## 3 Results  
The total study population consisted of 319 children between the ages of 5 and 12 years. The study group consisted of 174 subjects (67 males, 107 females) between 5 and 12 years (mean = 8.9 \(\pm\) 1.96); the prevalence of AR was 24.13% (42 subjects); the prevalence of asthma was 5.7% (10 subjects); 28% of the allergic/asthmatic subjects were prescribed drug therapy for AR/asthma (12 subjects) (Table 1).  
One hundred eight subjects had completed the orthodontic treatment cycle at the time the data were collected. Thirty-one children had a relapse (Table 2).  
The control group consisted of 145 subjects (64 males, 81 females) between 5 and 12 (mean = 9.7 \(\pm\) 1.93); the prevalence of AR was 15.17% (22 subjects); the prevalence of asthma was 4.13% (6 subjects, all suffered from AR) (Tables 1 and 2); 29% (8) of the allergic/asthmatic subjects were prescribed drug therapy for AR/asthma.  
There was a marginally significant association between the presence of AR and the presence of posterior crossbite (\(p\)-value = 0.05, odds ratio = 1.77). No significant association was found between posterior crossbite/og  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Crosbsite/Ogival Palate [n. 174 (\%)]** & **No Crossbite/Ogival Palate [n. 145 (\%)]** \\ \hline Age (mean) & 8.9 yr & 9.7 yr \\ \hline Sex & 67 Males (38.5\%) & 64 Males (44.1\%) \\  & 107 Females (61.5\%) & 81 Females (55.9\%) \\ \hline No allergic rhinitis (n.) & 132 (75.87\%) * & 123 (84.83\%) \\ \hline Allergic rhinitis (n.) & 42 (24.13\%) & 22 (15.17\%) \\ \hline No asthma (n.) & 164 (94.3\%) & 139 (95.87\%) \\ \hline Asthma (n.) & 10 (5.7\%) & 6 (4.13\%) \\ \hline Adenoid hypertrophy (n.) & 1 (2.4\%) & 2 (9.1\%) \\ \hline Tonsils hypertrophy (n.) & 1 (2.4\%) & 1 (4.5\%) \\ \hline Adenoidectomy (n.) & 4 (7.7\% of AR/Asthma patients) & 2 (7.1\%) of AR/Asthma patients) \\ \hline Anti-allergic therapy (n.) & 12 (27.2\% of AR/Asthma patients) & 8 (29\%) of AR/asthma patients) \\ \hline \multirow{3}{*}{Skeletric class (n.)} & 137 (21.26\%) & I 28 (19.31\%) \\  & II 90 (51.72\%) & II 102 (70.34\%) \\  & III 47 (27.01\%) & III 15 (10.34\%) \\ \hline \multirow{3}{*}{Dental class (n.)} & I 38 (21.83\%) & I 35 (24.13\%) \\  & II 106 (60.91\%) & II 97 (66.89\%) \\ \cline{1-1}  & III 30 (17.24\%) & III 13 (8.96\%) \\ \hline Maximillary width (mean) & 44.9 mm & 48.05 mm \\ \hline \hline \end{tabular}
\end{table}
Table 1: The number of children (%) affected by AR and asthma in the study and control groups (* \(p\) = 0.05 for AR; \(p\) = 0.61 for asthma).  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Stable Results** & **Relapse** \\ \hline No allergic rhinitis (n.) & 59 (76.6\%) & 21 (68\%) \\ \hline Allergic rhinitis (n.) & 18 (23.4\%) & 10 (32\%) \\ \hline No asthma (n.) & 70 (90.9\%) & 28 (90.3\%) \\ \hline Asthma (n.) & 7 (9.1\%) & 3 (9.7\%) \\ \hline n.: number of subjects. & & \\ \end{tabular}
\end{table}
Table 2: The number of stable cases and relapses in the allergic, no allergic rhinitis, asthma, and no asthma groups (\(p\) = 0.34).  
Using a model to investigate the variables that frequently affect the crossbite/ogival palate, it became apparent that only AR and age had a significant effect. Given AR, age has an inverse significant association with crossbite/ogival palate (every year the probability to have crossbite/ogival palate is about 90% of the previous one), instead given age, AR has a significant positive association with it (AR patients have almost double the probability of having crossbite/ogival palate with respect to non-AR patients). None of the other variables considered (sex, asthma, previous adenoidectomy, medical therapy, oral respiration, skeletric class) were selected by AIC to enter the final model, meaning that they did not appear to have a positive or negative association with crossbite/ogival palate (Table 3).  
No significant association was found between AR and/or asthma and the relapse of posterior crossbite after expansion treatment (\(p\)-value = 0.34).