## 4 Discussion  
The primary finding of this research is that pre-operative transverse index, following orthodontic treatment, is associated with >2 mm horizontal shifts at point Id, one-year post-surgery for Class II patients. This finding may implicate the effect of transverse discrepancy on post-surgical stability. Additionally, the prediction of stability based on YTI_CR yielded AUROC of 0.88, which is considerably high. Addressing transverse discrepancies is a fundamental goal of orthodontic treatment and may be relevant to achieving post-treatment occlusal stability [16; 20]. However, occlusal stability does not necessarily translate to post-surgical stability. This study's results indicate that YTI is correlated with post-surgical stability, suggesting that adequate occlusal alignment may influence surgical outcomes. While sagittal discrepancies have been known to affect post-surgical stability, to the best of our knowledge, this study is the first to uncover the impact of transverse discrepancies [2]. The average post-surgical change of the subjects was less than 2 mm, possibly disguising the troublesome cases. As [PERSON] et al. addressed, there are a certain portion of problematic cases and statistics based on normal distribution which may be misleading when used to describe post-surgical responses [5]. [PERSON] et al. reported that skeletal position changes greater than 2 mm after surgery are clinically significant [2; 5]. Therefore, our sample was divided into two groups with and without clinically significant changes. Among 22 patients, 9 experienced horizontal mandibular changes greater than 2 mm. Posterior mandibular displacement (in other words, relapse) was observed in seven (31.8%) patients. This result is in accordance with previous findings on the incidence of relapse after mandibular advancement for Class II/high angle patients [21; 22]. The risk of post-surgical instability is known to be associated with diverse factors, such as operative procedure, the extent and direction of relocation, fixation, age and growth potential, orthodontic recurrence and unsecured occlusion [3]. Of all potential factors, preoperative mandibular plane angle and fixation methods were commonly reported to be associated with relapse [21; 22; 23]. In our cohort, such factors were homogenous between the groups except gender and preoperative YTI, subsequently leading to further investigation of prediction based on this index. Considering that surgical results of men were thought to be more stable than those of women postoperatively [24], YTI may show more association with stability considering the confounding effects. [PERSON] et al. reported that YTI provided superiority over other transverse values regarding reliability [25], which aligns with the high reliability of measurements in this study. It should be noted that YTI was initially introduced in the measurement of the transverse discrepancy of non-extracted dentures; however, in this study, all but three were extracted. This dominance of lower premolar extraction might have contributed to the larger YTI value than seen in other studies (\(-\)0.39 \(\pm\) 1.87 mm) [16; 14]. Since there was no significant difference in YTI between the groups, taking into consideration the extraction cases and also the proportion of extracted dentures, we inferred that the investigation was valid. This application of YTI to extracted dentures may expand the usage of this index in the future. Transverse issues can be associated with anteroposterior problems [26]. Inadequate transverse occlusion can possibly affect the incisal relationship [14]. Surgery cases would not be an exception. In this study, a subject with a greater YTI value tended to have better post-surgical stability. A possible explanation for this is that an adequate transverse occlusion could yield a more stable mandibular position shortly after surgery.