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

Finally, the validity of the approach adopted in this study is corroborated by the research framework for linking environmental and weather factors to the incidence of COVID-19 pro- posed in a recent study published by Zaitchik et al. [74]. Statistical analysis The statistical dependency of confirmed COVID-19 cases from environmental and meteoro- logical regressors is first performed by calculating and comparing Spearman and Kendall rank-order correlation coefficients. These coefficients provide a nonparametric measure of the monotonicity (i.e. strength and direction) of the relation between the number of confirmed COVID-19 cases (the output/dependent variable) and the input environmental and meteoro- logical variables. Unlike the Pearson correlation, the Spearman and Kendall rank-order corre- lations do not carry any assumptions about the normal distribution of the data and the linearity between the variables. The statistical significance of the association between input and output variables is determined using the two-sided p-value in order to measure both decreasing and increasing departures from the null hypothesis. Spearman’s and Kendall’s cor- relation coefficient values (ρ and τ) can range from +1 to -1. The sign of the coefficient indi- cates the direction of the association of ranks (+ positive,—negative), while its absolute value expresses magnitude. The closer the coefficient is to zero, the weaker the association between the ranks: an absolute value between 0.5 and 1 is considered to provide a strong correlation,

0.3 to 0.5 a moderate correlation, 0.1 to 0.3 a weak correlation, and <0.1 no correlation. Machine learning modeling The aim of the machine learning analysis is to assess the relative feature impact of factors con- tributing to COVID-19. Feature impact is computed by applying the Tree SHAP algorithm to a Gradient Boosted Regression Tree (GBRT) model. GBRT is an additive stochastic model that combines multiple sequentially connected weak learners (regression trees) in a way that each new learner fits the residuals from the previous step to optimize the overall predictive perfor- mance [75]. The resulting model can describe multiple nonlinear interactions and partial dependency with sufficient flexibility, remarkably high predictive accuracy, and robustness to missing data and outliers. The study uses the open source xgboost Python library which offers a highly efficient, flexi- ble, and portable implementation of GBRT [76]. The xgboost algorithm provides several ways to control overfitting, i.e., when the model fits the training data so closely that it fails to provide useful predictions when applied to new data. The first is to constrain the maximum depth of individual trees used in the boosting process to modulate the degree of feature interactions that the model can fit. The second is to control the number of samples that each tree leaf can contain to avoid forming imbalanced leaves that have a single or too few data points. The third and most important way is to control the learning rate. Overfitting is also reduced through the

use of randomization into the tree building process by subsampling the training set before deriving each tree, and subsampling features before searching for the best node split. Finally, xgboost provides a parameter that enables model regularization using "across trees" information. As a first step, we optimized the model hyperparameters using a grid-search method com- bined with a cross-validation approach specifically designed for this study. We first selected only the data records of geographical locations that presented at least 90 data points (about 3 months’ worth of data) filtering out about 12,000 observations from a total of 77,300. This strategy is intended to select a time window size that presents sufficient seasonal variation for each location. We then randomly selected 24 locations to be designated as a test set to measure 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 7 / 27