## 3 Discussion  
The volcano plot (Figure 1) shows that many more VOCs are differentially expressed in the presence of pitavastatin treatment at high concentration relative to pitavastatin administered at low concentration when both sets are compared to cancer without treatment. This aligns well with previously reported X-ray and micro-CT results, which showed that pitavastatin at high concentrations was an effective treatment, whereas when administered at low concentrations, no antitumor effect was observed [29]. Furthermore, the hierarchical heatmap (based on approach 1, Figure 2) shows similar results, where VOCs are mostly downregulated in the cancer class and in the pita low class relative to control and pita  
Figure 6: One-dimensional LDA plot where the model was trained to classify control from cancer week 3 and tested on cancer weeks 1-2, pita high and pita low samples (PH = pitavastatin high, PL = pitavastatin low, C = cancer). * \(p\)-value \(<\) 0.05, *** \(p\)-value \(<\) 0.001.  
high samples. VOCs in the pita high class are expressed similarly to the healthy controls, whereas the VOCs in the pita low samples are more similar to cancer week 1-3 samples. In a previous paper, we identified VOCs of breast cancer, some of which did change over time (modeling cancer progression) and some of which did not [23]. In this case, statistical methods were not trained to identify differences due to tumor progression, and therefore, were more in favor of those VOCs remaining consistently dysregulated. Employing PCA in approach 1 enabled the separation of sample classes of interest (Figure 3). Four VOCs (DCHM, 5M2H, DTB, and 2-HEX) were identified using LDA in approach 1 (Figure 4). Pita high samples showed significant differences relative to cancer in the direction of control samples, and pita low samples showed significant differences relative to control in the direction of cancer samples. There were also differences between pita high and pita low samples, and pita low demonstrated significant differences over time. Approach 2 was used to probe differences between each week of pita high and cancer week 3 (the endpoint). PCA was implemented on this set of VOCs, and no significant differences were observed between the samples of interest (Figure 5). LDA results using five VOCs (2-HEP, PDIB, TCB, DCHM, and 2-NON) identified through approach 2 (Figure 6) showed that pita high samples had significant differences in the direction of healthy samples (opposite direction of pita low and cancer samples). These results show that VOCs can predict the efficacy of pitavastatin treatments and mirror traditional analyses as early as the first week after tumor injection and treatment. The previous investigation on the efficacy of pitavastatin was conducted by micro-CT, X-ray analysis, mechanical testing, and histological imaging, which showed the same results as those obtained from VOCs in mouse urine, namely that pita high slows tumor progression and inhibits tumor-induced osteolytic lesions, whereas pita low does not alleviate osteolysis [29]. For an example, X-ray analysis and histological imaging showed decreased osteolytic lesions within pita high samples, whereas micro-CT images showed proximal tibia destruction due to tumors, which was alleviated upon administration of pita at high doses. Furthermore, pita high significantly increased the mechanical strength of the tibia, whereas pita low did not [29]. Interestingly, many of the VOCs have been previously reported as biomarkers for breast cancer. For example, 2-HEX and many other ketone bodies have been reported by [PERSON] et al. [30] and in our previous studies [17; 23] to be potential biomarkers of breast cancer, as they are biological products of lipid peroxidation. Ketones have also been implicated as potential biomarkers for other diseases, including hypoglycemia and different cancer types [4; 31; 32; 33]. In our previous studies, ketone expression was downregulated in the presence of mammary tumors.