Lateral Cephalometric Parameters Variations and Machine Learning Models Among Skeletal Class II &amp; III Malocclusion of Arab Orthodontic Patients

doi:10.21203/rs.3.rs-4177516/v1

Background

The World Health Organization considers malocclusion one of the most essential oral health problems. This disease influences various aspects of patients' health and well-being. Therefore, making it easier and more accurate to understand and diagnose patients with skeletal malocclusions is necessary.

Objectives

The main objective of this research is to reveal novel knowledge concerning the cephalometric parameters among Arab patients, who are citizens of Israel, which are crucial for skeletal deformities classes II and III diagnosis. We compared the differences between the subgroups of gender (male and female) and age for each cephalometric parameter. Furthermore, we examined the correlation between these parameters among the different groups. Finally, we conducted a principal component analysis to detect the most valuable parameters to predict classes II and III and applied machine learning models.

Methods

This quantitative, observational study is based on data from the Orthodontic Center, Jatt, Israel. The experimental data consisted of the coded records of 583 Arab patients who were diagnosed as Class II or III according to the Calculated_ANB.

Results

The group comparison analysis showed that the most significant differences are available between different classes. Nevertheless, unlike many previous studies, we found differences between males and females within the same class. This was demonstrated in the parameters including NL-NSL angle, PFH/AFH ratio, SNB angle, SN-Pg angle, and ML-NSL angle of class III patients, but not in class II patients. Interestingly, this ethnic group of patients also revealed many differences in the different age groups within the same class; these differences were significant in the parameters NL-ML angle, ML-NSL angle, PFH/AFH ratio, facial axis, gonial angle, + 1/NA angle, + 1/NA (mm) in class II age groups, and + 1/NL angle, + 1/SNL angle, + 1/NA (mm), Wits appraisal, and interincisal angle the results showed that the Calculated_ANB correlated with many other cephalometric parameters when comparing two groups that belong to different classes. The Principal Component Analysis (PCA) results showed that we explained about 67% of the variation within the first two PCs. Finally, we used all parameters for the general Machine Learning (ML) model to calculate the importance of each parameter to the model. The stepwise forward Machine Learning models demonstrated the ability of the parameters Wits appraisal and SNB angle to predict the classification with 0.93 accuracy, compared to 0.95 accuracy when the general model predicted class II and III classifications.

Conclusion

There is a significant relationship between many cephalometric parameters within the different groups of gender and age. This study highlights the high accuracy and power of Wits appraisal and the SNB angle in evaluating the classification of orthodontic malocclusion.

Malocclusion

Class II

Class III

Cephalometric parameters

Disease classification

The World Health Organization (WHO) considers malocclusion one of the most essential oral health problems after caries and periodontal disease [1, 2], and in 1987, included malocclusion under the heading of Handicapping Dento Facial Anomaly, defined as “an anomaly which causes disfigurement, or which impedes function, and requiring treatment if the disfigurement or functional defect was likely to be an obstacle to the patient’s physical or emotional well-being” [3]. According to a meta-analysis that was performed by Lombardo et al. (2020), the worldwide prevalence of malocclusion (all classifications) was 56% (95% CI: 11-99), without gender differences. The highest prevalence was reported in Africa (81%) and Europe (72%), followed by America (53%) and Asia (48%) [4, 5]. Skeletal class II malocclusion (SCIIMO) accounts for over one-third of all malocclusions worldwide and is more frequent in Caucasians [2]. In contrast, Skeletal class III malocclusion (SCIIIMO) is the least frequent, with a mean frequency of 7.2%. Reports have shown that the countries with the lowest prevalence index were Italy (1.6%), Nigeria (1.6%), and Jordan (1.4%) [6, 7]. Class II is usually defined as a change in the relationship between the two jaw (Maxilla and Mandible) bases, with a protruded position of the upper jaw to the mandible (maxillary protrusion or maxillary prognathism) or a mandibular retrusion (mandibular retrognathism) or a combination of both situations [2, 8]. Class III is usually defined as a change of the relationship between the two jaw (Maxilla and Mandible) bases, with the mandible protruding (mandibular prognathism) from the upper jaw or a retrusion of the upper jaw (maxillary retrognathism (midface) or a combination of both conditions [1, 6].

Previous studies defined malocclusion is a complicated disorder produced by the combination of multiple factors, such as genetics, environment, ethnic factors, nonnutritive sucking habits, impaired nasal breathing, and functional atrophy of the maxilla [6, 9–12]. Several genes were reported earlier and found to be associated with SCIIMO development, including FGFR2, MSX1, MATN1, MYOH1, ACTN3, GHR, KAT6B, HDAC4, and AJUBA [13]. Furthermore, it is suggested that functional alterations, such as temporomandibular disorders (TMD), are more prevalent in SCIIMO [14]. Restrictions of the vertical or horizontal mandibular range of motion, including the Temporomandibular joint (TMJ) sounds and pain of the masticatory muscles or TMJ [15]. Recent literature shows emerging evidence that the etiology of TMD is most accurately explained by the biopsychosocial model [16, 17].

A previous meta-analysis showed most associated genes with SCIIIMO including MYO1H (rs10850110), BMP3 (rs1390319), GHR (rs2973015,rs6184, rs2973015), FGF7(rs372127537), FGF10(rs593307), and SNAI3(rs4287555) (p < .05) explained most of the variation across the studies, associated to vertical, horizontal, or combined skeletal discrepancies [18].

The diagnosis of skeletal deformities depends on accurate measurement of distance, planes, and angles according to landmarks of hard and soft tissues using lateral cephalogram and cone-beam computed tomography (CBCT), which are then traced to assess the craniofacial relationships of the teeth to the jaws and the jaws to the rest of the facial skeleton to aid in orthodontic diagnosis [19, 20]. Many approaches are applied to diagnose skeletal malocclusion. According to Steiner [21], analysis was made according to the ANB angle (SNA - SNB) for classes II and III as follows - ANB angle with values >4° = Class II, and ANB angle with values <0° = Class III.

According to Jacobson [22], the Wits appraisal and ANB angle define the relation between the two jaws, with an advantage of the ‘Wits” appraisal over that of the conventional ANB angle, with a more reliable indication of the extent or severity of anteroposterior skeletal disharmony of the jaws [22]. In the following years, a variety of studies demonstrated equations that consider the individual properties of the ANB angle. For instance, in 1977, Panagiotidis and Witt [23] demonstrated an equation for ANB individual as: ANB_ind = (−35.16 + 0.4 · SNA + 0.2 · ML-NSL). Järvinen estimated the ANB individual as: ANB_ind = (ANB − (0.472 × SNA) + (0.204 × SN-MP) − 43.386) [24], and Wits appraisal as: Wits = (1.636 × ANB – 0.512 × NSL/OL – 0.830 × SNA + 71.36) [25]. In a separate study that was done on the Chinese population, the derived equations were: ANB_ind = (0.42 × (SNA) + 0.31 × (SN-MP) – 41.1) for males; ANB_ind = (0.31 × (SNA) + 0.20 × (SN-MP) – 28.9) for females [26].

Very recently, Paddenberg et al. [27] established improved and extended regression equations for equations derived by Panagiotidis/Witt and Järvinen for ANB individual and Wits appraisal [27]. It is well documented that ANB individual (Calculated_ANB), and Wits appraisal are considered to be the most used cephalometric parameters for malocclusion diagnosis. According to Paddenberg et al [27], in order to determine the skeletal sagittal, usually the measured ANB angle or Wits appraisal are compared to a specific norm value, which determined according to empirically epidemiological in the general population.

According to a cross-sectional study done on SCIIIMO South Korean and Spanish participants, the results of the varimax factorial analysis (VFA) and cluster analysis (CA), showed a distinct distribution of the two ethnic groups , as well differences within the same ethic group [28]. According to Dehesa-Santos et al., cluster 1 was predominantly Spanish, and clusters 2 and 3 were mainly South Korean, with opposite phenotypes of mandibular projection and craniofacial pattern [28]. On another study, that compared the craniofacial characteristics of skeletal and dental SCIIMO traits from Indian and Vietnamese individuals, found that ANB angle was significantly greater in males (+1.4 deg) and females (+1.9 deg) in the South Indian individuals. In addition, this study found differences in the plane angle, articular angle, anterior facial height and lower anterior facial height, and found that SCIIMO was more severe in the South Indian compared to the Vietnamese adults [29]. In a study that evaluated age, ethnic and sex differences in the prevalence of clinically meaningful malocclusions three ethnic US populations (non-Hispanic White, non-Hispanic Black and Mexican Americans) and three age groups (17-26, 27-36 and 37-46 years), found that the prevalences of mandibular II, overjet and overbite increase with age, while the prevalence of posterior crossbite decreases. In addition, this research found that males have a higher prevalence of mandibular incisor irregularity, overbite, open bite and reverse overjet. Finally, the research found differences in the prevalence between the three ethnic groups [30, 31].

