## 2 Results  
### Differences in Urinary Volatile Profile of BC Patients vs. Controls  
In this study, the performance of the urinary volatile profile for discrimination of BC (urothelial carcinoma) patients (\(n=53\)) from cancer-free controls (\(n=56\)) was evaluated. Most of the BC patients were diagnosed with NMIBC (Table 1), comprising stage Ta/Tis (\(n=26\)) and T1 (\(n=17\)), and the remainder 19% were diagnosed with MIBC, including stages T2 (\(n=4\)), T3 (\(n=4\)) and T4 (\(n=2\)). The combination of two different sample preparation and extraction protocols for volatile profiling of urine enabled the detection of a total of 220 chromatographic peaks [120 in volatile organic compounds (VOCs) protocol and 100 in volatile carbonyl compounds (VCCs) protocol]. The analytical precision was first checked through the projection of the quality control (QC) samples (\(n=24\)), acquired intermittently throughout the analytical experiment, and of all urine samples under study in a principal component analysis (PCA) model (Figure S1). The tighter clustering of the QC samples revealed that the data was not affected by technical variation and presented good quality for multivariate analysis. The partial least squares-discriminant analysis (PLS-DA) model obtained for the urinary volatile profile of BC patients and controls after variable selection (109 observations \(\times\) 4184 variables) is shown in Figure 1a. The scores scatter plot depicted a satisfactory separation between groups with a moderate predictive ability (\(Q^{2}=0.350\), Figure S2), high AUC (0.902) and 72% sensitivity, 91% specificity and 82% accuracy (Figure 1b). The volatile metabolites unveiling variable importance to the projection (VIP)\(>1\) and statistically different levels between BC and controls are shown in the volcano plot (Figure 1c). Eleven metabolites were found down-regulated in BC, including aldehydes (2-furaldehyde, 2-methylbutanal, formaldehyde and hexanal), ketones (2-butanone and 4-heptanone), terpenoids (carvone and piperitone), one heterocyclic compound ((1S,5R)-1,5-dimethyl-6,8-dioxabicyclo [3.2.1]octane) and two unknowns, whereas twelve were upregulated, including alkanes (2-methylnonane, 2,4-dimethylheptane, 2,6-dimethylnonane), aromatic compounds (1-methylnaphthalene, 2-methylnaphthalene, 1,2,4-trimethylbenzene and \(p\)-cesol) and four unknowns (Table 2, Table S1). From these, 2-furaldehyde and 4-methyloctane disclosed the highest AUC (0.800 and 0.787, respectively) and statistical significance (\(p\)-value \(<0.0001\) after FDR correction). \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Group**} & **Number of Samples** & \multirow{2}{*}{**Age Range (years)**} & **Mean Age \(\pm\) SD** \\  & **(F/M)** & & **(years)** \\ \hline Cancer-Free Controls & 56 (16/40) & 45–66 & 51.9 \(\pm\) 5.2 \\ BC Patients & 53 (14/39) & 43–87 & 68.9 \(\pm\) 10.6 \\ Ta/Tis & 26 (6/20) & 43–87 & 68.6 \(\pm\) 10.8 \\ T1 & 17 (6/11) & 53–83 & 72.0 \(\pm\) 8.9 \\ T2 & 4 (1/3) & 51–69 & 62.0 \(\pm\) 7.5 \\ T3 & 4 (1/3) & 43–80 & 65.3 \(\pm\) 15.0 \\ T4 & 2 (0/2) & 65–70 & 67.5 \(\pm\) 2.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Demographic and clinical data of cancer-free individuals and BC patients. Considering the set of seventeen discriminant compounds formally or putatively identified, i.e., volatiles denoted as L1 and L2 in Table 2 and excluding the six unknowns, the classification performance of BC vs. controls (Figure 1d) was similar to that of the matrix used to construct the PLS-DA model, with 70% sensitivity, 89% specificity and 80% accuracy, notwithstanding the lower AUC (0.851). Regarding the performance of this set to detect each tumor stage (Table 3), very high sensitivity (94%) and AUC (0.910) were found for stage T1, whereas low sensitivity was found for stage Ta/Tis (65%) and \(\geq\)T2 (60%), despite high specificity (84% for stage Ta/Tis and 91% for \(\geq\)T2).