## 3 Results
### Multivariate Statistical Analysis of NMR Data  
PCA was initially applied to the complete data set to highlight possible metabolic differences among the urine samples of control and CRC subjects and to identify potential outliers (Figure S1 in Supporting Information). Based on [PERSON]'s T2 and DModX tests, two samples were considered outliers and were removed from the analysis (Figure S2 in Supporting Information). To optimize the separation between the CRC and C urine samples, the supervised OPLS-DA model was applied. As displayed in Figure 2, the OPLS-DA scores plot showed clear separation between the two groups of samples. To test the validity of the model, a permutation test on the PLS-DA model was performed. Results showed that the model was statistically valid, with a Q2 intercept value of \(-0.192\). To identify the metabolites that mainly contributed to group separation, an S-plot was constructed (Figure 3). As shown in Figure 3, the variables selected in the S-plot are indicated with a dotted rectangle and represent the metabolites responsible for differentiation in the OPLS-DA scores plot. Cutoff values for the covariance of \(|p|\geq 0.1\) and the correlation \(|p(\text{corr})|\geq 0.2\) were used. In the S-plot, the control samples were characterized, based on the discriminant regions, by high creatine, sn-glycero-3-phosphocholine, phenylacetylglycine, and proline (Figure 3 square A), whereas an increase in citrate, creatinine, acetoacetate, 3-hydroxybutyrate, 3-aminoisobutyrate, tyrosine, tryptophan, histamine, methylhistidine, and fucose characterized the CRC samples (Figure 3, square B). The relative concentrations of metabolites highlighted in the S-plot were verified with Chenomx NMR Suite 7.1 and were subjected to the Welch \(t\)-test to identify significant variations in concentration in the two groups. Significantly discriminant metabolites were characterized by VIP \(>1\) and \(p\leq 0.05\). After this analysis, 14 metabolites exhibited VIP \(>1\), but only acetoacetate, creatine, creatinine, histamine, phenylacetylglycine, and tryptophan showed significant variation (with \(p\leq 0.05\)) (Table 2). The relative concentrations, calculated by normalization of the molar concentration of each metabolite to the total molar concentration of all 14 metabolites for each sample in the two groups, were compared using box-and-whisker plots. As shown in Figure 4, the data obtained demonstrated that the CRC group showed increased relative levels of acetoacetate, creatinine, and histamine, whereas creatine, phenylacetylglycine, and tryptophan levels were lower compared to the C group. A ROC curve was constructed using only the metabolites with a significant statistical variation, and the area under the curve of the ROC analysis was found to be 0.879 (95% CI: 0.667-1), indicating high predictive accuracy of the model (Figure 5). Significantly, only 5/12 CRC patients had increased CEA levels (CEA \(>\) 2.5 ng/mL), showing 42% sensitivity. Figure 2: OPLS-DA scores plot of \({}^{1}\)H-NMR spectra of urine samples: C (full circle) and CRC (open circle) subjects. The OPLS-DA model was performed using one predictive and one orthogonal component and is described by R2X, R2Y, and Q2 values of 0.328, 0.957, and 0.539, respectively. Figure 4: Box-and-whisker plots showing an altered expression of metabolites including acetoacetate, creatine, creatinine, histamine, phenylacetylglycemic, and tryptophan between C and CRC patients. Median values are highlighted by solid lines. Statistical significance of the metabolites (\(p\leq 0.05\)) is presented in Table 2.  
Figure 3: S-Plot corresponding to the OPLS-DA model used to characterize the most significant variables associated with group C (dotted rectangle A) and CRC (dotted rectangle B) subjects. Cutoff values for the covariance of \(|p|\geq 0.1\) and for the correlation \(|p\) (corr)\(|\geq 0.2\) were used. Values of discriminant ppm regions are shown.