A new time-varying coefficient regression approach for analyzing infectious disease data

Since the beginning of the global pandemic of Coronavirus (SARS-COV-2), there has been many studies devoted to predicting the COVID-19 related deaths/hospitalizations. The aim of our work is to (1) explore the lagged dependence between the time series of case counts and the time series of death counts; and (2) utilize such a relationship for prediction. The proposed approach can also be applied to other infectious diseases or wherever dynamics in lagged dependence are of primary interest. Different from the previous studies, we focus on time-varying coefficient models to account for the evolution of the coronavirus. Using two different types of time-varying coefficient models, local polynomial regression models and piecewise linear regression models, we analyze the province-level data in Canada as well as country-level data using cumulative counts. We use out-of-sample prediction to evaluate the model performance. Based on our data analyses, both time-varying coefficient modeling strategies work well. Local polynomial regression models generally work better than piecewise linear regression models, especially when the pattern of the relationship between the two time series of counts gets more complicated (e.g., more segments are needed to portray the pattern). Our proposed methods can be easily and quickly implemented via existing R packages.