Until now, the literature does not provide an accurate model to predict the future need for orthognathic surgery in prepubertal patients with class III malocclusion. Because not all of these patients are candidates for later surgical correction, patient assessment and selection remain arbitrary with respect to diagnosis and treatment planning. The purpose of the present investigation was to analyze the value of classifying class III children before puberty into patients who can be effectively treated by orthopedic/orthodontic therapy alone and those who require orthognathic surgery. To obtain a robust model, the study design was multicentric (University Orthodontic Departments of Frankfurt, Heidelberg, and Würzburg). A total of 88 patients with class III malocclusion were grouped into orthopedic/orthodontic (n = 65) and surgery patients (n = 23), according to their records after puberty (mean age, 17 years three months). Discriminant analysis (DA) and logistic regression (LogR) were applied to 20 landmarks of the patients' cephalograms before puberty (mean age, nine years eight months) to identify the dentoskeletal variables that provide the best group separation and the best predictability of group membership, respectively. Both models were highly significant (P < .001), classifying 93.3% (DA) and 94.3% (LogR) of the patients correctly. The extracted variables were identical for both procedures: Wits appraisal, palatal plane angle, and individualized inclination of the lower incisors. The resulting equation of LogR was individual score = −7.968 − 1.323Wits − 0.363NL-NSL + 0.153[180 − (L1-ML) − (L1-MLind)]. We concluded that by means of multivariate statistics, prepubertal children with class III malocclusions may be classified into nonsurgery and surgery patients with high accuracy.

Class III malocclusion is one of the most severe dentofacial anomalies. Individuals with class III malocclusion frequently show combinations of skeletal and dentoalveolar components.1 Moreover, there are complex interactions of genetic and environmental factors, which may act synergistically or in isolation, or may cancel each other out.2 Compared with class I subjects, several aberrant cephalometric measurements have been reported in class III malocclusion patients, such as a shorter anterior cranial base length, a more acute cranial base angle, a shorter and more retrusive maxilla, more proclined maxillary incisors, more retroclined mandibular incisors, an excess of lower anterior face height, and a more obtuse gonial angle.2–8 Because no single morphologic feature is indicative of class III development, treatment outcome is extremely difficult to predict in class III children.9 

Ricketts10 introduced the computer-assisted growth prognosis—the so-called visual treatment objective—for prediction of individual treatment outcome. This method is based on empirically obtained mean growth increments, anticipating the influence of orthodontic treatment. However, the prognostic power of dental relationships, dentoskeletal relations, or soft-tissue configurations at the end of treatment was limited.11,12 In particular, overestimation of treatment influences was considered to be responsible for the low predictability of this method.13 Moreover, accurate individualized growth prediction was regarded as nearly impossible because of the diversity and variability of facial growth.14–16 

Because of the complexity of class III malocclusion, univariate statistical techniques turned out to be insufficient for diagnosis, treatment planning, and outcome prognosis.17 Instead, recent studies suggested that the relations between craniofacial structure and occlusion would be analyzed best by using a multivariate approach.18–20 Logistic regression (LogR) is one multivariate procedure that estimates the likelihood of a certain event occurring or a group membership.21–24 In orthodontic literature most of the studies using multivariate statistics explored the potential of discriminant analysis (DA).25–28 DA is specially designed to separate two groups of individuals taken from the same population. Until now, it has been successfully applied to separate class III patients from class I subjects.18,29,30 Furthermore, DA was used to predict treatment outcome and relapse of orthodontically treated class III patients.20,28,31–36 

Recently, a formula was developed to classify adult class III patients into a group that is treatable solely orthodontically and a group that requires orthognathic surgery.37 However, to date the literature does not provide an accurate multivariate model to distinguish between growing class III patients who can be treated successfully by orthodontics/orthopedics alone and class III patients who require surgical treatment after termination of dentofacial growth. Because most of the class III malocclusion patients already have undergone orthodontic/orthopedic treatment in early infancy, prediction of future craniofacial growth is an essential issue in clinical orthodontics.

Therefore, the purpose of the present investigation was to develop a statistical model classifying class III children before puberty into patients who can be effectively treated by orthodontic/orthopedic therapy alone and those who require future orthognathic surgery.

Subjects

For a sufficiently stable model that is also applicable to patients outside the study, a large sample size is a prerequisite. For this reason, the present analysis was based on the data of three different orthodontic centers (Department of Orthodontics, University Dental School of Frankfurt, Heidelberg, and Würzburg). The three participating universities are located in the same region in the middle part of Germany. The concept and modality of treatment of class III children were similar. In all three centers, treatment of class III malocclusion starts as soon as the malocclusion is detected. Besides chin-caps and reverse headgears, functional appliances are used as a rule, followed by a fixed appliance at the end of pubertal growth. Because of this convergence, pooling of the records was applicable.