Over the last decade, the field of dentistry has seen the emergence of artificial intelligence (AI), especially machine learning (ML), assisting in the image processing and making decisions [19].

In addition, deep learning algorithms has been applied in the cephalometric analysis, and many approaches have focused on the detection of cephalometric landmarks [32].

The non-uniformity among orthodontics regarding the definition of these landmarks, in addition to the quality of image, lead to significant different outcomes of landmark coordinates and geometrical parameters [19]. The most common AI fields in dentistry are classification, regression, detection, and segmentation [19]. The constrain with all the currently available equations for individualizing the ANB angle and Wits appraisal is the fact there are many different and variety of equations that were used. Therefore, the main aim of this study was to derive a new classification machine learning model that uses the most important parameters to predict whether it’s class II or III malocclusion among Palestinian Arab residents of Israel patients, a population can be considered as very permanent populations of this area with family histories dating back for numerous generations and with high levels of consanguinity.

To our knowledge, this is the first scientific report shows the comparisons on the cephalometric parameters of SCIIMO and SCIIIMO of Palestinian Arab ethnic minority who are citizen of Israel. In the present study, we present group comparison analysis that showed that most significant differences are available between SCIIMO and SCIIIMO of Palestinian Arab ethnic minority citizen of Israel. Our analysis has shown that in contrast to many previous studies, we found that there are differences between males and females within the same class, and between the different age groups within the same class. The results showed that the Calculated_ANB correlated with many other cephalometric parameters, when comparing two groups that belong to different classes. Results of the Principal Component Analysis (PCA) showed that within the first two PCs we explain about 67% of the variation. Finally, we used all parameters for general Machine Learning (ML) model to calculate the importance of each parameter to the model. The stepwise forward Machine Learning models demonstrated the ability of the parameters Wits appraisal and SNB angle to predict the classification in 0.93 accuracy, compared to 0.95 accuracy when general model to predict class II and III classifications.

Ethical Statement

All human samples presented in this study were assessed and treated according to current guidelines and following the Ethics Committee of the University of Regensburg ethics and regulations, the committee reviewed and approved this research project and study design with approval number 19-1596-101 (dated 13.11.2019). All patients were assessed and treated at the Orthodontic Research Center based on Jatt, Israel. All patients agreed to participate in this study signed a consent form, after explaining to them the project and the ultimate aims of this study. The experimental data consisted of the coded records of 583 patients of Palestinian Arab citizen of Israel that were diagnosed as Class II or III. All data collected as a part of the standard of care by the orthodontist's team, and not specially for this research. This is a quantitative, observational study, based on data generated in Orthodontic research Center, Jatt, Israel. The research sample consisted of 583 patients with Class II (n=283, 48.54%) and Class III (n=300,51.45%).

The inclusion criteria were, 1.Patients diagnosed with Class II (Calculated_ANB >1) or Class III (Calculated_ANB <-1) according to, Panagiotidis and Witt Calculated ANB (ANB – ANB individual) [23]; and 2. Patients that have available lateral cephalogram data. The mean age of Class II patients was 17 (M= 17, SD= 6.6), with an age range of 7-44. Among class II patients, females constituted more than half of patients (n=188,66%). Concerning Class III patients, the mean age of the patients was 18 (M= 18, SD= 8), with an age range of 6-54, and here also, females were more than half of the patients in this class (n=160,53%). Tables 1A and B summarize the full detailed information about the tested SCIIMO and SCIIIMO patients, respectively.

In this study we compared the differences between the subgroups based on gender and age for each cephalometric parameter of SCIIMO and SCIIIMO. Furthermore, we examined the correlation between these parameters among the different groups. Finally, we conducted a principal component analysis to detect the most valuable parameters and ML models to predict the classification.

Cephalometric variables

The following cephalometric parameters were the most important variables in this study analysis, full information and location of all the parameters are presented in Figure 1A, and described here as the Points and Landmarks- described in the lateral cephalogram including, 1)Nasion (N): The frontonasal suture at its most superior point on the curve at the bridge of the nose; 2) Sella (S): Sella is the midpoint of sella turcica or hypophyseal fossa or pituitary fossa; 3) Pterygoid point (Pt): Pterygoid point is the intersection border of the foramen rotundum and the posterior wall of pterygopalatine fossa in the lateral cephalogram; 4) Basion (Ba): The most inferoposterior point in the sagittal plane on the anterior rim of the foramen magnum—the tip of the posterior cranial base; 5) Orbitale (Or): Orbitale has been defined as the lowest point of the bony orbit; 6) Anterior Nasal Spine (ANS): The most anterior point on the maxilla at the level of the palate; 8) Posterior Nasal Spine (PNS): The most posterior point on the bony hard plate in the sagittal plane: usually the meeting point of the inferior and superior surfaces of the hard plate; 9) Subspinale (“A” Point) : The most posterior (deepest point on the anterior curve of the maxilla. “A” point is usually found 2 mm anterior to the apices of the maxillary central incisor root; 11) Supramentale (“B” point): The most posterior point of the bony curvature of the mandible below infradentale and above Pogonion. “B” point is usually found near the apical third of the roots of the mandibular incisors; 12) Pogonion (Pg): Pogonion is the most anterior point on the contour of the chin; 13) Menton (Me): Menton is the lowest point on the symphyseal outline of the chin; 14) Gonion (Go): Gonion is the most posteroinferior point at the angle of the mandible. It may be determined by inspection or by bisecting the angle formed by the junction of the ramal and mandibular lines, and extending this bisector through the mandibular border; 15) Articulare (Ar): The intersection of the three radiographic shadows: the inferior surface of the cranial base and the posterior surfaces of the necks of the condyles of the mandible; 16) Incision Superius Incisalis (+1, Usi): The incisal tip of the most anterior maxillary central incisor; 17) Incision superius apicalis (+1, Usa): The root apex of the most anterior maxillary central incisor; 18) Incision Inferius incisalis (-1, Lii): The incisal tip of the most anterior mandibular centralincisor; 19) Incision Inferius apicalis (-1, Lia): The root apex of the most anterior mandibular central incisor.

Subsequently, constructed lines and angles for the skeletal (vertical, sagittal, and growth) and dental analysis were drawn and calculated, respectively including, a) S-N Line: (SNL): The S-N line represents the anterior cranial base. It is constructed by connecting the points sella turcica and the Nasion; b) Palatal Plane (NL): The palatal plane is drawn by extending a line from the anterior nasal spine (ANS) to posterior nasal spine (PNS); c) Mandibular Plane (ML or Go-Me): The mandibular plane as a line connecting the points gonion and menton; d) AFH: Anterior facial height, the distance between N and Me; e) PFH: posterior facial height, the distance between S and Go; f) Mandibular Plane Angle (ML-NSL): The mandibular plane angle is formed by joining the mandibular plane to the anterior cranial base (S-N plane; g) NL-ML-Angel: Angle between mandibular base (ML) and maxillary base (NL), describing the divergence of the jaw bases; h) SNL-ML-Angle: The angle describes the inclination of the mandible (mandibular inclination) relative to the nasion-sella line (anterior skull base, SNL); i) SNL-NML-Angle: The angle describes the inclination of the nasion line (maxillary inclination, NL) in relation to the nasion-sella line (anterior skull base, SNL). Inclination of the maxilla relative to the anterior skull base; k) PFH/AFH: The ratio between posterior and anterior facial height; l) Gonion-Angle: Formed by the points Ar-Go-NSL, it is also referred to as the jaw angle, it is the angle between the mandibular ramus and the mandibular body; m) Facial axis: The angle formed between the lines N-Ba and Gn-Pt; n) Angle SNA: Is formed by joining the lines S-N and N-A. Relating the Maxilla to the Skull in the sagittal demintion; o) Angle SNB: Is formed by joining the lines S-N and N-B. Relating the Mandinle to the Skull in the sagittal demintion; p) Angle ANB: Is formed by joining the lines N-A and N-B. provides information on the relative positions of the jaws to each other. The ANB angle provides a general idea of the anteroposterior discrepancy of the maxillary to the mandibular apical bases; q) SN-Ba- Angle: Central saddle angle. It describes the extent of the skull base flexion; r) S-N-Pg-Angle: Facial angle; s) WIT’S appraisal: measures the extent to which the jaws are related to each other anteroposteriorly.

