We appreciate the comments of Dr Pandian et al related to our article “Effect of maxillary protraction with alternating rapid palatal expansion and constriction vs expansion alone in maxillary retrusive patients: a single-center, randomized controlled trial.” We will attempt to answer their queries in the order presented.

During the study, we did find that patients with larger overjet might require more treatment time. Obviously, the value of the pretreatment overjet may represent the degree of maxillary retrusion or mandibular protrusion. Because a large sample was hard to obtain, in our study, we did not restrict the pretreatment overjet to a smaller range. Some investigators have reported a research protocol that may improve research methods when facing such a confounding factor. In their studies, the posttreatment records were obtained after the same treatment duration in both groups. Due to ethical considerations, we did not use this protocol but performed a more common method, in which lateral cephalometric radiographs were taken at the beginning and end of treatment. However, to test the homogeneity of the patients in both groups, independent t tests were used to compare the 2 groups before treatment, including their ages and all the cephalometric values listed in our article. No significant difference was observed in the ages between the 2 groups, either integrally or for each sex ( P >0.05). No significant difference was found in the cephalometric values before treatment between the 2 groups ( P >0.05). The homogeneity of the values at baseline was considered good between the 2 groups.

The direction of elastic protraction, the intraoral point of force application, and the position of the maxillary center of resistance may play leading roles in maxillary rotation. As Dr Pandian et al mentioned, some other causes might also affect the results, such as the vertical movement of the maxillary teeth during treatment, the occlusal plane angle, and the anteroposterior position of the maxillary banded teeth before treatment.

We agree that using bonded rapid maxillary expansion might be more helpful for patients with a high mandibular plane. In this study, we focused more on the degree of maxillary forward movement after treatment. Because of the limitation of the sample size, we did not divide the patients into several groups and apply different types of expanders according to their mandibular plane angle. On the other hand, the duration of patient recruitment was 2 years, and the patients were treated according to the plan made at the beginning of the research. Thus, we could not predict their average mandibular plane angles.

It is really a good suggestion to investigate the 3-dimensional changes of the 2 protocols. We are indeed aware of the limitations of 2-dimensional films. In our study, we did not obtain any valuable results in the transverse direction. However, we have conducted a different clinical trial to investigate the 3-dimensional changes of maxillary protraction combined with alternating rapid palatal expansion and constriction vs expansion alone using cone-beam computed tomography. We hope that we can share the results of this study in the future.