Patients with craniofacial disorders such as cleft palate or craniosynostosis were excluded.

The patients were all Caucasians and met the following criteria for inclusion into the retrospective study:

I. Initial records (plaster casts, cephalograms, extraoral pictures) before pubertal growth spurt (mean age, nine years eight months; standard deviation [SD], one year six months):

  • presence of a class III molar relationship;

  • negative overjet;

  • Wits appraisal ≤−1 mm;

  • negative difference between ANB angle and individualized ANB angle.38 

II. Final records (plaster casts, cephalograms, extraoral pictures) after puberty (mean age, 17 years three months; at least four years after the initial records).

Three experienced orthodontists grouped the final records into a nonsurgery and a surgery group. For allocation to the nonsurgery group, the following treatment outcome criteria had to be fulfilled:

  • stable occlusion in sagittal, transversal, and vertical dimension;

  • correct overjet and overbite;

  • proper incisal inclination;

  • satisfying facial esthetics;

  • long-term stability.

Accordingly, the material for the study comprised the cephalometric radiographs of 88 class III malocclusion patients, 39 boys and 49 girls.

The orthodontic group consisted of 65 patients and the surgery group, 23 patients.

Methods

Because the lateral cephalograms were taken with different X-ray devices, all linear measurements were corrected by their respective magnification factors. The same investigator traced all films with 20 landmarks (Figure 1) and digitized the data using appropriate software (WinCeph, Dentev Compudent, Koblenz, Germany).

FIGURE 1.

Hard-tissue landmarks used in the study: S indicates Sella; Po, porion; Ba, basion; Ar, articulare; Go, gonial intersection; Me, menton; Pog, pogonion; B, point B; L1 apex, apex of the lower central incisor; L1 tip, tip of the lower central incisor; U1 tip, tip of the upper central incisor; U1 apex, apex of the upper central incisor; A, point A; Ans, anterior nasal spine; Pns, posterior nasal spine; Ptm, pterygomaxillary fissure; Or, orbitale; N, nasion; ERP, ethmoid registration point; PocP, posterior point of the occlusal plane; and AocP, anterior point of the occlusal plane

FIGURE 1.

Hard-tissue landmarks used in the study: S indicates Sella; Po, porion; Ba, basion; Ar, articulare; Go, gonial intersection; Me, menton; Pog, pogonion; B, point B; L1 apex, apex of the lower central incisor; L1 tip, tip of the lower central incisor; U1 tip, tip of the upper central incisor; U1 apex, apex of the upper central incisor; A, point A; Ans, anterior nasal spine; Pns, posterior nasal spine; Ptm, pterygomaxillary fissure; Or, orbitale; N, nasion; ERP, ethmoid registration point; PocP, posterior point of the occlusal plane; and AocP, anterior point of the occlusal plane

Close modal

The following linear, proportional, and angular measurements were calculated (Figure 2a–e)—S-N: anteroposterior length of the cranial base; PoOr-NBa (∠): cranial deflection; ML-NSL (∠): divergence of the mandibular plane relative to the anterior cranial base; NSAr (∠): saddle angle; ArGoMe (∠): gonial angle; Goupper (∠): upper gonial angle; Golower (∠): lower gonial angle; SNB (∠): anteroposterior mandibular position to the anterior cranial plane; L1-ML (∠): axis of the lower incisor to the mandibular plane; individualized inclination of the lower incisors (∠) [180 − (L1-ML) − (L1-MLind)]: difference between 180° minus axis of the lower incisor to the mandibular plane and individualized L1-ML angle, according to the formula L1-MLind = 72.5 + 0.5ML-NL;39 Wits appraisal: length of the distance AO-BO (AO, intersection between a perpendicular line dropped from point A and the occlusal plane; BO, intersection between a perpendicular line dropped from point A and the occlusal plane); ANB (∠): anteroposterior relation of the maxilla and the mandible; ANB-ANBind (∠): difference between ANB angle and individualized ANB angle according to formula 7, ANBind = −35.16 + 0.4SNA + 0.2ML-NSL;38 M/M ratio: ratio of the anteroposterior length of the maxilla to the anteroposterior length of the mandible; NAPog (∠): angle of convexity; 1/1 (∠): angle between the axis of the upper and the lower incisor; SNA (∠): anteroposterior maxillary position to the anterior cranial plane; NL-NSL (∠): inclination of the palatal plane in relation to the anterior cranial base; U1-NSL (∠): axis of the upper incisor to the anterior cranial base; [(U1-NL) − (U1-NLind)] (∠): difference between the axis of the upper incisor to the palatal plane measured outside and the individualized U1-NL angle, according to the formula U1-NLind = 57.5 + 0.5ML-NL.39 

FIGURE 2.

