## 3 Results and Discussion
### Comparison of the Mean Value of Pre-Treatment Measurements in the Three Groups
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Group S** & \begin{tabular}{c} _p-Value_ \\ **(S-I)** \\ \end{tabular} & **Group I** & \
\begin{tabular}{c} _p-Value_ \\ **(I-E)** \\ \end{tabular} & **Group E** &
\begin{tabular}{c} _p-Value_ \\ **(E-S)** \\ \end{tabular} \\ \hline Overjet (mm) & \(4.5\pm 4.2\) & NS & \(3.9\pm 2.5\) & NS & \(3.8\pm 2.0\) & NS \\ Overbite (mm) & \(-4.2\pm 1.7\) & NS & \(-3.0\pm 1.0\) & NS & \(-3.5\pm 0.8\) & NS \\ ANB (\({}^{\circ}\)) & \(6.0\pm 1.8\) & NS & \(4.8\pm 2.1\) & NS & \(3.6\pm 1.4\) & NS \\ Wits appraisal (mm) & \(-1.4\pm 4.1\) & NS & \(-2.0\pm 4.7\) & NS & \(-4.0\pm 1.3\) & NS \\ FMA (\({}^{\circ}\)) & \(42.0\pm 5.0\) & \(0.002\) ** & \(33.6\pm 4.3\) & NS & \(28.5\pm 3.3\) & \(0.000\) ** \\ Lower facial height (\({}^{\circ}\)) & \(57.4\pm 4.4\) & NS & \(53.3\pm 6.7\) & NS & \(50.1\pm 2.2\) & \(0.023\) * \\ Palatal plane (\({}^{\circ}\)) & \(4.9\pm 3.5\) & NS & \(2.9\pm 3.1\) & NS & \(3.2\pm 3.8\) & NS \\ U1 to FH (\({}^{\circ}\)) & \(114.8\pm 8.0\) & NS & \(117.7\pm 6.8\) & NS & \(120.2\pm 5.7\) & NS \\ FMIA (\({}^{\circ}\)) & \(45.0\pm 8.2\) & NS & \(50.1\pm 6.5\) & NS & \(46.8\pm 6.8\) & NS \\ IMPA (\({}^{\circ}\)) & \(92.7\pm 11.4\) & NS & \(92.0\pm 13.4\) & NS & \(102.0\pm 8.1\) & NS \\ UM height (mm) & \(28.8\pm 2.4\) & NS & \(26.8\pm 2.3\) & \(0.009\) ** & \(24.5\pm 3.4\) & \(0.009\) ** \\ UI height (mm) & \(34.0\pm 4.1\) & NS & \(30.8\pm 2.7\) & NS & \(29.5\pm 2.8\) & \(0.046\) * \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of pre-treatment mean values among the three groups. reference value. It has been widely used in the medical and dental fields and also in orthodontics [26; 27]. Based on the results of Table 2, FMA, UM height, and UI height, which have \(p\)-values less than 0.05 and are appropriate as vertical indicators, were selected using ROC analysis. Table 3 shows that the AUC values of the ROC curves for Group S and Group I are the highest in FMA (Figure 6a). This indicates that FMA has better diagnostic accuracy in determining whether orthognathic surgery or molar intrusion is required. On the other hand, UM height and UI height have low AUC and are less reliable as criteria for open bite treatment (Figure 6b,c). The measurement of tooth height was considered to be biased because of the measurement errors that may occur on the cephalometric film where the left and right sides overlap and also because of individual differences in tooth size and length. In other words, these measurements are not suitable enough as a criterion for the diagnosis of open bite. Table 4 also showed the highest AUC value for FMA (Figure 7a), but the value was lower than that of the results in Table 3. The AUC values for UM height and UI height were low (Figure 7b,c), as shown in Table 3. These results suggest that the borderline between orthognathic surgery and molar intrusion is clearer than the borderline between molar intrusion and anterior tooth extrusion. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Variable** & **AUC** &
\begin{tabular}{c} **Cutoff** \\ **Point** \\ \end{tabular} & \(p\)**-Value** & **95\% CI** & **Sensitivity** & **Specificity** \\ \hline FMA & 0.91 & 37.5 & 0.00 ** & 1.00 & 0.88 & 0.80 \\ UM height & 0.73 & 26.5 & 0.04 * & 0.47 & 0.98 & 0.50 & 0.9 \\ UI height & 0.72 & 31.0 & 0.05 & 0.48 & 0.50 & 0.80 \\ \hline \hline \end{tabular}  
* NS: not significantly different;
* \(p<0.05\), *
* \(p<0.01\): statistically significant difference.  
\end{table} 
Table 3: Results of the ROC curve analysis for Group S and Group I.  
Figure 6: (**a**) The ROC curve of FMA measurement (between molar intrusion treatment and surgical orthodontic treatment); (**b**) the ROC curve of upper molar height measurement (between molar intrusion treatment and surgical orthodontic treatment); (**c**) the ROC curve of upper incisor height measurement (between molar intrusion treatment and surgical orthodontic treatment). The cutoff point was determined as the value with the highest sensitivity and specificity.