Finally, we calculated the tooth axis of the upper and lower incisors positions and angles (Figure 1B), including, 1)Maxillary Incisor Position: The maxillary incisor is related to the N-A plane both by angular as well as linear measurements and Nasion sella line (NSL) by angular as detailed, a) +1/NL° Angle: incisor to NL reading in degrees indicates the relative angular relationship of the upper incisor teeth; b) +1/NSL° Angle: incisor to NSL reading in degrees indicates the relative angular relationship of the upper incisor teeth; c) +1/NA ° Angle: incisor to N-A reading in degrees indicates the relative angular relationship of the upper incisor teeth; and d) +1/NA mm: the upper central incisor to N-A reading in millimeters provides information on the relative forward or backward positioning of the incisor teeth to the N-A line, 2) Incisor Mandibular Plane Angle (1-ML): It is formed by the intersection of the mandibular plane with a line passing through the incisal edge and apex of the root of the mandibular central incisor (Tooth Axis) as detailed, a) -1/NB° Angle: The lower central incisor to N-B reading in degrees indicates the relative axial inclination of these teeth; b) -1/NB mm: The lower incisor to NB line measurement in millimeters shows the relative forward or backward positioning of these teeth to the N-B line; and c) -1/ML° Angle: The relative anteroposterior angulation of the lower incisor teeth is determined by relating the most protruding incisor tooth to the mandibular plane (ML). Finally, we calculated the Inter-incisal Angle which defined as the inter-incisal angle relates the relative position of the upper incisor to that of the lower incisor.

Data Analysis

Data analysis was performed using R software platform using the one-way analysis of variance tests (ANOVA), Post-Hoc analysis, Spearman Correlation, Principal Component Analysis (PCA), and Machine Learning models.

Machine Learning methods

Classification models

Classification models - Linear Discriminant Analysis (LDA), Support Vector Machine (SVM), K Nearest Neighbor (KNN), Random Forest (RF), and Classification and Regression Tree (CART). They were all applied using the K-fold cross-validation (K=10) implementation of the R package Caret.

Linear Discriminant Analysis (LDA)

LDA was proposed by R. Fischer in 1936. It consists in finding the projection hyperplane that minimizes the interclass variance and maximizes the distance between the projected means of the classes [33].

Support Vector Machine (SVM)

The machine conceptually implements the following idea: input vectors are non-linearly mapped to a very high-dimension feature space. In this feature space a linear decision surface is constructed [34]. This model can be relatively simple and flexible for addressing a range of classification problems. SVMs distinctively afford balanced predictive performance, even in studies where sample sizes may be limited [35].

K-Nearest Neighbors

The nearest neighbor decision rule assigns to an unclassified sample point the classification of the nearest of a set of previously classified points [36, 37]. In this study, Accuracy was used to select the optimal model using the largest value. The final value used for the model that includes Wits appraisal only was k = 9 (9 neighbors), and k=7 (7 neighbors) for the model that include Wits appraisal and SNB angle.

Random Forest (RF)

It is a classification that uses many decision trees. This algorithm is a combination of tree predictors such that each tree depends on the values of a random vector sampled independently and with the same distribution for all trees in the forest [38, 39]

Classification And Regression Tree (CART).

According to this method, data are partitioned along the predictor axes into subsets with homogeneous values of the dependent variable a process represented by a decision tree that can be used to make predictions from new observations [40].

Model Validation

We validated our models using the k-fold cross-validation approach. Cross-validation provides a simple and effective method for both model selection and performance evaluation, Under k-fold cross-validation the data are randomly partitioned to form k disjoint subsets of approximately equal size [41, 42]. K(10)-fold cross-validation was employed in this research.

Comparison of Cephalogram parameters

Our observations show that there are variations in cephalometric parameters in different gender and age groups within the same malocclusion class, and between the different classes. To evaluate the effect of gender and age on the cephalometric parameters results, we compared each group with the other groups with multiple comparison tests. Tables 2A-D show the multiple test correction performed, and the adjusted P-values were obtained by Tukey and significant values were at P < 0.01 and P < 0.05.

Comparison of Cephalogram parameters within the same classification

The results of our analyses showed that class III males were significantly higher than females within the same class in the parameters including PFH/AFH ratio, SNB angle, and SN-Pg angle (P<0.01). On the other hand, the results demonstrated that class III males were significantly lower than females within the same class in the parameters of SNL-ML angle, and NL-NSL angle (P<0.01) (Table 2A).

Our analysis has shown that Class II results showed that the parameters including NL-ML angle, SNL-ML angle, among patients who were older than 21, were significantly higher than younger patients (P<0.01). A contradicted relation was demonstrated class II parameters- PFH/AFH ratio, and facial axis, in these parameters patients that were older than 21, were significantly lower than younger patients (P<0.05). And finally, patients aged 14-20 were significantly lower than pediatric patients aged 0-13, in the parameters- gonialangle, +1/NA angle, +1/NA (mm) (P<0.05), Class II age differences summarized in Table 2B.

Class III results also demonstrated significant variations in different age groups, the results showed that the parameters +1/NL angle, +1/SNL angle, and +1/NA (mm), among patients that were older than 21, were significantly higher than younger patients (P<0.05). Whereas a contradicted relation was demonstrated in the parameters Wits appraisal, and interincisal angle, that showed that patients that were older than 21, were significantly lower than younger patients (P<0.05). The results also showed that patients aged 14-20 were significantly higher than pediatric patients aged 0-13 in the parameters - +1/NL angle, +1/SNL angle, and +1/NA (mm) (P<0.01). And finally, patients aged 14-20 were significantly lower than pediatric patients aged 0-13 in the Wits appraisal values (P<0.05) (Table 2B).

Furthermore, the results showed that specific gender and age groups can differ in the cephalometric parameters. For example, Class II females aged 21 or more, were significantly higher than younger females at the parameters - NL-ML angle, ML-NSL angle, and -1/NB angle (P<0.05). Whereas a reverse relation was demonstrated on facial axis, females aged 21 or more were significantly lower than younger females aged 14-20 (P<0.01). The results also showed that +1/NA angle in male patients aged 14-20, were significantly lower compared to male pediatrics aged 0-13 (P<0.05). Finally, the anatomic parameter -1/ML showed that class II females aged 14-20, were significantly higher compared to females aged 0-13 (P<0.01) and presented in Table 2C. Class III results showed that among males’ patients older than 21, the Wits appraisal was significantly lower compared to pediatric males aged 0-13.When comparing class III PFH/AFH ratio, male patients aged 14-20, were significantly higher than females, in the same age group (Table 2C).

Calculated_ANB (i.e., ANB- ANB individual)

Theresultsdemonstrated the clear differences of Calculated_ANB values between class II and III in all sub-groups of gender and age. When comparing class II with class III results, class II values are significantly higher than class III values (Figure 2 and Table 2D).

Cephalogram parameters variation within different classification (class II vs class III)

Our results demonstrated a large variety of significant differences when comparing different classifications and subgroups of gender and age, among the most significant parameters are gonial gonion angle, SNB angle, ANB angle, Calculated_ANB, SN-Pg angle, and Wits appraisal (Supplementary Table 1)

Heatmaps of Spearman Correlation

Global heatmaps correlation matrix of assessed cephalometric parameters under different classifications and sub-groups.

The overall heatmap correlation matrices of class II and III cephalometric parameters, both class II and class III results demonstrated many correlations between parameters. We can see a strong significant correlation between parameters in the same dimension. In both classes, the results demonstrated many correlations between Calculated_ANB and other parameters, among these correlations in class II including SNB angle (ρ=-0.333, P<0.01), ANB angle (ρ=0.568, P<0.01), -SN-Pg angle (ρ=-0.331, P<0.01), Wits appraisal (ρ=0.689, P<0.01), +1/SNL angle (ρ=-0.229, P<0.01), +1/NA angle (ρ=-0.275, P<0.01), +1/NA (mm) (ρ=-0.242, P<0.01), -1/ML (ρ=0.433, P<0.01), -1/NB angle (ρ=0.316, P<0.01), and -1/NB (mm) (ρ=0.221, P<0.01). Furthermore, the results demonstrated correlations between Calculated_ANB and many parameters in class III patients- Facial axis (ρ=-0.461, P<0.01), SNB angle (ρ=-0.661, P<0.01), ANB angle (ρ=0.823, P<0.01), SN-Ba angle (ρ=0.238, P<0.01), SN-Pg angle (ρ=-0.638, P<0.01), Go-Me (mm) (ρ=-0.210, P<0.01), Wits appraisal (ρ=0.552, P<0.01), ML-NSL angle (ρ=0.204, P<0.01), +1/NL angle (ρ=-0.323, P<0.01), +1/SNL angle (ρ=-0.353, P<0.01), +1/NA angle (ρ=-0.305, P<0.01), -1/ML (ρ=0.380, P<0.01), and -1/NB angle (ρ=0.224, P<0.01) (Figure 3A).