Linear and angular cephalometric measurements used in the study: S-N (mm) indicates anteroposterior length of the cranial base; PoOr-NBa (∠), cranial deflection; ML-NSL (∠), divergence of the mandibular plane relative to the anterior cranial base; NSAr (∠), saddle angle; ArGoMe (∠), gonial angle; Goupper (∠), upper gonial angle; Golower (∠), lower gonial angle; SNB (∠), anteroposterior mandibular position to the anterior cranial plane; L1-ML (∠), axis of the lower incisor to the mandibular plane; Wits (mm), length of the distance AO-BO (AO, intersection between a perpendicular line dropped from point A and the occlusal plane; BO, intersection between a perpendicular line dropped from point A and the occlusal plane); ANB (∠), anteroposterior relation of the maxilla and the mandible; M/M ratio, ratio of the anteroposterior length of the maxilla to the anteroposterior length of the mandible; NAPog (∠), angle of convexity; U1/L1 1/1 (∠), angle between the axis of the upper and the lower incisors; SNA (∠), anteroposterior maxillary position to the anterior cranial plane; NL-NSL (∠), inclination of the palatal plane in relation to the anterior cranial base; U1-NSL (∠), axis of the upper incisor to the anterior cranial base; and U1-NL (∠), axis of the upper incisor to the palatal plane measured outside

FIGURE 2.

Linear and angular cephalometric measurements used in the study: S-N (mm) indicates anteroposterior length of the cranial base; PoOr-NBa (∠), cranial deflection; ML-NSL (∠), divergence of the mandibular plane relative to the anterior cranial base; NSAr (∠), saddle angle; ArGoMe (∠), gonial angle; Goupper (∠), upper gonial angle; Golower (∠), lower gonial angle; SNB (∠), anteroposterior mandibular position to the anterior cranial plane; L1-ML (∠), axis of the lower incisor to the mandibular plane; Wits (mm), length of the distance AO-BO (AO, intersection between a perpendicular line dropped from point A and the occlusal plane; BO, intersection between a perpendicular line dropped from point A and the occlusal plane); ANB (∠), anteroposterior relation of the maxilla and the mandible; M/M ratio, ratio of the anteroposterior length of the maxilla to the anteroposterior length of the mandible; NAPog (∠), angle of convexity; U1/L1 1/1 (∠), angle between the axis of the upper and the lower incisors; SNA (∠), anteroposterior maxillary position to the anterior cranial plane; NL-NSL (∠), inclination of the palatal plane in relation to the anterior cranial base; U1-NSL (∠), axis of the upper incisor to the anterior cranial base; and U1-NL (∠), axis of the upper incisor to the palatal plane measured outside

Close modal

Fifteen films were selected randomly, retraced, and redigitized on two separate occasions two weeks apart. The method error was calculated as recommended by Dahlberg.40 The method error in locating and measuring was calculated by the formula:

where d is the difference between two registrations of a pair and n the number of double registrations.

Random errors ranged from 0.02 to 0.81 mm for the linear measurements and from 0.38° to 1.93° for the angular variables.

Systematic error was tested at the 10% level of significance, as recommended by Houston,41 and no systematic errors were found.

Statistical analysis

Data analysis was performed using SPSS PC + (version 9.0), the Statistical Package for the Social Sciences.

The arithmetic means (mean), SDs, medians (median), minima (min), and maxima (max) were calculated for each variable and group before treatment (T1). To assess differences between the craniofacial features of both groups at the start of treatment, the data were compared using Mann-Whitney U-test for independent samples (Table 2).

TABLE 2.

Significant Differences Between the Patients of the Nonsurgery and the Surgery Groups at the Beginning of Treatment

Significant Differences Between the Patients of the Nonsurgery and the Surgery Groups at the Beginning of Treatment
Significant Differences Between the Patients of the Nonsurgery and the Surgery Groups at the Beginning of Treatment

For multivariate statistics two procedures were applied to the set of data:

1. Discriminant analysis—DA was used to identify those dento-skeletal variables that best separate the patients who need orthognathic surgery for correcting the malocclusion from those who do not.

