## 3 Results and Discussion
### Chemometric Analysis of Urine Samples  
MetaboAnalyst 5.0 [40] was used to perform the statistical analysis. The variables were initially normalised to obtain a homogeneous distribution and generate reliable and interpretable models. The normalised matrix was subjected to univariate analysis using a \(t\)-test (\(p<0.05\)), in which the \(p\) values obtained proved that 7 of the 147 VOMs identified presented statistically significant differences between the analysed groups, the healthy subjects (control group), and oncological patients (PCa group) (Table 3). Some of these metabolites have been previously related to oncological pathologies, according to the Human Metabolome Database [8]. TDN has been detected in urine samples of colorectal, leukaemia, and lymphoma cancers, where it was found increasingly expressed in the samples of oncological patients [8]. About 3,5-dimethylbenzaldehyde, very little information has been published in the literature, but similar molecules, such as the isomer 2,5-dimethylbenzaldehyde or benzaldehyde, have already been related to prostate [41] and lung [62] cancers. For many VOMs related to the control group, such as D-carvone, 6-methylphenanthhedrine, \(\alpha\)-methylcinnamaldehyde, and 2-bromophenyl, a significant decrease in concentration was observed in the PCa group. Although the origin of some of these metabolites is known, most of them still need more detailed evaluation to establish a relationship with PCa. PLS-DA multivariate pattern recognition procedures use the information contained in the VOMs fingerprint as several variables to visualize group trends and clustering patterns, respectively, according to the separations among sample sets. The resulting PLS-DA analysis showed two well-separated groups, the PCa and the control groups (Figure 4a). Besides the significant difference between PCa patients and healthy subjects (control group) in terms of smoking habits and age, these factors did not contribute to the differences noted between both groups. When carrying out the discriminant statistical analysis by age and by smoking habits, it was verified that no cluster was formed associated with any of the target groups. Hence, it can be deduced that neither age nor the difference in the number of smokers between both groups influenced the separation obtained among the PCa cluster and control group cluster. The VIP scores plot describes the relative contribution of the metabolites to the variance between the two groups, where TDN and D-carvone showed the most significant contributions to the PCa and control groups, respectively (Figure 4b). The robustness of the generated PLS-DA model was evaluated by 10-fold CV (Figure 4c), and to assess the significance of class discrimination, a permutation test was performed (Figure 4d). The resulting PLS-DA analysis showed two well-separated groups. The VIP scores plot describes the relative contribution of the metabolites to the variance between the two groups. TDN and D-carvone showed the most significant contributions to the PCa and control groups, respectively. Hierarchical clustering was performed, resulting in a dendrogram and heatmap (Figure 5). The heatmap created using Euclidean distance measure with the 15 statistically significant VOMs illustrated the correlations between these VOMs and the sample groups (Figure 5b). This hierarchical cluster analysis showed that each cluster of the studied groups was well-defined by a distinct panel of metabolites. For instance, D-carvone, \(p\)-cymenene, and 2-bromophenyl \(p\)-tert-butylphenol were the metabolites most associated with the control group, whereas 3,5-dimethylbenzaldehyde, MMT, TDN, and 2-ethyl-1-hexanol were highly correlated with the PCa group. To evaluate the performance of the potential biomarker models, the multivariate exploratory receiver operating characteristic (ROC) curves were generated by Monte Carlo cross-validation (MCCV), using 2/3 of the samples to evaluate feature importance, and the remaining 1/3 were used to validate the created models (Figure 6a,b).