Gender and Age variation

The heatmaps for each sub-group revealed many specific significant correlations. The correlations show substantial differences between the sub-groups, specially between the Calculated_ANB and the other parameters. Our analysis of Class IIsub-groups correlations showed that the Calculated_ANB correlated highly with measured ANB angle in females aged 0-13 (ρ=0.700, P<0.01), females aged 14-20 (ρ=0.682, P<0.01), Males older than 21 (ρ=0.601, P<0.01). On the other hand, there was a weak correlation between the Calculated_ANB and measured ANB on the other class II subgroups. In addition, a strong correlation was observed between the Calculated_ANB and the Wits appraisal, in all class II subgroups (Figure 3B).

The analysis of Class IIIsub-groups results showed a powerful significant, positive correlation between the Calculated_ANB and measured ANB in all gender and age subgroups, the minimum correlation coefficient among this correlation in all groups was ρ=0.707 (P<0.01). In addition, the results showed significant negative strong correlation between the Calculated_ANB and measured _SNB angle with a minimum correlation coefficient of ρ=-0.601 (P<0.01), while this correlation wasn’t available at class II. Furthermore, in all class III subgroups, there was a moderate to strong correlation between the facial axis with the Calculated_ANB, and here also this relation was more notable than in class II subgroups (Figure 3C).

Principal Component Analysis (PCA)

To estimate better our data structure, and to gain thorough knowledge about the most informative and variant parameters in our data, we ran a PCA analysis. In this analysis, we included all cephalometric parameters. After normalizing our data, the results demonstrated that the first component explains more than half of the total variance (47.87%). Taking the second component will add 19.58% for the data variance, which means that taking the first two components only will explain about 67.46% of the variation in our data, and if we take until the fourth component, we will explain 90.67% of the variance in our data (Table 3A). To better understand which components are included in the first two components, the loading matrix, showed high positive values for ML-NSL angle. On the other hand, a negative value for SN-Pg angle, SNB angle, facial axis, and PFH/AFH ratio. In the second component, the parameters with a positive high value the parameters gonial angle, ML-NSL, and NL-ML angle, and parameters with high negative values are -1/ML, Wits appraisal, Calculated_ANB, and ANB angle. The specific details of all parameters are represented in Table 3B.

Subsequently, we calculated the contribution of each parameter to the first four components using the cosine squared function. The results showed that the parameters: SN-Pg angle, ML-NSL angle, PFH/AFH ratio, NL-ML angle, and SNB angle, are the most contributing to the first four components (Figure 4A). Finally, as presented in Figure 4B, we can observe a similar result with a different visualization to the contribution of each parameter to the PCA analysis.

Machine Learning Models

One of the aims of this study was to utilize and perform machine learning (ML) models, that will provide and suggest the most accurate classification from all the cephalometric parameters. In the previous section, we focused on PCA analysis, to capture the max variance explained by each variable. In this section we worked on revealing a machine learning models that can be used, that can be replaced with Calculated_ANB and measured ANB angle. When we performed ML model based on all parameters (general model), in the LDA, and RF models we received 0.95 accuracy (Accuracy = 0.95, Kappa = 0.90) in classification class II and III. From the model that contained all the parameters, we summarized the importance of each parameter to the model, as it’s visualized at Figure 5.

At the first stage we conducted ML model using the most important variable that followed the Calculated_ANB and measured ANB angle. The first model included the Wits appraisal only, in the LDA and SVM models we received an accuracy of 0.90 (Accuracy = 0.90, Kappa = 0.80) (Figures 6A-B). The second model included the Wits appraisal, and the SNB angle, the accuracy increased to 0.93 in the KNN model. Finally, the addition of the third and fourth didn’t significantly change the machine learning model results (Table 4).

Herein the results of the extended machine learning models that include the first two variables (Wits appraisal and SNB angle), the results were to our satisfaction in predicting the result. The highest mean accuracy value was obtained by KNN, with score 0.93 (Accuracy = 0.93, Kappa = 0.86). CART, SVM, and RF revealed high score of approximately 0.91 (Accuracy = 0.91, Kappa CART = 0.83, Kappa SVM = 0.83, Kappa RF = 0.82). Finally, the LDA model also has a high accuracy score of 0.89 (Accuracy = 0.89, Kappa = 0.79) (Figure 7A). At the next level, we calculated the importance of each parameter in the most powerful model (i.e., KNN model), according to Fisher et al. [43]. The results revealed that the most important variable in the model is Wits appraisal, followed by SNB angle (Figure 7B).

As a follow up, we compared the actual classification in 70% of our patients (the validation data of the model) compared to the predicted classification, and we received the following result: 184 class II patients were classified as class II both by the model and by the Calculated_ANB, 202 class III patients were classified as class III both by the model and by the Calculated_ANB, which means approximately 0.93 accuracy (Table 7C). In order to understand the confounder effect, such as gender and age, we repeated the previous model with same cephalometric parameters and included gender and age as additional variables. The KNN model here also was with highest accuracy (Accuracy = 0.93, Kappa = 0.86). Finally, regarding the importance of each variable results, Wits appraisal is still the most important variable, followed by SNB angle, age, and lastly gender.

The main objective of this research is to reveal novel knowledge concerning the cephalometric parameters, which are crucial for malocclusion classification diagnosis. We started with detecting the alterations in the parameters within the same classification but different sub-groups of gender and age, then continued learning the correlations between these parameters, especially the correlation between different parameters and Calculated_ANB that considered one of the gold standard tests for malocclusion diagnosis. We continued with studying the variability explained by each parameter, via the PCA analysis, and finally used the most important variables to apply new Machine Learning Models, that can be a base for uniform way of malocclusion classification.

Different Groups Comparisons

The results showed that that there are many significant differences between different sub-groups of gender and age [44]. On some parameters we found differences between these sub-groups within the same class, and in most of the parameters we found differences between sub-groups of different classification. Many previous studies demonstrated that there is no significant difference between males and females [45]. In a research that study Lateral cephalograms obtained from 105 Chinese subjects with Class II, there was no significant differences for any of the parameters, between males and females [45]. These results also supported by Sharma and Xin [46], that found only six parameters that slightly different between males and females.

On the other hand, a previous study results from adolescent groups found that the maxilla was placed protrusively (R2ANS; R2A), while the mandible was found to be larger both in the position and dimension (CoGn; R2M) in Class II male subjects. In the same study , class III results showed no difference in vertical and sagittal dimensions [47]. Our analysis has shown that the gender comparison didn’t reveal any variations between males and females within class II variables.

The age subgroups comparisons revealed many variations that happen through age. In summary, the parameters NL-ML angle, and ML-NSL angle increased with age. And PFH/AFH ratio, and facial axis, gonial angle, +1/NA angle, +1/NA (mm) decreased with age. On a study that was obtained by Bergman et al. [48] on class I patients, found that there are parameters that increased (nasal projection, lower face height, chin projection, chin-throat length, upper and lower lip thickness, upper lip length, and lower lip–chin length), decreased (were interlabial gap and mandibular sulcus contour) or remained constant (facial profile angle, nasolabial angle, lower face percentage, chin-throat/lower face height, lower face–throat angle, upper incisor exposure, maxillary sulcus contour, and protrusion of both the upper and lower lips) between age 6 to 18 years old [48]. On another study that investigated the changes on 4 cephalometric angles: SNA, SNB, ANB, and SN/GoMe, found that All 4 angles showed linear changes over time. SNA (0.1-0.3 per year) and SNB (0.2-0.4 per year) increased, whereas ANB (0.1-0.2 per year) and SN/GoMe (0.2-0.6) decreased [49]. Our results showed that ML-NSL angle results increased over time, and these can be corresponding with van Diepenbeek et al. results that showed an increase in SNA angle over time (40).

Our results showed that there are many differences between males and females within class III patients, these variations were in PFH/AFH ratio, SNB angle, SN-Pg angle, NL-NSL angle, andML-NSL angle. Taner et al. [47] research found that male and female subjects were found to have similar maxillary and mandibular Vertical and Sagittal location, except R2PNS and R2ANT, which were larger in males. When comparing class III age effect, the results showed that the parameters +1/NL angle, +1/SNL angle, and +1/NA (mm), among patients that were older than 21, were significantly higher than younger patients. Whereas a contradicted relation was demonstrated in the parameters Wits appraisal, and interincisal angle, that showed that patients that were older than 21, were significantly lower than younger patients.

