Bayesian spatio-temporal modeling of count data with application to drug overdose

Count data are quite common in modeling dependent datasets, e.g. longitudinal data, spatial data, etc. In disease mapping, we often come across count data collected from different geographical regions over time. Statistical models have been developed for analyzing such datasets, but computational complexities have always remained an issue. In this paper, we adapt a Bayesian latent Gaussian model for analyzing spatial count data with some temporal components as well. In particular, we use two specific models, i.e. CAR and SAR models, for handling the spatial dependence, and consider an autoregressive structure for the temporal part. The spatio-temporal dependence is modeled by several specifications of the interaction component with some linear constraints that make the model identifiable. We analyze yearly data on the number of emergency room/inpatient visits for any drug overdose from 159 counties of Georgia, USA. We use Integrated Nested Laplace Approximation (INLA) in R for our computation instead of Markov chain Monte Carlo (McMC) since INLA can fit complex space-time models more quickly. Our analysis reflects some interesting space-time interactions for some counties, and provides posterior temporal trends for certain surrounding counties as well.