*2.3. Statistical Analysis*

The normal distribution of data was ascertained through the Kolmogorov-Smirnov test. Comparisons between F-T2DM and control participants for normally distributed continuous variables were performed by *t*-test statistics. The non-parametric test Mann-Whitney U was applied to assess differences for non-normally distributed continuous data. Differences in categorical variables between groups were determined via χ2 statistics. Descriptive analyses were performed using the GraphPrism 5.03 software (GraphPad Software, Inc., San Diego, CA), with statistical significance set at *p* < 0.05.

#### *2.4. Partial Least Squares-Discriminant Analysis and Double Cross-Validation Procedures*

In order to unveil possible differences in circulating amino acid patterns between F-T2DM and control participants, a multivariate classification strategy based on partial least squares-discriminant analysis (PLS-DA) modeling was adopted [38]. PLS-DA is a classification method particularly suited for dealing with highly correlated predictors, as it is based on projecting the predictors (measured variables) onto a reduced subspace of latent variables (LVs; directions in space) of highest covariance with the responses, i.e., providing the maximum separation between classes. In order to validate the results of PLS-DA modeling and rule out the possibility that good results were obtained because of chance correlation, a procedure based on repeated double cross-validation (DCV) and permutation tests was used [39,40]. DCV consists of spitting the samples to obtain two cross-validation loops, an internal loop for model building/model selection and an outer loop that mimics external (test set) validation. The DCV procedure is repeated a sufficient number of times such that estimates do to depend on one specific sample splitting. This allows evaluating the consistency of model parameters and the confidence intervals for model predictions. To assess the statistical significance of the obtained predictions, the figures of merit which summarize the classification accuracy in repeated DCV [i.e., number of misclassifications (NMC), area under the receiver operating characteristic curve (AUROC), and discriminant (DQ2)] are compared with their distribution under the null hypothesis, which is estimated non-parametrically through permutation tests with 1000 randomizations. A more detailed description of the procedure can be found elsewhere [41]. PLS-DA and DCV were run under Matlab R2015b environment by means of in-house written functions (freely downloadable at: https://www.chem.uniroma1.it/romechemometrics/research/algorithms/plsda/).
