Title: Bayesian Segmentation Modeling for Longitudinal Epidemiological Studies

Abstract:

Coronavirus disease 19 (COVID-19) is an ongoing global pandemic. As a data science approach to conquer this novel infectious disease, an unprecedented amount of longitudinal data is being generated every day. Characterizing the temporal change of those publicly available COVID-19 data enables to evaluate the effectiveness of mitigation interventions such as school closures, stay-at-home orders, and business reopening in different regions. It will also help us identify latent events such as virus mutations. In this paper, by combining an established stochastic SIR model with Bayesian inference, we propose a Bayesian hierarchical model to detect multiple change points based on the daily active infectious cases while estimating the reproductive numbers between all pairs of adjacent change points. Our change-point detection model is built upon a Bayesian Poisson piecewise regression with conjugate priors. This novel model can 1) mimic the epidemiological dynamics with certain conditions; 2) provide uncertainty estimates both in the number and time of change points; 3) adjust any explanatory time-varying covariates that may affect the case numbers. We employed Markov chain Monte Carlo algorithms to sample from the posterior distribution and achieved high efficiency via novel techniques. On simulated data, we demonstrated that our approach can improve the accuracy of the change point detection for a common multiple change-point search method. Applying the proposed methods into U.S. states, we found that the detected change points correlated well with the times of publicly announced interventions. We also demonstrated that the SIR model integrated with change point information provided a better short-term forecast. In all, our novel model facilitates the evaluation of public health interventions, identifies latent events that influence the spreading rates, and yields a better short-term forecast of active infectious cases.