Previous studies have mainly focused on evaluating the soft tissue changes of skeletal Class I and Class II extraction patients [21, 22]. In this study, the correlation between subjective facial profile esthetics and objective cephalometric measurements in skeletal Class II patients, and the correlation between facial profile changes and cephalometric measurement changes during camouflage extraction treatment, were first assessed. We found a strong association between objective measurements and subjective assessment of profile esthetics, and we used three machine-learning models to predict posttreatment profile esthetics.

Compared to skeletal Class I patients, skeletal Class II patients often have associated facial deformity, which can affect the facial profile. Which cephalometric measurement is most related to facial profile esthetics in skeletal Class II patients? To date, there have been no studies to answer this question. In this study, lip protrusion and incisor position, particularly lower lip protrusion, were first found to be a critical factor in evaluating the facial profile esthetics. In our previous study, the distance between facial-axis point (FA) of maxillary incisor and G line (GALL), which was proposed by Andrews et al., was more convenient and stable for evaluating facial profile esthetics in skeletal Class I patients [23]. While, to evaluate the facial profile esthetics of skeletal Class II patients, FA-GALL is not as sensitive as U1-APo distance, which considered both maxillary incisor position and maxillary bone position. Hence, the FA-GALL and U1-APo distance are recommended to evaluate facial profile esthetics in skeletal Class I and Class II patients, separately. Interestingly, the maxillary incisor position (U1-APo distance) showed a stronger correlation with facial profile esthetics in adult patients, whereas the mandibular incisor position (L1-APo distance) was more sensitive in adolescent patients. In addition, the chin morphology (Pog-NB distance) showed a positive correlation with facial profile esthetics. Our findings are consistent with Huang et al., who found that lip protrusion, incisor position, and chin morphology are the key measurements correlated with the profile esthetics of bimaxillary protrusion patients (ANB angle: 4.76 ± 1.91) [15]. Hence, a harmonious lower third of the face plays an important role in facial profile esthetics. As for the skeletal pattern, the sagittal skeletal patterns (ANB angle) have a significant influence on facial profile evaluation. In our study, the patients mainly had mandibular retrusion (SNB angle: 77.14 ± 3.39); maxillary positions (SNA angle: 83.79 ± 3.67) were relatively normal. This finding is in agreement with the findings of Krooks et al., reporting that sagittal skeletal dimension is the most important factor when evaluating facial profile esthetics [24].

For skeletal Class II patients, camouflage extraction treatment can mask the skeletal deformity through dental compensation and improve the facial profile. However, an unattractive dished-in profile may also occur if the anterior teeth are excessively retracted [7]. In our study, the amount of maxillary anterior teeth retraction (ΔU1-GALL) was significantly correlated with esthetic change in the facial profile. The mean value of maxillary anterior teeth retraction was 4.88 mm, and the facial profile was significantly improved after camouflage extraction treatment (the VAS score increased from 65.89 to 77.60). The increase in nasolabial angle followed by extraction of maxillary anterior teeth had a positive influence on facial profile esthetics, indicating that a relatively obtuse nasolabial angle was acceptable in skeletal Class II patients. Waldman et al. also reported that the nasolabial angle of Class II patients improved after maxillary premolar extraction and reported a ratio of 1:3.8 between upper lip retraction and maxillary incisor retraction [25]. The retraction of anterior teeth in the adolescent group (ΔU1-GALL = 4.61 ± 1.21 mm) was lower than that in the adult group (ΔU1-GALL = 5.12 ± 1.39 mm), probably due to less use of mini-screws in adolescent patients.

It is commonly known that changes in the lower lip after anterior tooth retraction is highly predictable compared to changes in the upper lip [26]. In this study, we first found that the position of the lower lip (lower lip to E plane) was the key factor correlated with the profile esthetics of skeletal Class II patients, and improving the protrusive lower lip can achieve a pleasing facial profile. Lower lip protrusion has previously been reported to mainly depend on the maxillary incisor position instead of the mandibular incisor position [27, 28]. Indeed, the change in lower lip to the E plane and U1-GALL in our study were both found to have critical influences on subjective evaluation of facial profile esthetics during camouflage extraction treatment. Interestingly, maxillary incisor retraction (ΔU1-GALL) was significantly correlated with changes in VAS score in adult patients but failed to be significantly correlated in adolescents. There was a strong and significant correlation between the retraction of lower incisors (ΔL1-APo distance) and the increase in VAS scores in adolescent patients. These results might suggest that the retraction of lower incisors in adolescent patients and upper incisors in adult patients are important in improving facial profile during camouflage extraction treatment.

