## 4 Discussion  
Our null hypothesis was rejected because the multivariate analysis showed that the alveolar bone density on the unsuccessful side was significantly lower than on the successful side, with a significant correlation between the success or failure of the mini-screw and the sidedness of habitual chewing. To our knowledge, our study is the first to elucidate the intra-individual factors using a split-mouth design [30], wherein the orthodontic mini-screws were inserted bilaterally, with mini-screw loss only on one side, which helped diminish the influence of the systemic host factors, the inter-individual factors, that act as confounders. Our findings strongly support those of previous studies that concluded that bone density is related to the stability of mini-screws [8; 11; 12]. This is also the first study to examine the stability of orthodontic anchor screws in relation to masticatory functions, such as habitual chewing. Therefore, our findings may be meaningful for clinicians. There was no significant difference in bilateral alveolar cortical bone thickness in the same regions in an individual [31]. In our study, the alveolar cortical bone thickness was 0.97 \(\pm\) 0.29 mm on the right side and 0.97 \(\pm\) 0.25 mm on the left side (Table S3), without \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & & \multicolumn{4}{c}{**Univariate**} & \multicolumn{4}{c}{**Multivariate**} \\  & **Failure** & & \multicolumn{4}{c}{**95\% CI**} & \multicolumn{4}{c}{**95\% CI**} \\  & **Rate (\%)** & & **PR** & **Min** & **Max** & \(p\)**-Value** & **PR** & **Min** & **Max** & \(p\)**-Value** \\ \hline \multicolumn{10}{l}{Habitual chewing} \\ Preferred side & 30.8 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & \\ Non-preferred side & 69.2 & 2.25 & 1.14 & 4.442 & * 0.019 & 2.22 & 1.12 & 4.41 & * 0.02 \\ No preference & 50 & 1.625 & 0.524 & 5.039 & 0.4 & 1.4 & 0.44 & 4.4 & 0.57 \\ \hline \multicolumn{10}{l}{Cortical bone thickness} \\  & Grp. 1 & 64.5 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ Grp. 2 & 37.1 & 0.574 & 0.269 & 1.226 & 0.152 & 0.65 & 0.29 & 1.48 & 0.31 \\ Grp. 3 & 46.4 & 0.72 & 0.358 & 1.447 & 0.356 & 0.75 & 0.36 & 1.57 & 0.45 \\ \hline \multicolumn{10}{l}{Bone density} \\  & Grp. 1 & 55.2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ Grp. 2 & 69 & 1.25 & 0.648 & 2.412 & 0.506 & 1.06 & 0.51 & 2.2 & 0.89 \\ Grp. 3 & 25 & 0.453 & 0.186 & 1.101 & 0.081 & 0.4 & 0.16 & 1.01 & 0.05 \\ \hline \multicolumn{10}{l}{Insertion site} \\  & Between U5 and U6 & 50 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ Between U6 and U7 & 50 & 1 & 0.394 & 2.541 & 1 & 0.27 & 1.98 & 0.54 & \\ \hline \multicolumn{10}{l}{Years of experience} \\  & Grp. 1 & 50 & 1 & 1 & 1 & 1 & 1 & 1 & \\ Grp. 2 & 50 & 1 & 0.445 & 2.246 & 1 & 1.04 & 0.44 & 2.43 & 0.94 \\ Grp. 3 & 50 & 1 & 0.504 & 1.985 & 1 & 1.23 & 0.6 & 2.51 & 0.57 \\ \hline \multicolumn{10}{l}{Cons} \\ \hline \end{tabular} Abbreviations: CI, confidence interval; PR, prevalence ratio; min, minimum; max, maximum.  
\end{table} 
Table 2: Multilevel Poisson regression analysis of the association of each factor with unilateral mini-screw loss. *: \(p\) < 0.05.  
a significant difference between the two sides, which agrees with a previous study [31]. However, there was a tendency for the successful side to have a larger width diameter of 1.01 \(\pm\) 0.27 mm, when compared to the 0.93 \(\pm\) 0.27 mm width diameter on the unsuccessful side. [PERSON] et al. [8] reported that the mini-screw loss rate increased significantly when alveolar bone thickness was less than 1.0 mm. Considering that the mean cortical bone thickness of the unsuccessful side in the present study was 0.93 mm, the sample size should be increased to investigate the cortical bone thickness in detail required for mini-screw stability. The alveolar bone density was significantly greater on the successful side than on the unsuccessful side, suggesting that bone density may be related to mini-screw stability, consistent with a previous study [15].