# Terahertz Time-Domain Spectroscopy of Glioma Patient Blood Plasma: Diagnosis and Treatment
## 3 Results
Graphs of the cumulative explained variance to find the maximum allowed number of PCs for the blood plasma of glioma patients and donors, and the blood plasma of glioma patients and patients with SCD, are given in the Supplementary Materials (Figure S1). A steeper curve indirectly indicates that the first PCs contain more valuable data. The smoother ones indicate an even contribution of the PCs and the need to analyze more combinations of them. PCA score plots for different pairs of studied groups are presented in Figure 6. There was no perfect separation of groups, and the most difficult data for linear separation corresponded to Case 1 (glioma patients versus healthy donors). Additional figures, illustrating the impact of data standardization and the choice of PC combinations, are presented in the Supplementary Materials (Figures S2-S4). This means that two dimensions, provided by PCA and t-SNE for visual analysis, are not sufficient to differentiate groups under study. At the third stage, the separability of the data was analyzed using a predictive model based on the linear kernel SVM, XGBoost, and RF. The classifier quality was estimated using a Receiver Operating Characteristics (ROC) curve and area under the curve (AUC) analysis. The ROC curve plotted the sensitivity vs. (1-specificity), and the AUC displayed the area under the ROC. Details about ROC-AUC analysis and corresponding ROC-AUC curves are presented in the Supplementary Materials (Figure S5). The results are summarized in Table 2. Here, the AUC value was averaged over all training and testing set implementations according to the 10-fold cross-validation and presented in terms of mean and standard deviation values. As can be seen from Table 2, the AUC mean value was higher for the XGBoost and RF data models, and simultaneously their AUC variance was lower compared to that of linear kernel SVM. This means that XGBoost and RF show the best separation of the group of patients with glioma from healthy donors and patients with SCD. At the final stage, informative frequencies were identified. The results are shown in Figure 7.  
According to Figure 7, the informative frequencies differ for various groups, although there is also an intersection, often with different contributions for cases 1 and 2. Tree-based ensemble methods were shown to work more accurately than the SVM method. However, the informative frequencies may not coincide, which indicates the instability of the methods. This is owing to the heterogeneity of the data of patients with gliomas, and we will obtain more robust ML models with an increasing amount of samples. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case Number** & **Averaged AUC, Linear Kernel SVM** & **Averaged AUC, RF** & **Averaged AUC, XGBoost** \\ \hline Case 1 & 0.72 \(\pm\) 0.3 & 0.82 \(\pm\) 0.25 & 0.82 \(\pm\) 0.21 \\ Case 2 & 0.70 \(\pm\) 0.3 & 0.84 \(\pm\) 0.20 & 0.81 \(\pm\) 0.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Averaged AUC for Cases 1 and 2 and linear kernel SVM, RF, and XGBoost classifiers. Figure 6: PCA score plots for Case 1 (glioma patients versus healthy donors, (**a**)) and Case 2 (glioma patients versus patients with SCD, (**b**)). Linear separation border between classes is shown for Case 2. Among the patients with glioma, there were five pairs of patients whose blood plasma samples were taken before and a week after the surgical intervention to remove the tumor. ML methods were applied to establish differences in the THz spectra before and after the surgery. It can be assumed that some specific features of an individual patient were leveled and differences in the spectra may be associated with the presence or absence of the tumor. Figure 8 shows the mean and variance of the THz spectra of glioma patients before the surgery and 7 days after the surgery. The graph of the cumulative explained variance to determine the maximum allowable number of PCs is presented in the Supplementary Materials (Figure S6).