Another reason for facial profile improvement in adolescent patients was nose and mandibular growth during treatment. The nose prominence and SNB angle both showed a mild positive correlation with the change in VAS score (r = 0.135 and r = 0.129, separately). The lower facial height significantly increased and showed a negative correlation with the change in VAS score (r = − 0.261). Hence, it is important to note that the sagittal growth of the mandible is favorable for improving facial profile esthetics of skeletal Class II adolescent patients, while vertical growth of the mandible is unfavorable. The change in MP-SN angle and lower facial height in adult patients also showed negative correlations with the change in VAS score, indicating that an increase of lower facial height in skeletal Class II extraction patient could lead to an undesirable profile. Our results were consistent with the results of Shoukat Ali et al., which concluded that lower facial height significantly influences facial attractiveness, and an increase in lower facial height is considered less attractive [29]. Hence, vertical control should be considered when treating skeletal Class II extraction patients. It should be also mentioned that the facial profile of adolescent still changes after orthodontic treatment due to growth. Zierhut et al. reported progressive flattening of the facial profile could occur in adolescent after orthodontic extraction treatment, which was associated with the nose and chin growth [30]. Hence, excess retraction of anterior teeth is not recommended for adolescent. Our prediction model could reflect the posttreatment facial profile esthetics; however, the long-term profile esthetic change should be further considered for adolescent.

For skeletal Class II patients, the standard cephalometric norms should not be selected as the treatment goal. In this study, the retraction of maxillary central incisor (ΔU1-GALL) and lower lip (Δ lower lip to E plane), the increase of nasolabial angle and decrease of lower facial height, were positively correlated with the subjective assessment of profile esthetics, indicating that the camouflage treatment goal should be considered in skeletal Class II patients. Hence, the first hypothesis, that there was a strong correlation between some objective cephalometric measurements and subjective assessment of profile esthetics in skeletal Class II extraction patients, was accepted.

Artificial intelligence algorithms are widely used in orthodontic field for diagnosis and prediction, which can assist orthodontists in treatment planning [31, 32]. At present, it has been reported to identify cephalometric landmarks, detect periodontal disease, diagnose dentoskeletal classification and establish treatment plan [33, 34]. Xie et al. constructed an artificial neural network, with 80% accuracy, to determine whether premolar extraction is needed during the orthodontic treatment [35]. For mild and moderate skeletal Class II patients, orthodontists and patients are faced with the dilemma of whether to perform camouflage extraction treatment or orthodontic-orthognathic treatment. The individual prediction of posttreatment facial profile esthetics after camouflage extraction is essential for skeletal Class II patients. The prediction model could help patients decide whether the camouflage extraction treatment will satisfy their esthetic expectations and help orthodontists optimize a treatment plan. For those predicted to have an undesirable posttreatment facial profile, orthodontic-orthognathic treatment is preferred over camouflage extraction treatment. At present, prediction of posttreatment facial profile esthetics is mainly performed for orthognathic surgery patients [36,37,38]. To the best of our knowledge, this is the first study to predict the posttreatment facial profile esthetics of skeletal Class II extraction patients using a machine-learning method.

Our predictive model was based on patient age; 16 pretreatment measurements, which were highly and significantly correlated with facial profile esthetics according to Pearson correlation results; and the designed incisor position, ΔU1-SN, ΔL1-MP, and ΔU1-GALL, which could be planned before treatment. Comparisons of different machine-learning methods indicated that the accuracy and fitting effect of RF was superior to those of other models. The mean absolute error of RF was 3.106, which could preliminarily assist orthodontists and patients in treatment planning. In RF prediction model, all input variables contributed to the output variable. Among these, pretreatment upper lip protrusion (upper lip to E plane), pretreatment chin morphology (Pog-NB) and upper incisor retraction (ΔU1-GAll) contributed the most to the prediction model, indicating the importance of these aspects when treating skeletal Class II extraction patients. For a skeletal Class II patient with a protruded upper lip and a prominent chin, camouflage extraction treatment with upper incisor retraction could achieve a pleasing facial profile. In addition, age also played an important role in the prediction model. Hence, the treatment plan might be different between adult and adolescent patients. Based on our pilot results, the prediction of posttreatment facial profile esthetics using the RF algorithm was practical and accurate (Fig. 3). Thus, the second hypothesis of this study was also accepted.

Considering that changes in soft tissue have low predictability, the main limitation of this study was the small sample size. Further study with a larger sample size should be performed to validate our results and construct a prediction model with better performance. Besides, the facial profile esthetics is highly influenced by race. Nongthombam et al. have reported the difference of facial profile preference in different ethnicity [39]. Hence, our results were limited to Mongolian race. The evaluation and prediction of the facial profile esthetics in different human races should be further analyzed.