## 3 Results  
### Samples Without Any Treatment  
First, we analyzed the urine samples directly [25], without any alteration except for adding a small amount of sodium chloride to adjust the ionic strength of the urine and promote the formation of VOCs. The PLS-LDA analysis was used to assess VOC features capable of classifying the urine samples in the group of COVID-19 patients or the group of healthy controls. The signals obtained were not of high intensity, and the spectra had to be processed to eliminate the signals generated by the fiber itself, which absorbs the VOCs during the analysis. However, they enabled us to achieve a good separation between the two groups analyzed, COVID-19 patients and healthy individuals (Figure 1). As shown on the score plots (Figure 1A), there is a good separation of the two groups. The pseudospectral representation of the tpLoadings indicates signals of the GC-MS spectrum which are most important in the separation observed in the PLS-LDA model (Figure 1B). The peaks of the negative tpLoadings correspond to compounds present at higher concentrations in COVID-19 patients, while the positive tpLoadings correspond to compounds found at higher concentrations in healthy individuals. These volatile compounds may appear or disappear in urine as a result of the metabolic alterations caused by COVID-19 [5; 8]. GC-MS spectra allow for effective classification, but identifying which peaks correspond to the different VOCs was difficult. To improve identification, once the peaks were identified, we integrate the region where each peak is located. Before applying any mathematical classification model, we eliminate the integrals associated with peaks that appear due to the degradation of the fiber used to absorb volatile compounds in the GC-MS technique. The fiber is made of a silicon compound (polydimethylsiloxane), which is released during the analysis itself. To identify the VOC peaks that differ between the groups of COVID-19 patients and healthy controls, we used the SPA (Subwindow Permutation Analysis) algorithm [32]. This algorithm identifies and classifies the values of the peak integrals that are most important for distinguishing between the groups. SPA is based on the COSS (Conditional Synergistic  
Figure 1: (**A**) Score plots of the three components of the PLS-LDA model for GC-MS spectra of urine samples from COVID-19 patients (red diamonds) and healthy controls (blue circles); (**B**) tpLoadings pseudospectrum from PLS-LDA model for GC-MS spectra of urine samples from COVID-19 patients and healthy controls. The intensity of the peaks (positive or negative) in the pseudospectrum is determined by the most significant spectral shift regions in the PLS-LDA model. The model performances were the following: R2X = 0.35, R2Y = 0.86, and AUC = 1. (*) Selected peaks appearing in Table 2.  
Score) value for variable selection (Figure 2). COSS is defined as -log10(\(p\)-value); thus, a \(p\)-value of 0.05 corresponds to a COSS value of 1.3. Several variables have much higher COSS values, indicating \(p\)-values much lower than 0.05 (Figure 2). Figure 3 shows the peaks contributing the most to the group separation, and their boxplot peak area. Among the peaks selected as most important following SPA classification, more intense peaks were found in both patients with COVID-19 and healthy controls, which would indicate alterations in metabolism [5; 8]. Figure 2: COSS values of the variables selected by the SPA algorithm as most important for determining the separation between groups of untreated urine samples from COVID-19 patients and healthy controls. Table 2 presents the 15 signals with the highest COSS values (lowest \(p\)-value), the compounds identified according to the Wiley library [27], the confidence percentage of the identification, and whether the compound was found at higher concentrations in COVID-19 or healthy controls group. These compounds are often present in urine samples and are associated with secondary metabolism or environmental contaminants [34; 35; 36; 37; 38].