To avoid redundancy among the various variables, stepwise variable selection was performed to obtain a model with the smallest possible set of significant cephalometric parameters. The independent variables were included in the model according to the 5% level of significance. The first variable selected was the one with the smallest value of Wilks' lambda, where lambda is the ratio of the within-group sum of squares divided by the total sum of squares. We chose the subsequent variables by recalculating lambda for each of the variables, and the variable with the next lowest value was selected. For each stage, a test was done to ascertain whether the inclusion of the respective variable in the model would significantly improve prediction.

Unstandardized discriminant function coefficients were calculated for each selected variable together with a constant. This leads to an equation that assigns a score to each patient. For each group, DA results in a mean score over all known cases in the relevant group. The dividing line halfway between these scores shows to which of the two groups an individual case belongs (critical score: mean value of group centroids of the two groups).

2. Logistic regression—LogR is a variation of ordinary regression, applicable when the observed outcome is restricted to two values, which represent the occurrence (where surgical intervention is necessary for correction of the class III anomaly) or nonoccurrence (where no surgical intervention is necessary for correction) of an outcome event. It produces a formula that predicts the probability of the occurrence of an event as a function of the independent variables. The global P-value of the final model was based on the likelihood ratio test, evaluating the total influence of all variables in the model. The P-values of the single variables that entered the model were calculated by the Wald test.

Because the study was based on lateral cephalometric landmarks only, the skeletal transverse component of class III malocclusion was not considered.

Univariate cephalometric analysis

Descriptive statistics for all cephalometric variables for both patient groups at T1 are listed in Table 1. The levels of significance at P-values of *P < .05, **P < .01, and ***P < .001 between the no surgery and the surgery groups are given in Table 2.

TABLE 1.

Means (mean), Standard Deviations (SDs), Medians (median), Minima (min), and Maxima (max) of the Nonsurgery and Surgery Groups at the Beginning of Treatment

Means (mean), Standard Deviations (SDs), Medians (median), Minima (min), and Maxima (max) of the Nonsurgery and Surgery Groups at the Beginning of Treatment
Means (mean), Standard Deviations (SDs), Medians (median), Minima (min), and Maxima (max) of the Nonsurgery and Surgery Groups at the Beginning of Treatment

Significant intergroup differences were found for parameters representing the sagittal maxillo-mandibular relationship as indicated by ANB, ANB-ANBind, and Wits appraisal. In addition, significant differences were given for length of the anterior cranial base, anteroposterior position of the mandible, ratio between length of the maxilla and length of the mandible and angle of convexity, lower gonial angle, individualized axis of the lower central incisors, and interincisal angle.

In contrast, there were no significant differences in the position and inclination of the upper jaw, the axis of the maxillary central incisors, the cranial deflection, as well as the parameters describing the direction of craniofacial growth (NL-NSL, ML-NSL, NSAr, Goupper) (Table 2).

Multivariate cephalometric analysis

Discriminant analysis

Stepwise variable selection of DA resulted in a significant model of three variables. The variables selected were Wits appraisal (F likelihood to remove = .000), NL-NSL (F likelihood to remove = .010), and [180 − (L1-ML) − (L1-MLind)] (F likelihood to remove = .020). Unstandardized discriminant function coefficients of the selected variables, along with a calculated constant (Table 3), led to the following equation that provides individual scores for the assignment of a new case to the nonsurgery or the surgery group:

The critical score was −0.653, which is the mean value of group centroids of the two groups (Table 3). Each new case with a class III malocclusion that will show an individual score higher than the critical score will probably be treated successfully by orthodontics/orthopedics alone. On the other hand, a new class III patient with a more negative individual score than the critical score should be treated by combined orthodontic-orthognathic therapy after termination of craniofacial growth.

TABLE 3.

Discriminant Analysisa

Discriminant Analysisa
Discriminant Analysisa

The percentage of correctly classified cases was 93.2% (Table 4). Only 4.6% of the patients in the nonsurgery group and 13.0% of those in the surgery group, respectively, were misclassified. Then, sensitivity amounted to 0.87, and the specificity scored was 0.932. (Table 4).

TABLE 4.

Classification Results of the Discriminant Analysisa

Classification Results of the Discriminant Analysisa
Classification Results of the Discriminant Analysisa

Linear regression

Forward conditional stepwise procedure was run for LogR. Again, the variables Wits appraisal, NLNSL, and [180 − (L1-ML) − (L1-MLind)] entered the model, resulting in the following equation (Table 5):

The overall percentage of correctly classified cases was 94.3. Only one patient of the nonsurgery group was misclassified, whereas four patients of the surgery group were wrongly classified.

