Bayesian hierarchical time-varying distributed lag nonlinear model: applications in the short-term association between ambient temperature and daily confirmed cases of COVID-19

Environmental epidemiological studies are often interested in the short-term association between environmental exposure and health responses through daily time-series data analysis across multiple locations. The distributed lag nonlinear model is one of the most frequently adopted approaches to estimate the association through the exposure-response function. Our study proposes a novel Bayesian methodology for estimating the exposure-response functions for multiple subjects through a hierarchical approach while incorporating decaying lag effects and considering intertwined nonadditive interactions in the exposure, lag, and time dimensions through a negative binomial distribution. We develop Markov Chain Monte Carlo and variational Bayes algorithms for estimation. To validate the methodology, we provide some empirical results using simulated datasets and a real dataset to investigate the short-term relationship between ambient temperature and COVID-19 incidence in the United States.