## 2 Results
### Differences in Urinary Volatile Profile of BC Patients vs. Controls
Finally, the potential influence of age on the levels of the twenty-three statistically different metabolites was investigated through correlation (Table S2). As very low correlation coefficients (\(\left.\left|\,r\,\right|\leq 0.3\right)\) were found for all metabolites, it may be concluded that age differences did not significantly contribute for the metabolic alterations detected between BC and controls. Figure 1: **(a)** PLS-DA scores scatter plot and **(b)** receiver operating characteristic (ROC) curve obtained for urinary volatile profile (VOCs and VCCs concatenated matrix), after variable selection (109 observations \(\times\) 4184 variables), of BC patients (green squares, \(n=53\)) and cancer-free controls (black circles, \(n=56\)). **(c)** Volcano plot representing the set of twenty-three urinary volatile metabolites changing between BC patients and cancer-free controls. **(d)** ROC curve obtained for the set of seventeen discriminant volatiles (109 observations \(\times\) 17 metabolites) that were formally (L1) and putatively (L2) identified. Metabolite abbreviations: 1-MNaph, 1-methylnaphthalene; (1S)-DDO, (1S)-1,5-dimethyl-6,8-dioxabicyclo[3.2.1] octane; 1,2,4-TB, 1,2,4-trimethylbenzene; 2-But, 2-butanone; 2-Fur, 2-furaldehyde; 2-MB, 2-methylbutanal; 2-MN, 2-methylnonane; 2-MNaph, 2-methylnaphthalene; 2,4-DH, 2,4-dimethylheptane; 2,6-DN, 2,6-dimethylnonane; 4-Hept, 4-heptanone; 4-MO, 4-methyloctane; Carv, carvone; Form, formaldehyde; Hex, hexanal; Pip, piperitone; \(p\)-Cre, \(p\)-cresol (4-methylphenol); U1-6, unknown 1-6. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Metabolite \({}^{\bullet}\)** & **Effect Size \(\pm\)** & **Variation \(\pm\)** & **\(p\)-Value** & **Original** & **\(p\)-Value FDR \({}^{\circ}\)** & **AUC** & **Down- or** & **HMDB ID** & **Potential** \\  & **ES\({}_{\bf{Set}}\)\({}^{\bullet}\)** & **Uncertainty (\%)** & **Original** & **\(p\)-Value FDR \({}^{\circ}\)** & **AUC** & **Up-Regulated** & **HMDB ID** & **Biochemical Pathway** \\ \hline _Alkames_ & \(2\)-Methylwhonance \({}^{\ell,12}\) & \(0.56\pm 0.38\) & \(58.6\pm 15.4\) & \(0.0390\) & \(0.0477\) & \(0.615\) & \(\uparrow\) & – & – \\
2-4-Dimethylphone \({}^{\ell,12}\) & \(0.81\pm 0.39\) & \(183.2\pm 23.6\) &  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Metabolite \({}^{a}\)** & \begin{tabular}{c} **Effect Size \(\pm\)** \\ **ESg \({}^{b}\)** \\ \end{tabular}  & \begin{tabular}{c} **Variation \(\pm\)** \\ **Uncertainty (\%)** \\ \end{tabular}  & \begin{tabular}{c} _p-Value_ \\ **Original** \\ \end{tabular}  & \begin{tabular}{c} _p-Value_ \\ **Original** \\ \end{tabular}  & \begin{tabular}{c} _p-Value_ \\ **Update FDR \({}^{c}\)** \\ \end{tabular}  & \begin{tabular}{c} **AUC** \\ **Up-Regulated** \\ \end{tabular}  & \ \begin{tabular}{c} **Down- or** \\ **Holb ID** \\ \end{tabular}  & \begin{tabular}{c} **Potential** \\ **Biochemical Pathway** \\ \end{tabular}  \\ \hline \hline \multicolumn{7}{c}{_Actunes_} \\
2-Butanone (butanol-2-one) \({}^{c,LI}\) & \(-0.54\pm 0.38\) & \(-23.8\pm 9.5\) & 0.0004 & 0.0012 & 0.697 & \(\downarrow\) & HMDB0000474 & Fatty acid metabolism (\(\beta\)-oxidation) [12] \\
4-Hepanone (heptan-4-one) & \(-0.33\pm 0.38\) & \(-38.6\pm 27.7\) & 0.0003 & 0.0010 & 0.703 & \(\downarrow\) & HMDB0004814 & Fatty acid metabolism (\(\beta\)-oxidation) [12] \\ \hline \multicolumn{7}{c}{_Torequids_} \\ Carvone (2-methyl-5-(propyl-1-2-en-2-yl)) & \(-0.66\pm 0.39\) & \(-62.3\pm 25.5\) & 0.0001 & 0.0004 & 0.715 & \(\downarrow\) & HMDB00035824 & carbohydrate (metabolissons) [16] \\ \multicolumn{7}{c}{_G.L.1_} \\ \multicolumn{7}{c}{_Piperitone_} \\ (3-methyl-9-propan-2-2-1-1-0) & \(-0.44\pm 0.38\) & \(-57.5\pm 34.1\) & 0.0019 & 0.0037 & 0.673 & \(\downarrow\) & HMDB0034975 & Lipid metabolism [17] \\ \multicolumn{7}{c}{_Malicious_} \\ Unknown 1 \({}^{c,LI}\) & \(0.45\pm 0.38\) & \(75.0\pm 23.5\) & 0.0157 & 0.0225 & 0.634 & \(\uparrow\) & \(-\) & \(-\) \\ Unknown 2 \({}^{c,LI}\) & \(0.72\pm 0.39\) & \(153.2\pm 24.0\) & -0.0001 & 0.0003