## 3 Results  
Demographic and clinical variables were correlated with VE-ABI. For numerical variables, a small but significant correlation between age and VE-ABI (r = 0.17, \(p\) = 0.04) was found, whereas no significant correlation was found between BMI and VE-ABI (r = \(-\)0.02, \(p\) = 0.83). For binary variables we found a significant difference in VE-ABI as a function of gender (males vs. females, t = 2.25, df = 144, \(p\) = 0.03) and smoking habit (smokers vs. non-smokers, t = 2.32, df = 144, \(p\) = 0.02). For the GLM analysis, the average cross-validated weights (\(\beta\)s) associated to the different PPG features and their associated statistics are reported in Table 1.  
Figure 4 reports the comparison between VE-ABI and PPG-ABI. Figure 4a shows the correlation between PPG-ABI and VE-ABI (r = 0.79; \(p\) = \(\sim\)0), whereas Figure 4b reports the Bland-Altman plot analysis of the same variables. The t-test between the VE-ABI and PPG-ABI did not show significant difference (t = \(-\)0.07; df = 145; \(p\) = 0.55), indicating the absence of bias in VE-ABI estimation. The root mean square error (RMSE) of the estimation was 0.13. Importantly, the correlation of the multivariate estimation, i.e., PPG-ABI, with VE-ABI (r = 0.79) was statistically superior to the univariate correlations (vs. r = 0.08, z = 8.38, \(p\) = \(\sim\)0 for MaxArm; vs. r = 0.18, z = 7.52, \(p\) = \(\sim\)0 for MaxAnkle; vs. r = 0.11, z = 8.13, \(p\) = \(\sim\)0 for SlopeArm; vs. r = 0.26, z = 6.81, \(p\) = \(\sim\)0 for SlopeAnkle; vs. r = \(-\)0.19, z = 7.43, \(p\) = \(\sim\)0 for TDArm; vs. r = \(-\)0.35, z = 5.97, \(p\) = \(\sim\)0 for TDAhkle; vs. r = 0.62, z = 2.93, \(p\) = \(2\times 10^{-3}\) for Ankle-Arm). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Normalized (z-scored) Regressor** & \(\beta\)**-Value** & **t-Stat** & \(p\)**-Value** \\ \hline MaxArm & 0.03 & 0.438 & 0.662 \\ MaxAnkle & 0.17 & 2.526 & 0.013 \\ SlopeArm & 0.02 & 0.329 & 0.743 \\ SlopeAnkle & 0.14 & 1.941 & 0.054 \\ TDArm & 0.09 & \(-\)1.270 & 0.206 \\ TDAnkle & \(-\)0.20 & \(-\)2.559 & 0.012 \\ Ankle-Arm & 0.51 & 7.782 & \(\sim\)0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Average cross-validated \(\beta\)-values and relative t-scores and \(p\)-values estimated through general linear model (GLM) in ankle-brachai index (ABI) prediction. Figure 4: (**a**) Correlation plot of PPG-ABI and VE-ABI; (**b**) Bland–Altman plot of PPG-ABI and VE-ABI. Since statistical differences in VE-ABI as a function of gender were found, and the sample numerosity in the male and female group was comparable, the cross-validated GLM approach was performed again by separating the two groups. This analysis was performed to assess if the prediction capabilities of the multivariate model was different as a function of gender. The PPG-ABI vs. VE-ABI correlations obtained for the different groups were r = 0.69 for males and r = 0.61 for females; this difference in correlation was not statistically significant (z = 0.82, \(p\) = 0.21). Figure 5 reports the ROC of PPG-ABI, estimated employing the whole sample population, in assessing cardiovascular risk (0.9 \(\leq\) VE-ABI \(\leq\) 1.4 vs. 0.9 VE-ABI \(<\) 0.9 or VE-ABI \(>\) 1.4). A ROC area under the curve (AUC) of 0.85 was found. At a specific threshold, an accuracy of 88%, a sensitivity of 75% and a specificity 91% were obtained. The confusion matrix is reported in Table 2.  
The AUC retrieved with a multivariate approach (AUC = 0.85) was significantly different [49] from the AUCs obtained employing univariate analysis from standalone PPG features (vs. AUC = 0.46, z = 4.80, \(p\) = \(\sim\)0 for MaxArm; vs. AUC = 0.51, z = 4.12, \(p\) = \(3.8\times 10^{-5}\) for MaxAnkle; vs. AUC = 0.32, z = 7.12, \(p\) = \(\sim\)0 for SlopeArm; vs. AUC = 0.37, z = 6.21, \(p\) = \(\sim\)0 for SlopeAnkle; vs. AUC = 0.36, z = 6.38, \(p\) = \(\sim\)0 for TDArm; vs. AUC = 0.35, z = 6.56, \(p\) = \(\sim\)0 for TDAnkle; vs. AUC = 0.52, z = 3.99, \(p\) = \(6.7\times 10^{-5}\) for Ankle-Arm).