## 4 Discussion
\begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline  & \multicolumn{4}{c}{**Univariable**} & \multicolumn{4}{c}{**Multivariable**} \\ \hline
**Variables** & & **Beta** & **SE** & \(p\) & **Beta** & **SE** & \(p\) \\ \hline Sex & M & 0.181 & 1.008 & 0.857 & & & \\  & F & 0.000 & & & & & \\ \hline Vertical facial pattern & Short & 0.098 & 1.326 & 0.941 & & & \\  & Normal & \(-\)1.041 & 0.845 & 0.218 & & & \\  & Long & 0.000 & & & & & \\ \hline Loading time (month) & & & & & & & \\ Extraction/non-extraction & Non-ext & \(-\)0.894 & 0.941 & 0.342 & & & \\  & Ext & 0.000 & & & & & \\ \hline Cortical bone density (HU) & unit = 1000 & 0.035 & 0.005 & \(<\)0.001 & 0.027 & 0.007 & \(<\)0.001 \\  & Cancellous bone density (HU) & unit = 10 & 0.021 & 0.013 & 0.101 & & & \\ \hline Immediate/delayed loading & delayed & 0.000 & & & & 0.000 & & \\  & immediate & \(-\)0.151 & 0.685 & 0.826 & \(-\)0.199 & 0.673 & 0.767 \\ \hline Root proximity \({}^{\star}\) & I & 0.000 & & & & 0.000 & & \\  & II & \(-\)0.857 & 0.649 & 0.098 & \(-\)0.214 & 0.626 & 0.733 \\  & III & \(-\)3.600 & 1.026 & 0.187 & \(-\)3.196 & 0.981 & 0.001 \\ \hline Position change \({}^{\star\star}\) & Yes & \(-\)1.283 & 1.078 & 0.234 & & & \\  & No & 0.000 & & & & & \\ \hline Replacement \({}^{\star\star}\) & Yes & \(-\)3.878 & 1.515 & 0.011 & \(-\)3.499 & 1.325 & 0.008 \\  & No & 0.000 & & & 0.000 & & \\ \hline \hline \end{tabular}  
* Root proximity classified by [PERSON] et al. [19]. ** Change in implant site during installation. \({}^{\star\star\star}\) Replanted in the same site 2–3 months after failure of micro-implant. SE, standard error for beta.  
\end{table} 
Table 5: Regression analysis for loading time. the micro-implant sites are at a greater risk of micro-implant failure compared to patients with normal or low mandibular plane angles. Similarly, other studies [42; 43] have reported a greater cortical bone thickness in patients with hypodivergent growth patterns, which are considered to be an adaptive response to the increased functional loading. However, our results suggest that cortical bone thickness is not associated with micro-implant success. Rather than the cortical bone thickness, the cortical bone density was found to be a factor for micro-implant success. Cortical bone density showed statistical significance in the multivariable linear regression model for loading time (\(p<0.001\)) and borderline non-significance (\(p=0.061\)) in the survival analysis. The primary stability of micro-implants is dependent on mechanical retention, and, thus, bone quality is known to be an important factor [43; 44; 45]. [PERSON] et al. [43] have reported that stress distribution in alveolar bone is dependent on cortical bone density and thickness. [PERSON] et al. [45] have found a higher success rate for orthodontic micro-implants in patients with high cancellous and total bone densities. As the failure rate is reported to be greater in the mandible than in the maxilla [32], the retromolar area has been suggested as a stable position for the micro-implants in the mandible, showing the greatest cortical bone density in the mesiobuccal site [46]. The timing of the loading had no significant effect on the success rate. [PERSON] et al. [47] observed the screw to bone contact after micro-implant placement and concluded that tapered implants show greater bone contact compared with the straight implants. Moreover, the bone contact shows no difference between immediate loading and delayed loading in the tapered implants. Other factors associated with immediately loaded micro-implants are screw length and rotational moment applied to the micro-implant. Among the immediately loaded micro-implants, those with a length of 3 mm show higher failure rates than those with a length of 6 mm [48]. [PERSON] et al. [49] suggested that a counterclockwise rotational moment applied to micro-implants can increase the risk of failure. Root proximity has been considered as a significant factor affecting micro-implant stability and success.