Our results also showed that patients aged 14-20 were significantly higher than pediatric patients aged 0-13 in the parameters - +1/NL angle, +1/SNL angle, and +1/NA (mm). And finally, patients aged 14-20 were significantly lower than pediatric patients aged 0-13 in the Wits appraisal values. These results aligned with Diepenbeek et al. [49], that found changes in 4 cephalometric angles, a changes that indicate the trends in facial and dental development as subjects grow in age. The results demonstrated the clear differences between class II and III in all sub-groups of gender and age in the Calculated_ANB parameter, in all comparisons class II results were significantly higher than class III. No differences were found between the gender and age groups within the same class. Our Calculated_ANB results are consistent with many previous studies. In a previous research that study the differences between class III treatment plans (surgery or not), the results showed that both class III patients that didn’t need surgery, and those who need surgery, have a negative mean of Calculated_ANB (-3.85 and -7.47 respectively) [50]. Klocke et al. [51] study patterns in the primary dentition among class II patients, and found that the mean of Individualized ANB (in different equation) for two research groups of class II are 3.9 and 3.5 respectively. The results showed that both class II and III cephalometric parameters demonstrated many correlations between parameters. We can see a strong significant correlation between parameters in the same dimension. In both classes, the results demonstrated many correlations between Calculated_ANB and other parameters, among these correlations in class II patients –SNB angle, ANB angle, SN-Pg angle, Wits appraisal, and -1/ML, -1/NB angle. These results also demonstrated correlations between Calculated_ANB and many parameters in class III patients- facial axis, SNB angle, ANB angle, SN-Pg angle, Wits appraisal, +1/NL angle, +1/SNL angle, +1/NA angle, and -1/ML angel.

Previous report by Jan et al. [52] showed that bivariate analysis demonstrated that the ANB angle and Wits appraisal were significantly correlated (ρ=0.469, P=0.00). Moreover, another study showed that statistically significant correlations were found among seven sagittal parameters. The correlation was very strong between AXB and AF-BF distance, A-B plane and ANB angle, AXB and FABA, and AF-BF distance and FABA, whereas, there was a weak correlation between ANB and beta angle [53]. In a study that was performed by Saad et al. [54], found that the measurement with most statistically significant and highly correlated relationship with Calculated_ANB (with different formula) is ANB angle followed by Wits appraisal value. In addition, this study found that Calculated_ANB has not significantly correlation with SNA or SN-GoMe angles.

To estimate better our data structure, and to gain thorough knowledge about the most informative and variant parameters in our data, we conducted a PCA analysis for our data, included all cephalometric parameters. The results of the PCA were very satisfying, PC1 explains about half of the variations, and the addition of PC2+PC3+PC4 explained 90.67% of the variance in our data. Regarding the main variables that contributed to the first two PCs, the results demonstrated that in the first PC the variable ML-NSL angle has high positive values. And a negative value for SN-Pg angle, SNB angle, facial axis, and PFH/AFH ration.. In the second component, the parameters with a positive high value the parameters gonial angle, ML-NSL, and NL-ML angle, and parameters with high negative values are -1/ML, Wits appraisal, Calculated_ANB, and ANB angle.

In a previous study that performed PCA to cephalometric results, 68.2% of the total sample variability was explained in the first 5 principal components. The most significant principal component, accounting for 29% explaining the variability, was the divergence of skeletal pattern; the second principal component, adding 20% for variability, was the anteroposterior maxillary relationship [55]. Furthermore, a previous study that used 16 measurements using Steiner analysis [21], identified 5 principal components, which cover 88.545% from the total variance of variables, The rotated components matrix showed that the components correspond to the following measurements order: SND, Maxl-NA, 1I-NB S-E and ANB [56].

Our Machine Learning results demonstrated an approach that suggests using universal two cephalogram parameters that predict skeletal malocclusion with sufficient accuracy, to determine either it’s class II or III. The model that predicts the classification with 0.93 accuracy included Wits appraisal and SNB angle.

Taraji et al. [58] conducted a study involving 182 participants that aimed to identify critical morphological features in post circumpubertal Class III treatment and appraised the predictive ability of machine learning algorithms for diagnosing skeletal class III. Furthermore, the authors stated that there were no statistical differences in demographic characteristics between the two groups (P > .05), which is in line with our findings. The present results suggest that neither gender nor age did significantly contribute to the variability of the presented model. In the same study, Wit's appraisal, anterior overjet, and Mx/Md ratio were found as a key predictors [58].

Based on the results and new data revealed, we were able to conclude that:1. There was gender and age effect in class II and III patients; 2. The heatmap correlations revealed that there are many correlations between Calculated_ANB and other cephalometric parameters; 3. PCA can be an amazingly effective tool to simplify many parameters to two PCs that explains about 67% of the variability; 4. Wits appraisal and SNB angle predict the classification in a remarkably high accuracy Machine Learning Model (0.93); and finally 5.The gender and age did not improve the accuracy, but they may still important for the diagnosis process. In summary, the study provides valuable insights into the complex nature of malocclusions and presents machine learning as a promising approach for advancing of personalized orthodontic diagnostics and treatment.

Author Contributions: Conceptualization, F.A.I., P.P. and N.W.; methodology, I.M.L., O.Z., K.M.,O.A., S.M., S.K., A.W, E.P. and C.K.; validation, F.A.I.; investigation, I.M.L., O.Z., K.M., N.W., O.A., S.M., S.K. and C.K.; resources, F.A.I., P.P., N.W., S.K. and C.K.; data curation, I.M.L., O.Z. and K.M.; writing—original draft preparation, K.M. and I.M.L.; writing—review and editing, P.P., N.W. and F.A.I.; supervision, F.A.I., P.P. and N.W.; project administration, F.A.I.; funding acquisition, F.A.I., P.P. and N.W. All authors have read and agreed to the published version of the manuscript.

Funding: This study was supported by a core fund from Tel Aviv University, orthodontic research center, and the University Hospital of Regensburg.

Institutional Review Board Statement: According to current guidelines and following the Ethics Committee of the University of Regensburg ethics and regulations, the committee reviewed and approved this research project and study design with approval number 19-1596-101 (dated 13.11.2019)

Informed Consent Statement: Informed consent was obtained from all subjects involved in the study, as shown in supplement # 2.

Data Availability Statement: Data can be accessed via the corresponding author.

Conflicts of Interest: The authors declare no conﬂict of interest.

