  This paper develops a large-scale Bayesian spatio-temporal binomial
regression model for the purpose of investigating regional trends in antibody
prevalence to Borrelia burgdorferi, the causative agent of Lyme disease. The
proposed model uses Gaussian predictive processes to estimate the spatially
varying trends and a conditional autoregressive model to account for
spatio-temporal dependence. Careful consideration is made to develop a novel
framework that is scalable to large spatio-temporal data. The proposed model is
used to analyze approximately 16 million Borrelia burgdorferi test results
collected on dogs located throughout the conterminous United States over a
sixty month period. This analysis identifies several regions of increasing
canine risk. Specifically, this analysis reveals evidence that Lyme disease is
getting worse in some endemic regions and that it could potentially be
spreading to other non-endemic areas. Further, given the zoonotic nature of
this vector-borne disease, this analysis could potentially reveal areas of
increasing human risk.
