Incidence of COVID-19 and Connections with Air Pollution Exposure variable and finds that it is highly significant. The overall model fit improves as indicated by the AICc and R2. The estimate for PM2 _._ 5 remains relatively unchanged and significant. While one would expect that case severity contributes to higher cases, as increased symptom severity may lead to higher case detection, the result suggests otherwise. One explanation is that high hospital admission occurred in areas with a weak case detection policy. In particular, if the disease goes unnoticed for long, the number of terminally ill patients can grow because they do not receive appropriate treatment in time. In this case, low case numbers can coincide with high hospital admission numbers. To investigate further whether the proxy captures a valuable signal related to symptom severity, appendix section 6.2.5 provides additional results that try to explain the case severity proxy using the other available predictors. These additional results find that age, male gender, and the share of population with overweight are positively associated with increased case hospitalization rates. This is in line with earlier identified risk groups (Ruan, 2020), suggesting that the proxy does capture a relevant case severity signal.

Taken together, the evidence suggests a significant positive relationship between case density and PM2 _._ 5 concentrations. However, there are still some limitations to the basic regression results presented here. The standard linear regression model may not be perfectly suitable for modeling the number of cases per 100,000 inhabitants due to the non-negative nature of the data and a right skew in the case density distribution. Strong violations of the correct-specification assumption can result in biased estimates, for instance because the models assess linearity on an additive scale while the phenomenon is multiplicative. Instead of assessing the data on the original scale as a multiplicative error model with a changing variance function, this issue is often addressed by rewriting the model as an additive error model on the log-scale with constant variance. This is appropriate as long as the log transformation is appropriate to normalize the data. To assess whether the simple estimations presented here are prone to a strong bias, section 6.2.2 investigates the residual distribution and re-analyzes the data using a log-type power transformation from a family of functions that allows for zeros. The results highlight that when the data is appropriately scaled and multiple diagnostics confirm that the Normality assumption is in fact valid, PM2 _._ 5 is still a highly significant positive predictor of case densities. Earlier studies on the role of ambient fine particles in the transmission risk of airborne disease have instead relied on Poisson-type regressions using count data. While these regressions are not entirely appropriate as they do not account for the highly significant geographical relationships in the data, section 6.2.1 presents Poisson-type results that allow for over-dispersion to show that the main conclusions are also robust to this specification choice.

# **4.2 Nonlinear analysis of March 22 cases per 100,000 inhabitants**

Instead of working on a transformed scale to address some of the highlighted issues, it is also possible to tackle the problem nonlinearly on the original scale. This might also lead to interesting results on important thresholds in the data. In particular, one might expect particulate matter to only contribute to COVID-19 incidence after concentrations surpass a certain critical threshold, or expect pollution dependencies to vary with unobserved weather variables including humidity and temperature (Chen et al., 2017b,a; Peng et al., 2020). In a recent study, Sajadi et al. (2020) have already shown that there could be a relationship 9