TABLE 5.

Logistic Regressiona

Logistic Regressiona
Logistic Regressiona

The grouping of the sample according to LogR is shown for Wits appraisal in Figure 3.

FIGURE 3.

Box plots of Wits appraisal of correctly classified nonsurgery patients (n = 64) and surgery patients (n = 19), and misclassified surgery patients (n = 3) in applied DA

FIGURE 3.

Box plots of Wits appraisal of correctly classified nonsurgery patients (n = 64) and surgery patients (n = 19), and misclassified surgery patients (n = 3) in applied DA

Close modal

The sensitivity amounted to 0.985, and the specificity was 0.826 (Table 6).

TABLE 6.

Classification Results of Logistic Regressiona

Classification Results of Logistic Regressiona
Classification Results of Logistic Regressiona

Prediction of craniofacial growth is one of the most relevant objectives in orthodontic diagnosis and treatment planning. Particularly in growing individuals, it is necessary to determine whether the dentofacial dysplasia can be corrected by orthodontic/orthopedic means alone or whether surgical procedures have to be applied.42 

To date, information about craniofacial growth pattern is primarily based on cephalometric analysis. Although general growth rates, increments, and directions can be predicted with some degree of accuracy, individual growth prognosis is limited because of the wide range of variability, which is mainly related to heredity, gender, and ethnic background.15,42 

Most attempts at the prediction of treatment-related changes and outcome in orthodontics relied on single biometric parameters. However, application of multivariate statistics was the exception.

Despite its advantages over the use of univariate procedures, the following limitations of this multivariate technique have to be kept in mind: (1) multivariate models based on cephalometric analysis are hampered by the difficulties of precise landmark identification,9,43–45 (2) the selected measurements might not comprise all the variables needed to separate the groups accurately,9,14,18,25 (3) the sample sizes are too small for a sufficiently robust discriminant model that is applicable to patients outside the study,18 and (4) the differences between both groups might be too small to allow a clear group separation.18 

Most of the studies exploring the potential of DA in orthodontics have been concerned with the facial characteristics of different races.25–28 Multivariate technique has been successfully applied to separate class III patients from class I subjects.18,29,30 Furthermore, it has been useful for prediction of treatment outcome and relapse in class III patients treated with singular appliances like the chin-cup or a special treatment modality like tooth extraction.20,28,31–36 

The aim of the present study was to predict the need for surgical intervention in adolescent children with class III malocclusion. For this reason, multivariate techniques were applied, the DA and the LogR.

The decision as to what kind of treatment is indicated usually is based on degree of anteroposterior and vertical skeletal discrepancy, inclination and position of the incisors, and dentofacial appearance. Several lateral cephalometric studies have been conducted to elucidate the growth pattern in class III subjects when compared with eugnathic subjects and to show up the effects of orthopedic therapy and the stability of treatment outcome.3–8,32,33,46 However, only a few studies have been undertaken to establish some threshold values for pretreatment identification of patients for whom orthognathic correction would be necessary.

The “three envelopes of discrepancies” from Proffit and Ackerman47 represent a guideline for differentiation between orthodontic and combined orthodontic-surgical treatment. Critical limitation for orthodontic treatment was seen in an upper incisor protrusion of two mm combined with a lower retrusion of three mm. Kerr et al48 tried to establish cephalometric yardsticks to objectify treatment decision. The most important factors that differentiated between the surgery and the orthodontic patients in this study were size of the anteroposterior discrepancy, inclination of the lower incisors, and appearance of the soft-tissue profile. The vertical dimensions, eg, gonial angle and y-axis, were of limited relevance for treatment decisions. Based on the overlaps of “box-and-whisker plots,” the following critical values were set up: ANB: −4°; M/M ratio: 0.84; lower incisor inclination: 83°; and Holdaway angle: 3.5°. However, univariate statistics are not insufficient to reflect complex craniofacial relationships.9,22,49 For these reasons, multivariate statistics were used in the present study to separate the patients into the nonsurgery and the surgery groups.

The prerequisite for a powerful model is a relatively large sample. Thus, when an unknown patient has to be classified, his measurements will not fall outside those used in generating the model.33 On this account, a multicentric study design was chosen.

Stepwise variable selection of both DA and LogR generated a three-variable model producing the most efficient separation between the nonsurgery and the surgery groups. The variables chosen were identical: (1) Wits appraisal, (2) NL-NSL, and (3) individualized inclination of the lower incisors. The classification power of the model was 93.2% for DA and 94.3% for LogR.

