## 2 Materials and Methods
### Data Analysis  
Analyses of non-spectral data were performed using SPSS software (IBM SPSS Statistics, v. 25). Variables without a normal distribution were described by their median and interquartile range (IQR). All acquired serum and synovial-fluid spectra files from both time points were imported in MATLAB(R2015b (8.6.0.267246); The Mathworks, Natick, MA, USA) for the successive data processing which was carried out utilizing in-house written scripts. For each sample, at each time point, the average of the replicate spectra was used for analysis. Prior to any modeling, the data were preprocessed by the first derivative (using the Savitzky-Golay algorithm [16] with 19 points window and second-order polynomial) followed by mean centering. Modeling was conducted in two different stages. At first, multilevel simultaneous component analysis (MSCA) was used to verify whether there could be any significant difference between the spectra of the same samples measured after short- and long-term storage. Indeed, MSCA can be considered as a multivariate generalization of repeated measurements ANOVA [17; 18]. In particular, the overall (preprocessed) spectral matrix \(\mathbf{X}\) is partitioned into the individual contributions of between-sample (\(\mathbf{X}_{b}\)) and within-sample (\(\mathbf{X}_{w}\)) systematic sources of variability plus the residuals (\(\mathbf{X}_{res}\), i.e., the variation not accounted for by the model), according to  
\[\mathbf{X}=\mathbf{X}_{b}+\mathbf{X}_{w}+\mathbf{X}_{res}\]  
In particular, the effect of sample aging on the spectroscopic signal is related to the within-sample variation described by \(\mathbf{X}_{w}\) and can be quantified as the sum of squares of the elements in that matrix. The significance of the contribution is evaluated by comparing such effect with its distribution under the null hypothesis, which is estimated by means of a permutation test [19]. On the other hand, if the effect is found to be significant, its impact on the spectroscopic signal can be interpreted by PCA of the associated matrix \(\mathbf{X}_{w}\). In the present study, MSCA analysis was conducted independently on the serum and synovial fluid samples. In a second stage, to verify whether MIR analysis of synovial fluid or serum samples could provide the basis for a reliable discrimination between OA and control even after long-term storage and if the same spectroscopic markers could be found as when analysis was carried out after short-term storage, supervised pattern recognition (classification) models were built and validated [20]. Due to its ability to deal with highly collinear predictors (e.g., spectral variables), partial least squares discriminant analysis (PLS-DA) was selected [21; 22]. The PLS-DA method is based on projecting the data onto a low-dimensional sub-space of latent variables, which are relevant to highlight differences between the groups. Accordingly, model building is required to identify the optimal dimensionality of such subspace. On the other hand, the quality of the predictive models, which can be summarized by different figures of merit, such as sensitivity, specificity, overall classification accuracy, and the area under the ROC curve (AUC), needs to be evaluated on samples not used for model development, to avoid over-optimistic results. Accordingly, to build the models and validate the prediction results and the identified spectroscopic markers, a repeated double cross-validation (rDCV) procedure coupled with permutation tests was adopted [23; 24]. Double cross-validation (DCV) is a resampling procedure where the available samples are split according to two nested loops of cross-validation: the outer loop samples are treated as external validation samples, which do not take part either in model building or in model selection; indeed, optimization of the model parameter is carried out on the inner loop samples.