Association between air pollution and COVID‐19 disease severity via Bayesian multinomial logistic regression with partially missing outcomes

Recent ecological analyses suggest air pollution exposure may increase susceptibility to and severity of coronavirus disease 2019 (COVID‐19). Individual‐level studies are needed to clarify the relationship between air pollution exposure and COVID‐19 outcomes. We conduct an individual‐level analysis of long‐term exposure to air pollution and weather on peak COVID‐19 severity. We develop a Bayesian multinomial logistic regression model with a multiple imputation approach to impute partially missing health outcomes. Our approach is based on the stick‐breaking representation of the multinomial distribution, which offers computational advantages, but presents challenges in interpreting regression coefficients. We propose a novel inferential approach to address these challenges. In a simulation study, we demonstrate our method's ability to impute missing outcome data and improve estimation of regression coefficients compared to a complete case analysis. In our analysis of 55,273 COVID‐19 cases in Denver, Colorado, increased annual exposure to fine particulate matter in the year prior to the pandemic was associated with increased risk of severe COVID‐19 outcomes. We also found COVID‐19 disease severity to be associated with interactions between exposures. Our individual‐level analysis fills a gap in the literature and helps to elucidate the association between long‐term exposure to air pollution and COVID‐19 outcomes.