## 3 Results  
### Feature Selection and Importance  
The analysis of feature importance is depicted in Table 2. As can be observed, age is the most significant predictor of aPWV and a critical factor in arterial stiffness, showing the highest mean increase in MSE. Other important variables include SBP and DBP variables, which also show notable influences on the model's predictive accuracy. Furthermore, anthropometric parameters such as height and WC, although featuring lower in the ranking, still contribute to the model, suggesting their relevance in predicting arterial characteristics. However, it can be appreciated that while the positive increments in MSE for these features affirm their utility, the relatively high standard deviations across the results indicate considerable variability in their impact across different iterations of cross-validation. To complement the \(\Delta\)MSE-based ranking of feature importance, a SHAP (SHapley Additive exPlanations) analysis was also performed on the trained Random Forest model. Figure 2 shows the global SHAP summary plot, where features are ranked according to their average contribution to the model predictions across all samples. As illustrated, age and Systolic Blood Pressure (SBP) are the most influential features, displaying the widest spread in SHAP values and consistently contributing to increased predicted aPWV. These are followed by DBP, BMI, and Waist Circumference, which also show moderate impact. In contrast, variables such as HbA1c, AGEs, Resting Heart Rate (RHR), Sex, and Tobacco Quantity show minimal influence, with SHAP values clustered around zero across individuals. In the development of the following predictive models, the initial set of 13 variables was reduced to the eight most relevant features based on their importance in both permutation-based \(\Delta\)MSE analysis and the SHAP interpretability framework. The retained variables were as follows: age, SBP, DBP, PP, Height, WC, BMI, and Weight, which consistently showed the highest contribution to model performance across both methodologies. It is important to highlight that PP and BMI are derived variables, rather than direct measurements. Therefore, the core of the model is based on six directly measurable physiological parameters, which are routinely collected in standard clinical practice. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Feature** & \(\Delta\)**MSE Mean** & \(\Delta\)**MSE Std** \\ \hline Age & 1.5136 & 0.3149 \\ SBP & 0.0637 & 0.0269 \\ DBP & 0.0057 & 0.0056 \\ PP & 0.0032 & 0.0056 \\ Height & 0.0027 & 0.0027 \\ WC & 0.0015 & 0.0018 \\ BMI & 0.0010 & 0.0045 \\ Weight & 0.0010 & 0.0035 \\ Sex & 0.0001 & 0.0002 \\ Smoking Status & 0.0001 & 0.0003 \\ HbA1c & \(-\)0.0002 & 0.0014 \\ RHR & \(-\)0.0003 & 0.0012 \\ AGEs & \(-\)0.0008 & 0.0025 \\ \hline \hline \end{tabular} Abbreviations: \(\Delta\)MSE = increase in Mean Squared Error after variable permutation, averaged over the 10 iterations of 10-fold cross-validation; Std = standard deviation across those 10 iterations; SBP = systolic blood pressure; DBP = diastolic blood pressure; PP = pulse pressure; WC = waist circumference; BMI = body mass index.  
\end{table} 
Table 2: Feature importance based on permutation-based method using a Random Forest model. Additionally, Sex and Smoking Status were excluded from the final selection due to their negligible impact on the model's predictive performance, as shown in both the \(\Delta\)MSE and SHAP analyses. Including variables with low statistical relevance could introduce unnecessary noise rather than improving accuracy. Furthermore, their categorical nature differs from the rest of the selected variables, which are all continuous, possibly complicating model optimization and compatibility with certain machine learning algorithms. Similarly, HbA1c, AGEs, and RHR were also excluded. Despite being continuous, these variables exhibited very limited predictive contribution and would require additional biochemical or specialized assessments.