## 3 Results
### The ML-10 Model  
To determine whether the ML-10 and the reduced version ML-2 outperform the traditional BQ in predicting patients at a high versus low risk of OSA, we conducted a comparative analysis using the same threshold used in the standard BQ (\(\text{AHI}\geq 5\)). By employing the same \(\text{AHI}\geq 5\) threshold across all models, we ensured a consistent basis for comparison, enabling a clear understanding of the potential advantages offered by integrating ML techniques into the traditional BQ assessment. Figure 1 presents the ROC space comparing the three models (BQ, ML-10, and ML-2), and Table 3 reports the calculated metrics. Consider Figure 1. By maintaining the BQ level of sensitivity (through a horizontal displacement in the ROC space from BQ coordinates to point A10), the ML-10 model showcased a remarkable specificity of 73%, significantly outperforming the BQ (53%). This improvement indicates the ML-10 model's enhanced capability to correctly identify individuals without OSA at a fixed sensitivity, thereby reducing the incidence of false positives. Conversely, when aligning with the BQ specificity level (via a vertical displacement from BQ to point B10), the ML-10 model demonstrated a sensitivity of 93%, a substantial increase from the BQ (82%). This indicates the ML-10 model' superior ability to accurately detect individuals at a high risk of OSA at a fixed specificity, lowering the risk of overlooking affected patients.  
Figure 1: ROC comparison among the standard BQ, the BQ enhanced through Machine Learning (ML-10), and the simplified BQ (BQ-2, [22]) enhanced through Machine Learning (ML-2). \(\text{AHI}\geq 5\) was used as the cutoff. Although some statistical software also associates AUC values with classifiers with binary output (when just one point exists in the ROC space), we preferred to neglect this feature and only drew the particular BQ working point (red point in the plot) that gives the BQ performance in terms of fixed sensitivity and specificity. A2 and A1 are the intersection points of a horizontal line from BQ, with the ML-2 and ML-10 ROC curves. B2 and B10 are the same for a vertical line (see text for details).  
Additionally, ML-2 also showed (smaller) improvements when compared to the conventional BQ, and (as expected) its figures of merit were smaller than those of ML-10 (points A2 and B2 in Figure 1).  
Recognizing the importance of a nuanced clinical evaluation, we expanded our analysis to investigate how well the ML-10 and ML-2 models distinguish between patients across different levels of OSA severity. This step involved utilizing two AHI thresholds (\(\text{AHI}\geq 15\), and \(\text{AHI}\geq 30\)) commonly referenced in the literature to categorize OSA severity as moderate to severe, and severe, respectively [1]. The outcomes of this comprehensive evaluation are presented in Figure 2 and Table 4. Before all, we realized that the AUCs for ML-10 (0.85 and 0.88) were (slightly) better than the AUCs for ML-2 (0.82 and 0.87), being \(\text{AHI}\geq 15\) and \(\text{AHI}\geq 30\), respectively. Then, by arbitrarily selecting the ones that yield the highest accuracy as the optimal thresholds for the classifier output (therefore precisely defining working points in the ROC space), the performance of the ML-10 model consistently remained high across the two AHI thresholds and larger than that of ML-2, except in one case where, compared to the ML-10 model, ML-2 had higher sensitivity when assessing moderate to severe OSA with a cutoff of \(\text{AHI}\geq 15\) (88% vs. 70%, at similar Accuracy): this is not particularly relevant because we also remark that the corresponding specificity is lower than ML-10's.  
Figure 2: ROC curve comparison between the ML-10 and the ML-2 models in assessing OSA severity at two cutoffs (\(\text{AHI}\geq 15\), \(\text{AHI}\geq 30\)).