Since its introduction by Riedel,50 ANB angle is the most commonly used cephalometric measurement to describe skeletal relationships between the maxilla and the mandible. However, its validity as a true indicator of the anteroposterior jaw relationships has been questioned by the fact that Nasion is not a fixed point and any change in its anteroposterior position consequently affects ANB.51–54 In addition, the magnitude of the ANB angle is affected by rotation of the jaws relative to the cranial base.50,52,53 The “individualized ANB,” according to Panagiotidis and Witt,38 takes the angle between the mandibular planum and the Sella-Nasion line into account and by this, the vertical dimension. To uncouple the anteroposterior jaw relationships completely from the craniofacial reference, Jacobson42 introduced Wits appraisal. Here, the functional occlusal plane is used as a reference plane for defining the relation of the jaws. Thus, rotation of the jaws relative to the cranial reference plane does not affect the severity of jaw disharmony.

Various authors have investigated the degree of correlation between Wits appraisal and ANB angle, showing only a weak correlation between both variables.55–59 When analyzing the geometrical relationship between ANB angle and Wits appraisal, Jarvinen60 found that it is difficult to compare measurements based on different reference planes. Therefore, the conjunctive use of ANB angle and Wits appraisal was recommended as an appropriate method for clinical assessment of jaw relationships.30,61,62 

The validity of precise landmark identification of Wits appraisal has been questioned because the functional occlusal plane was considered as a major source of error. However, no statistically significant differences were found for repeated intraobserver measurements.63 In contrast, interobserver reproducibility was low. In the present study the same investigator traced all radiographs. Therefore, systematic error based on interobserver variance was eliminated.

The question of the stability of the occlusal plane during craniofacial growth has also been raised. Sherman et al64 assumed that Wits appraisal is affected by changes in the angulation of the occlusal plane during eruption of the permanent teeth. In contrast, Nanda and Merrill65 found that the inclination of the palatal plane was stable throughout the growth period and that the distance between the projections from points A and B on the palatal plane was the best indicator of the sagittal jaw relationship. In the present study, ANB angle, ANB-ANBind angle, and Wits appraisal showed highly significant differences between the nonsurgery and the surgery groups. However, of these variables, only Wits appraisal entered the DA as well as the LogR models. This and the fact that Wits appraisal was the first variable in both models point to its preponderance in separating both patient groups. In a comparable study with a group of 175 adult class III patients, Stellzig-Eisenhauer et al37 could also show the decisive character of Wits appraisal in classifying the patients into a group needing either surgery or a nonsurgical treatment approach. The second variable that was extracted into the models was the inclination of the palatal plane relative to the anterior cranial base. Children in the surgery group showed a less steep inclination of the palatal plane than did those in the nonsurgery group. Although this variable did not show a significant difference in both patient groups in the univariate comparison, it became important for patient selection in multivariate analysis.

In the literature to date, no article discusses the inclination of the palatal plane for further development of class III malocclusion. However, a less steep maxillary occlusal plane in combination with posterior vertical excess of the maxilla was described in adult class III malocclusion patients with an anterior open bite.6 Consistently, Tsang et al66 found that the palatal plane inclination correlates significantly with the severity of the anterior open bite. With respect to these findings, the less steep palatal plane before puberty, as seen in surgery patients, possibly constitutes an unfavorable condition for achievement of a stable overbite during adolescence.

The third value that entered the models was the lower inclination of the front teeth after correction for the interbase angle according to Schopf.39 As mentioned above, Proffit and Ackerman47 and Kerr et al48 already considered lower incisor inclination as one of the most decisive factors in the choice of orthodontics/orthopedics alone or orthognathic surgery. In the univariate analysis both the inclination of the lower front teeth to the mandibular plane and its individualization to the interbase angle tested highly significant. Moreover, Ishikawa et al30 found that among the compensatory dentoalveolar changes in class III malocclusion, lower incisor inclination was strongly related to the sagittal jaw relationship.

The predictive power of the discriminant model for identification of those class III patients for whom orthodontic treatment was sufficient was high. Only 4.6% of the nonsurgery patients were misclassified. In contrast, the percentage of misjudgment in patients who needed orthognathic surgery was 13.0%. For the LogR the overall classification was even slightly higher. Over 98% of the nonsurgery patients were correctly classified, which is 3.1% higher than for DA. In contrast, the grouping of the surgery patients worsened by −4.4% to 82.6%.

