## 3 Results
### Internal Validation and Model Performance  
Table 3 presents the performance of machine learning models during internal cross-validation, illustrating their efficacy in predicting aPWV. On the one hand, LR exhibited an \(R^{2}\) of 0.92 with an MSE of 0.1407, demonstrating its ability to capture linear relationships within the dataset. However, PR, incorporating second-degree terms, achieved the best overall performance, significantly improving the fit with an \(R^{2}\) of 0.95 and the lowest MSE (0.0806). This highlights the advantage of capturing nonlinear relationships in the data, suggesting that arterial stiffness estimation benefits from a more flexible regression approach.  
Figure 2: Global SHAP summary plot displaying feature importance based on the average absolute contribution of each variable to model predictions. Variables are ranked from top to bottom in order of decreasing importance.  
Furthermore, the NN model configured with three hidden layers (13, 96, 23) and a regulation parameter of 0.2369 demonstrated a strong balance between model flexibility and accuracy, achieving an \(R^{2}\) of 0.95 and an MSE of 0.0950. These results highlight the trade-offs between model complexity and predictive power, with PR and NN emerging as the most effective approaches based on the validation metrics. Finally, both SVR and BR achieved similar performance levels, with \(R^{2}\) values of 0.91 and 0.92, respectively. Their predictive accuracy remained slightly below that of NN and PR, which demonstrated superior fits to the data.  
Figure 3 shows the fit of the models on the training data using a 10-fold cross-validation scheme. The scatter plots illustrate the relationship between the predicted aPWV values (\(y\)-axis) and the true aPWV values (\(x\)-axis). The high concordance between the observation points and the perfect prediction line indicates strong model performance, as reflected by an \(R^{2}\) above 0.90, meaning that over 90% of the variability in aPWV is explained by the models. However, it is noticeable that, since the training dataset consists of apparently healthy patients, there is a higher concentration of points at lower aPWV values, while predictions for higher aPWV values tend to be less precise. This effect is particularly evident in models like LR, where discrepancies appear more pronounced at the upper end of the distribution.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **MSE** & **RMSE** & \(R^{2}\) & **Hyperparameters** \\ \hline LR & 0.1407 & 0.3716 & 0.9205 & — \\ PR & 0.0806 & 0.2817 & 0.9540 & Degree: 2 \\ BR & 0.1490 & 0.3757 & 0.9163 & Learning Rate: 0.4342, Estimators: 11, Min Leaf Size: 1, Predictors to Sample: 5 \\ SVR & 0.1658 & 0.3902 & 0.9094 & Kernel: Rbf, Scale: 1, Box Constraint: 1.5567, Epsilon: 0.1556 \\ NN & 0.0950 & 0.3048 & 0.9457 & Layers: 3, Regulation: 0.2369, Layer Sizes: 13, 96, 23 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Performance metrics (MSE, RMSE, \(R^{2}\)) and hyperparameters used for each model using exclusively the most relevant features.  
Figure 3: Scatter and residual plots for model performance during internal cross-validation. The **top row** shows the predicted vs. actual aPWV values, while the **bottom row** displays the residuals for each model. **Blue dots** represent individual data points. The **red dashed lines** indicate the identity line (**top row**) and zero-error line (**bottom row**), serving as references for ideal prediction and perfect residuals, respectively.