Cenzato N, Nobili A, Maspero C (2021) Prevalence of dental malocclusions in different geographical areas: scoping review. Dentistry J 9. https://doi.org/10.3390/dj9100117
Lone IM, Zohud O, Midlej K et al (2023) Skeletal Class II Malocclusion: From Clinical Treatment Strategies to the Roadmap in Identifying the Genetic Bases of Development in Humans with the Support of the Collaborative Cross Mouse Population. J Clin Med 12. https://doi.org/10.3390/jcm12155148
Balachandran P, Janakiram C (2021) Prevalence of malocclusion among 8–15 years old children, India - A systematic review and meta-analysis. J Oral Biol Craniofac Res 11:192–199. https://doi.org/10.1016/j.jobcr.2021.01.011
Lombardo G, Vena F, Negri P et al (2020) Worldwide prevalence of malocclusion in the different stages of dentition: A systematic review and meta-analysis. Eur J Paediatr Dent 21:115–122. https://doi.org/10.23804/ejpd.2020.21.02.05
Lone IM, Midlej K, Zohud O et al (2024) Global Map of Skeletal and Dental Malocclusion Prevalence: From Classes to Continents. J Dentistry Oral Disorders 10:1183
Zohud O, Lone IM, Midlej K et al (2023) Towards genetic dissection of skeletal class III malocclusion: A review of genetic variations underlying the phenotype in humans and future directions. J Clin Med 12. https://doi.org/10.3390/jcm12093212
Lone IM, Zohud O, Nashef A et al (2023) Dissecting the Complexity of Skeletal-Malocclusion-Associated Phenotypes: Mouse for the Rescue. Int J Mol Sci 24. https://doi.org/10.3390/ijms24032570
Maspero C, Galbiati G, Giannini L et al (2018) Class II division 1 malocclusions: comparisons between one- and two-step treatment. Eur J Paediatr Dent 19:295–299. https://doi.org/10.23804/ejpd.2018.19.04.8
Katz CRT, Rosenblatt A, Gondim PPC (2004) Nonnutritive sucking habits in Brazilian children: effects on deciduous dentition and relationship with facial morphology. Am J Orthod Dentofac Orthop 126:53–57. https://doi.org/10.1016/j.ajodo.2003.06.011
Peres KG, Barros AJD, Peres MA, Victora CG (2007) Effects of breastfeeding and sucking habits on malocclusion in a birth cohort study. Rev Saude Publica 41:343–350. https://doi.org/10.1590/s0034-89102007000300004
Heimer MV, Tornisiello Katz CR, Rosenblatt A (2008) Non-nutritive sucking habits, dental malocclusions, and facial morphology in Brazilian children: a longitudinal study. EORTHO 30:580–585. https://doi.org/10.1093/ejo/cjn035
de Sousa RV, Pinto-Monteiro AK, de Martins A CC, et al (2014) Malocclusion and socioeconomic indicators in primary dentition. Braz Oral Res 28:54–60. https://doi.org/10.1590/s1806-83242013005000032
George AM, Felicita AS, Milling Tania SD, Priyadharsini JV (2021) Systematic review on the genetic factors associated with skeletal Class II malocclusion. Indian J Dent Res 32:399–406. https://doi.org/10.4103/ijdr.IJDR_59_20
Rathi S, Gilani R, Kamble R, Bhandwalkar S (2022) Temporomandibular joint disorder and airway in class II malocclusion: A review. Cureus 14:e30515. https://doi.org/10.7759/cureus.30515
Schiffman EL, Truelove EL, Ohrbach R et al (2010) The Research Diagnostic Criteria for Temporomandibular Disorders. I: overview and methodology for assessment of validity. J Orofac Pain 24:7–24
Manfredini D, Lombardo L, Siciliani G (2017) Temporomandibular disorders and dental occlusion. A systematic review of association studies: end of an era? J Oral Rehabil 44:908–923. https://doi.org/10.1111/joor.12531
Dworkin SF, LeResche L (1992) Research diagnostic criteria for temporomandibular disorders: review, criteria, examinations and specifications, critique. J Craniomandib Disord 6:301–355
Dehesa-Santos A, Iber-Diaz P, Iglesias-Linares A (2021) Genetic factors contributing to skeletal class III malocclusion: a systematic review and meta-analysis. Clin Oral Investig 25:1587–1612. https://doi.org/10.1007/s00784-020-03731-5
Liu J, Chen Y, Li S et al (2021) Machine learning in orthodontics: Challenges and perspectives. Adv Clin Exp Med 30:1065–1074. https://doi.org/10.17219/acem/138702
Manosudprasit A, Haghi A, Allareddy V, Masoud MI (2017) Diagnosis and treatment planning of orthodontic patients with 3-dimensional dentofacial records. Am J Orthod Dentofac Orthop 151:1083–1091. https://doi.org/10.1016/j.ajodo.2016.10.037
Steiner CC (1953) Cephalometrics for you and me. Am J Orthod 39:729–755. https://doi.org/10.1016/0002-9416(53)90082-7
Jacobson A (1975) The Wits appraisal of jaw disharmony. Am J Orthod 67:125–138. https://doi.org/10.1016/0002-9416(75)90065-2
Panagiotidis G, Witt E (1977) Der individualisierte ANB-Winkel. Fortschr der Kieferorthopädie 38:408–416. https://doi.org/10.1007/BF02163219
Järvinen S (1986) Floating norms for the ANB angle as guidance for clinical considerations. Am J Orthod Dentofac Orthop 90:383–387. https://doi.org/10.1016/0889-5406(86)90004-1
Järvinen S (1988) Relation of the Wits appraisal to the ANB angle: A statistical appraisal. Am J Orthod Dentofac Orthop 94:432–435. https://doi.org/10.1016/0889-5406(88)90134-5
Paddenberg E, Proff P, Kirschneck C (2023) Floating norms for individualising the ANB angle and the WITS appraisal in orthodontic cephalometric analysis based on guiding variables. J Orofac Orthop 84:10–18. https://doi.org/10.1007/s00056-021-00322-1
Dehesa-Santos A, Park J-A, Lee S-J, Iglesias-Linares A (2024) East Asian and Southern European craniofacial class III phenotype: two sides of the same coin? Clin Oral Investig 28:84. https://doi.org/10.1007/s00784-023-05386-4
Sivakumar A, Nalabothu P, Thanh HN, Antonarakis GS (2021) A Comparison of Craniofacial Characteristics between Two Different Adult Populations with Class II Malocclusion-A Cross-Sectional Retrospective Study. Biology (Basel) 10:. https://doi.org/10.3390/biology10050438
Asiri SN, Tadlock LP, Buschang PH (2019) The prevalence of clinically meaningful malocclusion among US adults. Orthod Craniofac Res 22:321–328. https://doi.org/10.1111/ocr.12328
Lone IM, Zohud O, Midlej K et al (2023) Anterior Open Bite Malocclusion: From Clinical Treatment Strategies towards the Dissection of the Genetic Bases of the Disease Using Human and Collaborative Cross Mice Cohorts. J Pers Med 13. https://doi.org/10.3390/jpm13111617
Shin W, Yeom H-G, Lee GH et al (2021) Deep learning based prediction of necessity for orthognathic surgery of skeletal malocclusion using cephalogram in Korean individuals. BMC Oral Health 21:130. https://doi.org/10.1186/s12903-021-01513-3
Xanthopoulos P, Pardalos PM, Trafalis TB (2013) Linear Discriminant Analysis. Robust Data Mining. Springer New York, New York, NY, pp 27–33
Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20:273–297. https://doi.org/10.1007/BF00994018
Pisner DA, Schnyer DM (2020) Support vector machine. Machine Learning. Elsevier, pp 101–121
Cover T, Hart P (1967) Nearest neighbor pattern classification. IEEE Trans Inf Theory 13:21–27. https://doi.org/10.1109/TIT.1967.1053964
Qahaz N, Lone IM, Khadija A et al (2023) Host genetic background effect on body weight changes influenced by heterozygous smad4 knockout using collaborative cross mouse population. Int J Mol Sci 24. https://doi.org/10.3390/ijms242216136
Breiman L (2001) Random Forests. Springer Science and Business Media LLC. https://doi.org/10.1023/a:1010933404324
Lone IM, Nun NB, Ghnaim A et al (2023) High-fat diet and oral infection induced type 2 diabetes and obesity development under different genetic backgrounds. Anim Models Exp Med 6:131–145. https://doi.org/10.1002/ame2.12311
Krzywinski M, Altman N (2017) Points of significance: Classification and regression trees. Nat Methods 14:757–758. https://doi.org/10.1038/nmeth.4370
Cawley GC, Talbot NLC (2010) On over-fitting in model selection and subsequent selection bias in performance evaluation. The Journal of Machine Learning Research
Lone IM, Midlej K, Nun NB, Iraqi FA (2023) Intestinal cancer development in response to oral infection with high-fat diet-induced Type 2 diabetes (T2D) in collaborative cross mice under different host genetic background effects. Mamm Genome 34:56–75. https://doi.org/10.1007/s00335-023-09979-y
Fisher A, Rudin C, Dominici F (2019) All models are wrong, but many are useful: learning a variable’s importance by studying an entire class of prediction models simultaneously. J Mach Learn Res 20. https://doi.org/10.48550/arxiv.1801.01489
Watted N, Lone IM, Zohud O et al (2023) Comprehensive Deciphering the Complexity of the Deep Bite: Insight from Animal Model to Human Subjects. J Pers Med 13. https://doi.org/10.3390/jpm13101472
Lau JW, Hägg U (1999) Cephalometric morphology of Chinese with Class II division 1 malocclusion. Br Dent J 186:188–190. https://doi.org/10.1038/sj.bdj.4800059
Sharma BP, Xin C (2014) Comparative Cephalometric Analysis of Angle Class II Division 1 Malocclusion Between Nepalese and Chinese Subjects. Orthodontic Journal of Nepal
Taner L, Gürsoy GM, Uzuner FD (2019) Does gender have an effect on craniofacial measurements? Turkish J Orthod 32:59–64. https://doi.org/10.5152/TurkJOrthod.2019.18031
Bergman RT, Waschak J, Borzabadi-Farahani A, Murphy NC (2014) Longitudinal study of cephalometric soft tissue profile traits between the ages of 6 and 18 years. Angle Orthod 84:48–55. https://doi.org/10.2319/041513-291.1
van Diepenbeek AF, Buschang PH, Prahl-Andersen B (2009) Age-dependant cephalometric standards as determined by multilevel modeling. Am J Orthod Dentofac Orthop 135:79–87. https://doi.org/10.1016/j.ajodo.2006.11.025
Stellzig-Eisenhauer A, Lux CJ, Schuster G (2002) Treatment decision in adult patients with Class III malocclusion: orthodontic therapy or orthognathic surgery? Am J Orthod Dentofac Orthop 122:27–37 discussion 37. https://doi.org/10.1067/mod.2002.123632
Klocke A, Nanda RS, Kahl-Nieke B (2002) Skeletal Class II patterns in the primary dentition. Am J Orthod Dentofac Orthop 121:596–601. https://doi.org/10.1067/mod.2002.122827
Jan A, Bangash AA, Shinwari S (2017) THE CORRELATION BETWEEN WITS AND ANB CEPHALOMETRIC LANDMARKS IN ORTHODONTIC PATEINTS. Pakistan Armed Forces Medical Journal
Gul-e-Erum, Fida M (2008) A comparison of cephalometric analyses for assessing sagittal jaw relationship. J Coll Physicians Surg Pak 18:679–683
Saad A, Saqib N, Hamid WU (2007) Corelaton of corrected ANB angle with other sagital discrepancy indicators
Halazonetis DJ (2004) Morphometrics for cephalometric diagnosis. Am J Orthod Dentofac Orthop 125:571–581. https://doi.org/10.1016/j.ajodo.2003.05.013
Dascalu CG, Zegan G Statistical methods for variables space reduction in cephalometric studies. In: 2013 E-Health and, Conference B (2013) (EHB). IEEE, pp 1–4
Zhou Y, Mao B, Zhang J et al (2023) Orthodontic craniofacial pattern diagnosis: cephalometric geometry and machine learning. Med Biol Eng Comput. https://doi.org/10.1007/s11517-023-02919-7
Taraji S, Atici SF, Viana G et al (2023) Novel machine learning algorithms for prediction of treatment decisions in adult patients with class III malocclusion. J Oral Maxillofac Surg 81:1391–1402. https://doi.org/10.1016/j.joms.2023.07.137

Table 1A.

