## 3 Results
The PCA and PLS-DA analyses of the ternary system comprising Group A and Group B on Day 1 and the controls showed a very similar result to those for the previous binary system, where the patients were clustered together relatively well and patients were scattered among themselves without obvious differentiation between patient groups (results shown in Figure S1 in the supplement). PLS-DA analyses were further used to differentiate patient data on a given day. The results from these analyses can be summarised as follows (the best result, performance measured in accuracy): Day 1, accuracy of 0.73, R2 of 0.138 (one component); Day 3, accuracy of 0.76, R2 of 0.3905 (five components); and Day 7, accuracy of 0.72, R2 of 0.387 (four components). In all cases, Q2 values were negative, which suggests an overfitted model. In the next step, we employed the random forest (RF) discriminatory algorithm to obtain a more realistic estimation of the discriminatory power of the system since RF is relatively robust to overfitting and outliers [19]. The RF algorithm used included cross-validation via balanced subsampling. It worked with two-thirds of the data for training and the rest for testing for regression, and about 70% of the data for training and the rest for testing during classification to overcome the negative aspects of training and testing on the same data. This approach partially substitutes the validation on an independent data set. As input variables also for this algorithm, we used relative concentrations of metabolites in plasma expressed by the spectral integrals of particular NMR regions. In the case of highly correlating predictors, RF may label some of them as unimportant, so RF was launched 10 times. Within the RF re-runs, metabolites slightly permuted in the importance order. As an output from these analyses, receiver operating characteristic curve (ROC) curves were created. The ROC is defined only for binary systems, and it is created by plotting the true-positive rate against the false-positive rate at various threshold settings. An important output is the area under the curve (AUC), which represents ranking quality. The AUC of a ranking is 1 (the maximum AUC value) when all samples are truly assigned into the groups. An AUC of 0.5 is equivalent to randomly classifying subjects as either positive or negative (i.e., the classifier is of no practical utility) [20]. We ran RF discriminatory analyses for the systems of patients versus controls, Group A versus controls, Group B versus controls, and Group A versus Group B on Days 1, 3, and 7. The results of RF classifications are summarised in Table 3.  
Figure 1: PCA (**left**) and PLD-DA analyses (**right**) of the system: patients in the hospital on Day 1 versus controls; algorithms were fed by the relative concentrations of plasma metabolites, and analyses were run in metaboanalyst [16]. For significance testing among relative concentrations of plasma metabolites in patients against controls and patients' dynamic data, we used nonparametric ANOVA, known as the Kruskal-Wallis test. Due to the relatively low sample sizes, we continued with nonparametric testing via the Mann-Whitney U-test for the combination of binary data sets. The details are listed in Table 4. The Phe/Tyr ratio was also used as one variable. As the threshold to claim significance, the p-value was set to 0.05, as established. In the discussion, we did not strictly adhere to p-values, but we focused rather on the data behaviour visualised in the box plots.