Does climate help modeling COVID-19 risk and to what extent?

practices worldwide. Data quality, extensiveness, and uniformity are therefore subject to a cer- tain degree of uncertainty. Moreover, reports of confirmed COVID-19 cases tend to underesti- mate the actual number of infections because of asymptomatic patients and undetected COVID-19 deaths. For ease of purpose, we will assume that the number of confirmed COVID-19 cases is monotonically related to the true number of infections, recognizing that this is a simplification that may limit the significance of this study’s results. An additional but less impactful limitation emerges from the normalization of meteorologi- cal variables across different points within each area of interest where exposure to the virus has occurred. As previously described, weather conditions have been averaged across the ten most populous cities for each country-level location and the five most populated cities for the admin-level locations. This approach should provide a good approximation of the overall weather conditions under which the viral spread has occurred. We reason that population den- sity may have played a significant role in the spread of COVID-19. Furthermore, it is also likely that the majority of testing was carried out in major urban areas. Finally, selecting up to ten country-level and five admin-level cities can be expected to evenly spread the sampling across the most populated areas, as such an approach provides an average coverage of 75% or more of the entire population for most of the locations considered (S1 Fig). Methodology

The method used in this study combines three approaches to capture dependencies between confirmed COVID-19 cases and climate factors (see S2 Fig for a visual diagram summarizing the approach): • A statistical analysis based on Spearman’s and Kendall’s correlation coefficients • A machine learning model based on the Gradient Boosted Regression Tree algorithm paired with the Tree SHAP algorithm to perform feature importance analysis • An econometric model based on fixed effect panel regression analysis. The use of three distinct approaches is intended to provide independent analytic evidence. Of particular interest is the complementarity between machine learning and econometric approaches, where the first is intent on prediction while the latter focuses on explanation. As discussed in the literature, the use of a hybrid approach where machine learning modeling is paired with econometric analysis can help address relative weaknesses in the two methods by leveraging relative strengths [69–73]. For example, machine learning is better equipped to take advantage of structural heterogeneity in training data to make short-term predictions, whereas econometric methods are better at capturing long-term trends [73]. We can therefore expect that the results of machine learning and econometric analysis are not always going to coincide [73]. This lack of overlap points to the areas of relative improvement that can be obtained through a functional integration of the two methods. While appealing, such integration is chal-

lenging and largely remains a goal to be achieved, for which a better understanding of the dif- ferences and relative strengths/weaknesses is required [71]. In this regard, the present study contributes to advancing our understanding of the specific complementarities between machine learning and econometrics in a new domain of inquiry. The statistical analysis in turn provides the baseline due to its more basic analytic capacity in dealing with non-station- ary processes compared to machine learning and accounting for long terms trends compared to econometric analysis. PLOS ONE Does climate help modeling COVID-19 risk and to what extent? PLOS ONE | https://doi.org/10.1371/journal.pone.0273078 September 7, 2022 6 / 27