	Class II
Variable	N	M	Std. Dev.	Min	Pctl. 25	Pctl. 75	Max
Age	283	17	6.6	7	13	20	44
0<Age<13	89	31%
14<Age<20	130	46%
Age>21	64	23%
Female	188	66%
Male	95	34%
NL-ML angle	283	28	6.6	8.6	24	33	54
NL-NSL	283	8.1	3.6	1	6	9.9	42
PFH/AFH	283	65	5.4	50	62	68	82
gonialangle	283	129	7.6	106	124	134	150
Facial axis	283	88	4.6	70	85	91	102
SNA angle	283	83	3.7	74	80	85	94
SNB angle	283	76	5.2	7.8	74	78	84
ANB angle	283	7	5	-1.3	5.3	8.2	83
ANB_ind	283	5.2	1.6	1.5	4.1	6.3	10
Calculated_ANB (ANB – ANB_ind)	283	1.8	4.7	-4.9	1.1	2.3	76
SN-Ba angle	283	130	5.3	118	126	133	147
SN-Pg angle	283	77	3.6	65	74	79	86
S-N (mm)	283	60	12	20	58	64	92
Go-Me (mm)	283	56	11	19	53	61	90
Wits appraisal (mm)	283	-2.1	2.7	-12	-3.6	-0.1	3.9
ML-NSL angle	283	36	7.2	4.6	32	40	63
+1/NL angle	283	113	7.5	91	108	119	135
+1/SNL angle	283	105	8.2	78	100	110	125
+1/NA angle	283	22	12	-121	17	28	42
+1/NA (mm)	283	3.1	2.4	-2.8	1.3	4.7	13
-1/ML (anatomic)	283	95	9.3	9.5	91	101	120
-1/NB angle	283	28	7.4	3.4	24	33	50
-1/NB (mm)	283	5.6	3.1	-1.4	3.6	7.3	28
Interincisal angle	283	123	11	100	115	130	163

Table 1B.

	Class III
Variable	N	Mean	Std. Dev.	Min	Pctl. 25	Pctl. 75	Max
Age	300	18	8	6	13	22	54
0<Age<13	77	26%
14<Age<20	131	44%
Age>21	92	31%
Female	160	53%
Male	140	47%
NL-ML angle	300	29	6.8	12	24	33	55
NL-NSL	300	7.7	3.4	-1.7	5.3	10	18
PFH/AFH	300	65	5.7	50	61	69	82
Gonial_angle	300	135	7.9	110	130	141	160
Facial axis	300	91	5.5	73	88	95	104
SNA angle	300	82	4.1	70	79	85	94
SNB angle	300	82	4.8	66	79	85	95
ANB angle	300	-0.29	3	-8.1	-2.1	1.6	11
ANB_ind	300	4.9	1.6	-0.4	3.8	5.9	8.6
Calculated_ANB	300	-5.2	2.5	-12	-6.8	-3.6	3.2
SN-Ba angle	300	127	5.8	104	123	132	145
SN-Pg angle	300	82	5.1	64	79	86	95
S-N (mm)	300	58	12	10	56	64	95
Go-Me (mm)	300	58	13	10	54	65	100
Wits appraisal (mm)	300	-11	4.6	-25	-14	-7.5	1.2
ML-NSL angle	300	37	8.1	14	31	41	85
+1/NL angle	300	116	7.3	96	112	121	138
+1/SNL angle	300	108	13	10	103	114	135
+1/NA angle	299	27	7.3	7.7	22	31	66
+1/NA (mm)	299	4.4	3.4	-2.6	2.6	5.6	44
-1/ML (anatomic)	299	87	7.8	62	82	92	105
-1/NB angle	299	25	7	3.5	21	30	41
-1/NB (mm)	299	5.2	6.4	-0.8	2.6	6.4	97
Dental Interincisal angle	299	128	11	100	120	135	156

Table 2A.

Parameter	Group A _ Group B	Difference	Lower CI	Upper CI	Adj. P value
NL-NSL angle	III_Male-III_Female	-1.21	-2.24	-0.18	0.01
PFH/AFH	III_Male-III_Female	2.86	1.23	4.50	0.00
SNB angle	III_Male-III_Female	1.74	0.25	3.23	0.01
SN-Pg angle	III_Male-III_Female	2.13	0.84	3.43	0.00
ML-NSL angle	III_Male-III_Female	-3.30	-5.56	-1.04	0.00

Table 2B.

Parameter	Group A _ Group B	Difference	Lower CI	Upper CI	Adj. P value
Class II
NL-ML angle	II_Age>21-II_14<Age<20	4.51	1.63	7.40	0.00
ML-NSL angle	II_Age>21-II_14<Age<20	4.03	0.72	7.35	0.01
PFH/AFH	II_Age>21-II_14<Age<20	-2.42	-4.83	0.00	0.05
Facial axis	II_Age>21-II_0<Age<13	-2.65	-5.01	-0.29	0.02
Facial axis	II_Age>21-II_14<Age<20	-2.93	-5.13	-0.73	0.00
Gonial angle	II_14<Age<20-II_0<Age<13	-3.28	-6.31	-0.26	0.02
+1/NA angle	II_14<Age<20-II_0<Age<13	-4.24	-7.99	-0.48	0.02
+1/NA (mm)	II_14<Age<20-II_0<Age<13	-1.16	-2.30	-0.02	0.04
Class III
+1/NL angle	III_Age>21-III_0<Age<13	4.30	1.09	7.51	0.00
+1/SNL angle	III_Age>21-III_0<Age<13	5.89	1.22	10.56	0.00
+1/NA (mm)	III_Age>21-III_0<Age<13	1.44	0.16	2.73	0.02
Wits appraisal (mm)	III_Age>21-III_0<Age<13	-2.14	-3.82	-0.46	0.00
Interincisal angle	III_Age>21-III_0<Age<13	-5.55	-10.45	-0.66	0.02
+1/NL angle	III_14<Age<20-III_0<Age<13	3.87	0.89	6.86	0.00
+1/SNL angle	III_14<Age<20-III_0<Age<13	6.07	1.72	10.41	0.00
+1/NA (mm)	III_14<Age<20-III_0<Age<13	1.45	0.25	2.64	0.01
Wits appraisal (mm)	III_14<Age<20-III_0<Age<13	-1.70	-3.27	-0.14	0.02

Table 2C.

Parameter	Group A _ Group B	Difference	Lower CI	Upper CI	Adj. P value
Class II
NL-ML angle	II_Female_Age>21-II_Female_14<Age<20	4.99	1.19	8.80	0.00
ML-NSL angle	II_Female_Age>21-II_Female_14<Age<20	4.71	0.37	9.05	0.02
-1/NB angle	II_Female_Age>21-II_Female_0<Age<13	5.20	0.51	9.88	0.02
Facial axis	II_Female_Age>21-II_Female_14<Age<20	-3.45	-6.36	-0.55	0.01
+1/NA angle	II_Male_14<Age<20-II_Male_0<Age<13	-7.61	-14.50	-0.73	0.02
-1/ML (anatomic)	II_Female_14<Age<20-II_Female_0<Age<13	5.89	0.91	10.86	0.01
Class III
Wits appraisal (mm)	III_Male_Age>21-III_Male_0<Age<13	-2.78	-5.47	-0.10	0.03
PFH/AFH	III_Male_14<Age<20-III_Female_14<Age<20	3.45	0.28	6.63	0.02
Additional Variations
SN-ML angle	III_Male_14<Age<20-III_Female_Age>21	-5.07	-9.89	-0.26	0.03
PFH/AFH	III_Male_14<Age<20-III_Female_Age>21	4.50	0.81	8.19	0.00
Facial axis	II_Male_0<Age<13-II_Female_Age>21	3.62	0.14	7.11	0.03
SN-Pg angle	III_Male_Age>21-III_Female_0<Age<13	3.55	0.52	6.58	0.01
SN-Pg angle	III_Male_Age>21-III_Female_14<Age<20	2.76	0.20	5.32	0.02
+1/NL angle	III_Male_Age>21-III_Female_0<Age<13	6.16	1.08	11.24	0.00
+1/SNL angle	III_Male_14<Age<20-III_Female_0<Age<13	8.35	1.02	15.67	0.01
+1/SNL angle	III_Male_Age>21-III_Female_0<Age<13	9.71	2.32	17.09	0.00
+1/NA angle	II_Male_14<Age<20-II_Female_0<Age<13	-7.21	-13.77	-0.66	0.02

Table 2D.