Limitation of growth prediction is based on the fact that huge variation exists in timing, duration, and amount of growth in different components of the face.15,16 Also, individual response to orthodontic/orthopedic procedures is different in growing patients. There are cases that do not respond satisfactorily to treatment because of bizarre or unanticipated growth patterns or insufficient patient compliance.42 Consequently individual growth prediction is limited.

A further explanation for misjudgment of patients is that the cephalometric measurements used here did not encompass all the factors that clinically contribute to treatment outcome. Especially in borderline surgical patients, additional factors have to be considered, such as incisal guidance, soft tissue features, and dentofacial esthetics.9,14,20,25,26,67,68 Because class III patients also frequently show skeletal deficiencies in the transverse dimension, anteroposterior cephalograms are necessary to analyze this aspect of craniofacial development. If transverse components as well as the aforementioned factors could be included into the analysis, the predictive power of the multivariate model might increase.

Both multivariate statistical procedures yielded nearly the same result. The extracted variables were not only the same but were even selected in the same order. According to Press and Wilson,69 the two methods do not differ markedly in their results, which also is demonstrated by the data presented. The predictive power of the LogR model was slightly higher (94.3%) than the percentage of correct classification by DA (93.2%). The better result of the LogR procedure was due to a higher sensitivity (0.985). In contrast, the specificity of the LogR model was lesser (0.826) than the specificity resulting from DA (0.87). Because of the more serious consequences, misclassification of nonsurgical patients should be prevented primarily. For that reason the predictive model with the highest sensitivity has to be preferred, which in this study is the model of LogR.

Both, the LogR and the discriminant models were highly significant (P < .0001), classifying 94.3% and 93.2%, respectively, of the prepubertal class III malocclusion children correctly into patients who can be adequately treated by orthopedic/orthodontic therapy alone and those who require orthognathic surgery. The following three cephalometric variables were concordantly selected: Wits appraisal, inclination of the palatal plane, and individualized inclination of the lower incisors.

However, individual growth prediction based on multivariate models is limited because of the diversity and variability of facial growth and the individual response on orthodontic/orthopedic procedures. Moreover, additional factors that might also contribute to clinical treatment outcome, such as transverse components and facial esthetics, have not been considered in the present study.

This study required a large number of patients. We express our gratitude to Prof Dr Witt for providing access to the records of the Department of Orthodontics, Würzburg University, and for his kind support.

