## Materials and Methods
### Temporal Modeling Strategy  
In total there are 4017 original entries of data for each air pollutant and emergency hospital admissions defined. However, considering how air pollution and admissions do not correspond exactly in the time frames, as the repercussions of the first may not be noted in that exact moment, in hospital admissions four types of models were considered: D, W, WD, and WW (as shown in Figure 1). So, the temporal modeling strategy is summarized in Figure 1 and encompasses four models:  
* D: the used values were the daily ones, both for air pollution and hospital emergency admissions.
* W: consists of an average value for each week, with every week counted as one temporal occurrence in air pollution and in hospital emergency admissions.
* WD: this model comprises moving averages in the air pollution part, being the seven days before the hospital admissions (beginning on this day), and the day in which admissions are registered.
* WW: finally, this model consists of two moving averages, in the air pollutants and in hospital emergency admissions, pollution is averaged for the seven days before and admissions are averaged for the seven days after. It is based on a week before (pollution)/week after (admissions) approach to hospital visits.  
In terms of hospital emergency admissions, models D and WD are made with raw data, and models W and WW comprise a weekly average of admissions. As for air pollutants, only model D does not consist of an average value. This way, each model counts with 4017 (D), 573 (W), 4010 (WD), and 4003 (WW) observations, 4017 being the total number of days in the studied period. The models attempt to address the many possible temporal associations between air pollution and emergency hospital admissions; nevertheless, two of these models have the weekend problem--D and WD, as on these days admissions tend to be lower than in workdays, thus having unintended fluctuations. This was solved with the introduction of a dummy variable, which was marked as 1 for the workdays and 0 for the weekends; no dummy variable was needed in the remaining models as the moving average of seven days had already solved the aforementioned problem. As is universal knowledge, seasonality is also an issue in air pollution and emergency hospital admissions studies, hence dummy variables were inducted to control for seasonal confounding in all four models. These variables assumed the mean of daily observations for the month which they represent and 0 for the others. No control was done for national or municipal holidays.  
The association between levels of air pollution and emergency hospital admissions were analyzed through ordinary least squares (OLS) linear regression using the R (4.0.1) Statistical Computing Environment, following similar studies in LMA [41, 79, 106]. In OLS, the dependent variables were the emergency hospital admissions, and the independent variables were the air pollutants. Multicollinearity of air pollution was always tested by assessing the variance inflation factor (VIF), enabling a better selection of independent variables; also, the zero-waste covariance was observed through the Durbin-Watson test. This analysis produced 252 regression models (4 data models; 21 disease typologies; 3 municipalities), while the number of total possible associations ascends to 1260. The models were then selected by their statistical significance when the air pollution slope was inferior to 5% (\(p<0.05\)). After that, the semi-elasticity was calculated for the previously selected models. The semi-elasticity makes the comparison between the OLS regression models, the time-series studies with the Poisson regression, and the possible log-linear models (Risk Ratio effect measure).