## 3 Results

Table 2: Generalized estimating equation model (GEE) to assess the significant factors related to the success of micro-implants. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & **Groups** & \(n\) & **Mean** & **SD** & **Median** & **Minimum** & **Maximum** & \(p\)\({}^{*}\) \\ \hline Cortical bone & Success & 347 & 1.57 & 0.49 & 1.52 & 0.63 & 3.65 & 0.821 \\ thickness (mm) & Failure & 57 & 1.55 & 0.53 & 1.47 & 0.72 & 3.05 & \\  & Total & 404 & 1.56 & 0.5 & 1.51 & 0.63 & 3.65 & \\ \hline Cortical bone & Success & 347 & 1325.2 & 5545.03 & 1014.3 & 174.2 & 104,204 & 0.357 \\ density (HU \({}^{*}\)) & Failure & 57 & 985.88 & 274.56 & 944.6 & 509.8 & 1516.9 & \\  & Total & 404 & 1277.32 & 5140.33 & 1003.9 & 174.2 & 104,204 & \\ \hline  & Success & 347 & 317.24 & 268.85 & 302.5 & \(-\)495.9 & 1136 & 0.342 \\  & Failure & 57 & 276.42 & 291.26 & 242 & \(-\)495.9 & 840 & \\ density (HU) & Total & 404 & 311.48 & 272.11 & 282.5 & \(-\)495.9 & 1136 & \\ \hline \end{tabular} \({}^{*}\)HU, Hounsfield unit.  
\end{table} 
Table 3: Generalized estimating equation model used to assess the effect of bone density on the success of micro-implants. The marginal survival plot is shown in Figure 2. As a result of the marginal survival analysis, no statistically significant variables were observed. Variables that showed borderline non-significance (0.05 \(<\) \(p\) \(<\) 0.10) were cortical bone density (\(p\) = 0.061), loading protocol (\(p\) = 0.066 for immediate loading), and root proximity (\(p\) = 0.098 for type II, Table 4). The results of the regression analysis for the loading time are shown in Table 5. Cortical bone density (\(p\) \(<\) 0.001), root proximity (\(p\) = 0.001 for type III), and micro-implant replacement (\(p\) = 0.008) were identified as significant factors in multi-variable analysis. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline  & & \multicolumn{4}{c}{**95\% CI**} \\ \hline
**Variables** & & **HR** & **Lower** & **Upper** \\ \hline Sex & M & 0.967 & 0.657 & 1.424 & 0.866 \\  & F & 1.000 & & & \\ \hline Vertical facial pattern & Short & 1.272 & 0.720 & 2.247 & 0.688 \\  & Normal & 1.285 & 0.922 & 1.792 & 0.139 \\  & Long & 1.000 & & & \\ \hline \multicolumn{2}{l}{Extaction/non-extraction} & Non-ext & 1.243 & 0.851 & 1.817 & 0.260 \\  & Ext & 1.000 & & & \\ \hline Cortical bone density(HU) & unit = 1000 & 0.998 & 0.995 & 1.000 & 0.061 \\  & unit = 10 & 0.997 & 0.992 & 1.003 & 0.391 \\ \hline Immediate/delayed loading & delayed & 1.000 & & & \\  & immediate & 1.226 & 0.987 & 1.523 & 0.066 \\ \hline Root proximity * & I & 1.000 & & & \\  & II & 0.838 & 0.679 & 1.033 & 0.098 \\  & III & 1.203 & 0.777 & 1.862 & 0.407 \\ \hline Position change ** & Yes & 0.941 & 0.709 & 1.248 & 0.673 \\  & No & 1.000 & & & \\ \hline Replacement *** & Yes & 1.381 & 0.929 & 2.052 & 0.111 \\  & No & 1.000 & & & \\ \hline \hline \end{tabular}  
* Root proximity classified by [PERSON] et al. [19]. ** Change in implant site during installation. *** Replanted in the same site 2-3 months after failure of micro-implant. HR, hazard ratio; CI, confidence interval.  
\end{table} 
Table 4: Univariable marginal survival analysis for factors associated with micro-implant success. Figure 2: The marginal survival plot showing high overall survival rate for micro-implants.