## 3 Results
### Study Selection
Instead, after \"Treatment 1\" the AHI values in group 2, decreased from \(11.1\pm 0.7\)/h to \(5.4\pm 0.6\)/h. After \"Treatment 2\", the AHI values in group 2 decreased to \(0.9\pm 0.3\) same as group 1, obtaining an almost normalized level after the two treatment modalities. The case study carried out by [PERSON] showed a decrease in AHI from 18.9/h to 1.0/h two years and five months after orthodontic treatment. The random effects model calculation (n = 102 patients) demonstrate a mean difference of 5.11/h (95% CI = 4.58 to 5.64), overall effect z = 18.96, and \(p\) = 0.00001. The Q statistic is \(p\)\(<\) 0.00001 (significant heterogeneity) and I\({}^{2}\) = 97% (high inconsistency; see Figure 2). We acknowledged the high heterogeneity either within the study population and between the studies, so in order to take in account the most influent factor we choose fixed effect model that emphasize within study weight. We provided also random effect models to not compress between study variance. Lowest Oxygen Saturation. [PERSON] et al. did not report data about LSAT while mean oxygen saturation was provided by [PERSON] et al. All the studies except for [PERSON] et al., in which it was not reported, demonstrated an improvement of the lowest oxygen saturation level. Secondary Outcome. A sub-analysis was performed to understand if there were any differences between children who underwent previous AT and children who did not undergo AT (see Table 5)  
Not reported:  
* [PERSON] et al. and [PERSON] et al. did not report either tonsil sizes or whether any previous surgery was performed. Thus, these studies were excluded from the sub-analysis. Therefore, this sub-analysis was performed on 65 out of 102 children. Figure 2: Apnea-hypopnea index (AHI) mean difference and standardized mean difference before and after rapid maxillary expansion (RME). CI = confidence interval; IV = inverse variance; SD = standard deviation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Tonsil Status** & **Pre-RME AHI** & **Post-RME AHI** & **AHI\% Change** \\ \hline No tonsils, n = 17 & \(4.9\pm 0.6\) & \(0.9\pm 0.3\) & \(-82.4\%\) \\ Small tonsils, n = 23 & \(12.2\pm 2.6\) & \(0.4\pm 1.6\) & \(-97.7\%\) \\ Large tonsils, n = 24 & \(7.1\pm 4\) & \(3.3\pm 1.3\) & \(-56.4\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Pre and Post RME Outcomes Based on Prior Adenotonsillectomy and Tonsil Size. Previous AT:  
* [PERSON]'s case report subject was treated previously with AT, but the child did not respond to the treatment, done three years before the RME. * [PERSON] et al. investigated in group 1 the RME after AT in 16 children with narrow maxilla and with a narrow and high hard palate; their AHI improved from \(4.9\pm 0.6\)/h to \(0.9\pm 0.3\)/h. No prior surgery:
* [PERSON] et al. noted that their patients didn't undergo any prior surgery (small tonsils). * [PERSON] et al. excluded those previously treated with AT. They excluded children that had a history of prior OSAS therapies (including tonsillectomy and adenoidectomy). Before the placement of the RME device, all children underwent an otorhinolaryngological examination to grade their tonsillar hypertrophy (enlarged palatal tonsils) following a standardized scale ranging from 0 to 4 (large tonsils). Their study reported children presenting tonsillar hypertrophy as grade 2 (3 out of 10), grade 3 (5 out of 10), and grade 4 (2 out of 10). * [PERSON] et al. the used RME appliance in 14 children (group 2) that presented a grade 2 or larger tonsils and a narrow or high hard palate and a narrow maxilla, showing an improvement in AHI from \(11.1\pm 0.7\)/h up to \(5.4\pm 0.6\)/h in children with large tonsils. Comorbidities. The majority of the studies mentioned the exclusion of patients with comorbidities and syndromes.