Evaluation of Bayesian spatiotemporal infectious disease models for prospective surveillance analysis

Background COVID-19 brought enormous challenges to public health surveillance and underscored the importance of developing and maintaining robust systems for accurate surveillance. As public health data collection efforts expand, there is a critical need for infectious disease modeling researchers to continue to develop prospective surveillance metrics and statistical models to accommodate the modeling of large disease counts and variability. This paper evaluated different likelihoods for the disease count model and various spatiotemporal mean models for prospective surveillance. Methods We evaluated Bayesian spatiotemporal models, which are the foundation for model-based infectious disease surveillance metrics. Bayesian spatiotemporal mean models based on the Poisson and the negative binomial likelihoods were evaluated with the different lengths of past data usage. We compared their goodness of fit and short-term prediction performance with both simulated epidemic data and real data from the COVID-19 pandemic. Results The simulation results show that the negative binomial likelihood-based models show better goodness of fit results than Poisson likelihood-based models as deemed by smaller deviance information criteria (DIC) values. However, Poisson models yield smaller mean square error (MSE) and mean absolute one-step prediction error (MAOSPE) results when we use a shorter length of the past data such as 7 and 3 time periods. Real COVID-19 data analysis of New Jersey and South Carolina shows similar results for the goodness of fit and short-term prediction results. Negative binomial-based mean models showed better performance when we used the past data of 52 time periods. Poisson-based mean models showed comparable goodness of fit performance and smaller MSE and MAOSPE results when we used the past data of 7 and 3 time periods. Conclusion We evaluate these models and provide future infectious disease outbreak modeling guidelines for Bayesian spatiotemporal analysis. Our choice of the likelihood and spatiotemporal mean models was influenced by both historical data length and variability. With a longer length of past data usage and more over-dispersed data, the negative binomial likelihood shows a better model fit than the Poisson likelihood. However, as we use a shorter length of the past data for our surveillance analysis, the difference between the Poisson and the negative binomial models becomes smaller. In this case, the Poisson likelihood shows robust posterior mean estimate and short-term prediction results.