Sample size calculation
The sample size estimation was determined with a power calculation assessing superiority, with the significance level set at 0.05 and 80% power. With the α and β values set at 0.05 and 0.2, respectively, 66 patients per group were needed to disclose a difference of 25% between the groups in the proportion of patients with an increase of ≥1 DL during orthodontic treatment. With an expected attrition rate of 15%, a total number of 76 in each group was considered to be sufficient.