposed models are specially designed to handle the zero-inflation and over-dispersion in count data through Zero-Inflated Negative Binomial regression with random effects that vary across time and space within a Markov Chain Monte Carlo framework. Drawing on our knowledge and experience, we aim to provide a simple, unified, and publicly available software that can be applied in various disease mapping studies under the contemporary Bayesian framework.