## 3 Results  
### Age Prediction Using Fingerprints and Profiles  
Tables 3 and 4 report R\({}^{2}\) (Supplementary Figures S1-S6) and RMSE for the binned spectra and for the metabolite/lipoprotein matrices used as input datasets. The tables show the best-performing models trained and tested in the control population for each of the algorithms considered. Subsequently, we reported the performances of these models when tested on the patient population (using dn\({}^{2}\)PD patients and advPD patients) to evaluate whether the predicted age is consistent or not with the actual age and to enlighten a possible  
Figure 1: Schematic representation of the age prediction models. mismatch due to the disease (i.e., a biological age not corresponding to the chronological one). The best-performing model, trained on the control population, was used and tested in the patient population. For what concerns the models based on the bucket matrix, the best-performing methods in the healthy dataset are SVM and PLS, with an R\({}^{2}\) of 0.865 and 0.825, respectively. The lowest RMSE (6.273) was obtained for SVM, which can therefore be defined as the best-performing model in the control dataset. This score becomes much larger when dn\({}^{2}\)PD patients and advPD patients are used as a test set. This means that a high discrepancy between predicted and actual chronological age emerges in patients affected by PD. We also report the estimates obtained with the Klemera-Doubal model, showing how all three machine learning approaches (SVM, PLS, and ElasticNet) significantly outperform this model in terms of R\({}^{2}\). Similar considerations can be applied when using as input features the matrix of metabolites/lipoproteins, as shown in Table 4.  
For what concerns metabolite/lipoprotein predictions, as shown in Table 4, performances are slightly worse than the models built on binned spectra, reaching a maximum R\({}^{2}\) of 0.765 for the ElasticNet method with the lowest RMSE in the Ctr model. Again, dn\({}^{2}\)PD and advPD show a higher discrepancy when the chronological age is predicted. Therefore, we used the best SVM output model to identify those subjects with a predicted age that is at least 6 years over/underestimated by the model with respect to the chronological age, resulting in a total of 264 subjects. Of them, 7 advPD patients are predicted as older (with a mean difference between real and predicted age of 15.45 years and a standard deviation (SD) of 10.5) accounting for 31.81% of the total advPD population, while 9 advPD are predicted as younger (11.4 years; 4.87 years) accounting for 40.97% of the advPD population; 95 dn\({}^{2}\)PD patients are predicted as older (14.7 years; 6.4 years) accounting for 40.775% of the dn\({}^{2}\)PD population, while 39 dn\({}^{2}\)PD patients are predicted as younger with respect to their chronological age (10.0 years; 3.2 years) accounting for 16.73% of the total dn\({}^{2}\)PD population; 58 of the control population are predicted as older (10.5 years; 4.8 years), and 56 of the Ctr are predicted as younger (10.4 years; 9.3 years) accounting, respectively, for 13.8% and 13.3% of the total Ctr population. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model Based on Metabolites**} & \multicolumn{2}{c}{**Ctr**} & \multicolumn{2}{c}{**dn\({}^{2}\)PD**} & \multicolumn{2}{c}{**advPD**} \\  & **R\({}^{2}\)** & **RMSE** & **R\({}^{2}\)** & **RMSE** & **R\({}^{2}\)** & **RMSE** \\ \hline SVM Linear & 0.735 & 8.76 & 0.314 & 12.651 & 0.138 & 10.961 \\ ElasticNet & 0.756 & 8.422 & 0.236 & 11.044 & 0.014 & 13.562 \\ PLS & 0.739 & 8.704 & 0.095 & 15.157 & 0.043 & 10.423 \\ Klemera–Doubal.ytruc1 & 0.046 & 77.305 & 0.001 & 110.239 & 0.007 & 111.439 \\ Klemera–Doubal.ytruc2 & 0.318 & 24.903 & 0.039 & 27.304 & 0.0002 & 31.188 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Table reporting performance for SVM, PLS, and ElasticNet together with the baseline model of Klemera–Doubal, using metabolites/lipoproteins as input features.