Calculated_ANB - Group A _ Group B	Difference	Lower CI	Upper CI	Adj. P value
III_Female-II_Female	-6.94	-7.96	-5.91	0.00
III_Male-II_Female	-7.39	-8.45	-6.33	0.00
III_Female-II_Male	-6.38	-7.61	-5.15	0.00
III_Male-II_Male	-6.84	-8.10	-5.57	0.00
III_0<Age<13-II_0<Age<13	-5.89	-7.53	-4.25	0.00
III_14<Age<20-II_0<Age<13	-6.65	-8.09	-5.20	0.00
III_Age>21-II_0<Age<13	-7.19	-8.76	-5.62	0.00
III_0<Age<13-II_14<Age<20	-6.58	-8.10	-5.06	0.00
III_14<Age<20-II_14<Age<20	-7.33	-8.64	-6.03	0.00
III_Age>21-II_14<Age<20	-7.88	-9.31	-6.44	0.00
III_0<Age<13-II_Age>21	-6.01	-7.79	-4.22	0.00
III_14<Age<20-II_Age>21	-6.76	-8.37	-5.15	0.00
III_Age>21-II_Age>21	-7.30	-9.02	-5.59	0.00
III_Female_0<Age<13-II_Female_0<Age<13	-5.53	-8.13	-2.93	0.00
III_Female_14<Age<20-II_Female_0<Age<13	-6.55	-8.76	-4.35	0.00
III_Female_Age>21-II_Female_0<Age<13	-6.78	-9.33	-4.24	0.00
III_Male_0<Age<13-II_Female_0<Age<13	-6.18	-8.80	-3.56	0.00
III_Male_14<Age<20-II_Female_0<Age<13	-6.68	-9.09	-4.27	0.00
III_Male_Age>21-II_Female_0<Age<13	-7.45	-9.89	-5.02	0.00
III_Female_0<Age<13-II_Female_14<Age<20	-6.67	-9.00	-4.34	0.00
III_Female_14<Age<20-II_Female_14<Age<20	-7.70	-9.57	-5.82	0.00
III_Female_Age>21-II_Female_14<Age<20	-7.93	-10.20	-5.65	0.00
III_Male_0<Age<13-II_Female_14<Age<20	-7.32	-9.67	-4.97	0.00
III_Male_14<Age<20-II_Female_14<Age<20	-7.82	-9.94	-5.70	0.00
III_Male_Age>21-II_Female_14<Age<20	-8.60	-10.74	-6.45	0.00
III_Female_0<Age<13-II_Female_Age>21	-5.66	-8.24	-3.09	0.00
III_Female_14<Age<20-II_Female_Age>21	-6.69	-8.86	-4.51	0.00
III_Female_Age>21-II_Female_Age>21	-6.92	-9.44	-4.39	0.00
III_Male_0<Age<13-II_Female_Age>21	-6.31	-8.91	-3.72	0.00
III_Male_14<Age<20-II_Female_Age>21	-6.81	-9.20	-4.42	0.00
III_Male_Age>21-II_Female_Age>21	-7.59	-10.00	-5.18	0.00
III_Female_0<Age<13-II_Male_0<Age<13	-5.63	-8.35	-2.90	0.00
III_Female_14<Age<20-II_Male_0<Age<13	-6.65	-9.00	-4.30	0.00
III_Female_Age>21-II_Male_0<Age<13	-6.88	-9.56	-4.20	0.00
III_Male_0<Age<13-II_Male_0<Age<13	-6.28	-9.02	-3.53	0.00
III_Male_14<Age<20-II_Male_0<Age<13	-6.77	-9.32	-4.23	0.00
III_Male_Age>21-II_Male_0<Age<13	-7.55	-10.12	-4.98	0.00
III_Female_0<Age<13-II_Male_14<Age<20	-5.40	-8.09	-2.70	0.00
III_Female_14<Age<20-II_Male_14<Age<20	-6.42	-8.73	-4.11	0.00
III_Female_Age>21-II_Male_14<Age<20	-6.65	-9.29	-4.01	0.00
III_Male_0<Age<13-II_Male_14<Age<20	-6.05	-8.76	-3.33	0.00
III_Male_14<Age<20-II_Male_14<Age<20	-6.54	-9.06	-4.03	0.00
III_Male_Age>21-II_Male_14<Age<20	-7.32	-9.86	-4.78	0.00
III_Female_0<Age<13-II_Male_Age>21	-5.78	-9.66	-1.90	0.00
III_Female_14<Age<20-II_Male_Age>21	-6.80	-10.43	-3.18	0.00
III_Female_Age>21-II_Male_Age>21	-7.03	-10.88	-3.19	0.00
III_Male_0<Age<13-II_Male_Age>21	-6.43	-10.32	-2.54	0.00
III_Male_14<Age<20-II_Male_Age>21	-6.93	-10.68	-3.17	0.00
III_Male_Age>21-II_Male_Age>21	-7.70	-11.47	-3.93	0.00

Table 3A.

	Comp.1	Comp.2	Comp.3	Comp.4
Standard deviation	1.22	0.78	0.67	0.523
Proportion of Variance	0.47	0.19	0.14	0.08
Cumulative Proportion	0.47	0.67	0.81	0.90

Table 3B.

Parameter	Comp.1	Comp.2	Comp.3	Comp.4
NL-ML angle	0.26	0.28	0.18	0.16
NL-NSL	0.16	0.07	-0.11	-0.24
PFH/AFH	-0.29	-0.28	-0.09	0.03
Gonial angle	0.09	0.36	0.12	0.17
Facial axis	-0.32	-0.06	-0.07	-0.06
SNA angle	-0.15	-0.23	0.13	0.39
SNB angle	-0.32	0.07	0.04	0.22
ANB angle	0.25	-0.29	0.04	0.10
ANB_ind	0.14	0.04	0.23	0.42
Calculated_ANB (ANB – ANB_ind)	0.23	-0.33	-0.03	-0.02
SN-Ba angle	0.18	0.00	-0.07	-0.29
SN-Pg angle	-0.37	0.04	0.02	0.20
S-N (mm)	0.00	0.00	-0.06	-0.30
Go-Me (mm)	-0.07	0.06	-0.05	-0.28
Wits appraisal (mm)	0.19	-0.37	0.00	0.03
ML-NSL angle	0.30	0.30	0.11	0.03
+1/NL angle	-0.20	0.02	0.34	-0.18
+1/SNL angle	-0.20	-0.03	0.31	-0.06
+1/NA angle	-0.16	0.09	0.30	-0.25
+1/NA (mm)	-0.12	0.13	0.28	-0.27
-1/ML (anatomic)	0.06	-0.39	0.17	-0.13
-1/NB angle	0.14	-0.17	0.36	0.05
-1/NB (mm)	0.07	-0.01	0.25	-0.01
Interincisal angle	-0.07	0.14	-0.47	0.12

Table 4.

	Wits appraisal (mm)	SNB angle	SN-Pg angle	Best Model	Accuracy	Kappa
All parameters included - general model				LDA	0.95	0.91
Model 1	(+)	(-)	(-)	LDA, SVM	0.90	0.80
Model 2	(+)	(+)	(-)	KNN	0.93	0.86
Model 3	(+)	(+)	(+)	KNN	0.93	0.86

No competing interests reported.

Lateral Cephalometric Parameters Variations and Machine Learning Models Among Skeletal Class II & III Malocclusion of Arab Orthodontic Patients

Status:

Journal Publication

Version 1

Abstract

Figures

Introduction

Material and Methods

Cephalometric variables

Results

Discussion

Conclusion and future research

Declarations

References

Tables

Additional Declarations

Supplementary Files

Status:

Journal Publication

Version 1