1
Ngan
,
P.
,
U.
Hagg
,
C.
Yiu
,
D.
Merwin
, and
S. H.
Wie
.
Cephalometric comparisons of Chinese and Caucasian surgical Class III patients.
Int J Adult Orthod Orthognath Surg
1997
.
12
:
177
188
.
2
Battagel
,
J. M.
The aetiological factors in Class III malocclusion.
Eur J Orthod
1993
.
15
:
347
370
.
3
Sanborn
,
R. T.
Differences between the facial skeletal patterns of Class III malocclusion and normal occlusion.
Angle Orthod
1955
.
25
:
208
222
.
4
Jacobson
,
A.
,
W. G.
Evans
,
C. G.
Preston
, and
P. L.
Sadowsky
.
Mandibular prognathism.
Am J Orthod
1974
.
66
:
140
171
.
5
Schulhof
,
R. J.
,
S.
Nakamura
, and
W. V.
Williamson
.
Prediction of abnormal growth in Class III malocclusions.
Am J Orthod
1977
.
71
:
421
430
.
6
Ellis
,
E.
and
J. A.
McNamara
.
Components of adult Class III malocclusion.
J Oral Maxillofac Surg
1984
.
42
:
295
305
.
7
Guyer
,
E. C.
,
E. E.
Ellis
,
J. A.
McNamara
Jr
, and
R. G.
Behrents
.
Components of Class III malocclusion in juveniles and adolescents.
Angle Orthod
1986
.
56
:
7
30
.
8
Williams
,
S.
and
C. E.
Andersen
.
The morphology of the potential Class III skeletal pattern in the growing child.
Am J Orthod
1986
.
89
:
302
311
.
9
Johnston
,
L. E.
A statistical evaluation of cephalometric prediction.
Angle Orthod
1968
.
38
:
284
304
.
10
Ricketts
,
R. M.
Planning treatment on the basis of the facial pattern and an estimate of its growth.
Angle Orthod
1957
.
27
:
103
133
.
11
Greenberg
,
L. Z.
and
L. E.
Johnston
.
Computerized prediction: the accuracy of a contemporary long-range forecast.
Am J Orthod
1975
.
67
:
243
252
.
12
Toepel-Sievers
,
C.
and
H.
Fischer-Brandies
.
Validity of the computer-assisted cephalometric growth prognosis VTO (visual treatment objective) according to Ricketts.
J Orofac Orthop
1999
.
60
:
185
194
.
13
Witt
,
E.
and
I.
Köran
.
Studies on the validity of computer growth predictions.
Fortschr Kieferorthop
1982
.
43
:
139
159
.
14
Skieller
,
V.
,
A.
Björk
, and
T.
Linde-Hanson
.
Prediction of mandibular growth rotation evaluated from a longitudinal implant sample.
Am J Orthod
1984
.
86
:
359
370
.
15
Nanda
,
R. S.
The contributions of craniofacial growth to clinical orthodontics.
Am J Orthod Dentofacial Orthop
2000
.
117
:
553
555
.
16
Bishara
,
S. M.
Facial and dental changes in adolescents and their clinical implication.
Angle Orthod
2000
.
70
:
471
483
.
17
Keeling
,
S. D.
,
M. L.
Riolo
,
R. E.
Martin
, and
T. R.
Ten Have
.
A multivariate approach to analyzing the relation between occlusion and craniofacial morphology.
Am J Orthod Dentofacial Orthop
1989
.
95
:
297
305
.
18
Battagel
,
J. M.
The identification of Class III malocclusions by discriminant analysis.
Eur J Orthod
1994
.
16
:
71
80
.
19
Jäger
,
A.
,
O.
Zittlau
, and
H. G.
Luhr
.
Zur differentialdiagnostischen Wertigkeit von skelettalen, dentalen und Weichteilanalysen bei der Planung der kieferorthopädisch-kieferchirurgischen Therapie.
Fortschr Kieferorthop
1994
.
55
:
269
278
.
20
Franchi
,
L.
,
T.
Baccetti
, and
I.
Tollaro
.
Predictive variables for the outcome of early functional treatment of Class III malocclusion.
Am J Orthod Dentofacial Orthop
1997
.
11
:
80
86
.
21
Norusis
,
M. J.
Spss/PC+ Advanced Statistics V2.0.
Chicago, Ill: SPSS; 1988:1–39
.
22
Richmond
,
S.
,
N. A.
Aylott
,
M. E.
Panahei
,
B.
Rolfe
, and
E. A.
Tausche
.
2-Center comparison of orthodontist's perceptions of orthodontic treatment difficulty.
Angle Orthod
2001
.
71
:
404
410
.
23
Marcin
,
J. P.
,
A. D.
Slonim
,
M. M.
Pollack
, and
U. E.
Ruttimann
.
Long-stay patients in the pediatric intensive care unit.
Crit Care Med
2001
.
29
:
652
657
.
24
Stewart
,
S. H.
and
M. D.
Silverstein
.
Racial and ethnic disparity in blood pressure and cholesterol measurement.
J Gen Intern Med
2002
.
17
:
405
411
.
25
Kowalski
,
C. J.
,
C. E.
Nasjleti
, and
G. F.
Walker
.
Differential diagnosis of adult male black and white populations.
Angle Orthod
1974
.
44
:
346
350
.
26
Kowalski
,
C. J.
,
C. E.
Nasjleti
, and
G. F.
Walker
.
Dentofacial variations within and between four groups of adult American males.
Angle Orthod
1975
.
45
:
146
151
.
27
Nakasima
,
A.
and
M.
Ichinose
.
Role of parental variables in predicting facial growth after treatment of anterior crossbite.
Am J Orthod Dentofacial Orthop
1986
.
90
:
492
500
.
28
Tahmina
,
K.
,
E.
Tanaka
, and
K.
Tanne
.
Craniofacial morphology in orthodontically treated patients of Class III malocclusion with stable and unstable treatment outcomes.
Am J Orthod Dentofacial Orthop
2000
.
117
:
681
690
.
29
Miyajima
,
K.
,
J. A.
McNamara
Jr
, and
S.
Murata
.
A diagnostic index of vertical problems for Class III malocclusions.
Int J Adult Orthod Orthognath Surg
1997
.
12
:
189
195
.
30
Ishikawa
,
H.
,
S.
Nakamura
,
H.
Iwasaki
,
S.
Kitazawa
,
H.
Tsukada
, and
S.
Chu
.
Dentoalveolar compensation in negative overjet cases.
Angle Orthod
2000
.
70
:
145
148
.
31
Stensland
,
A.
,
P. J.
Wisth
, and
O. E.
Boe
.
Dentofacial changes in children with negative overjet treated by a combined orthodontic and orthopaedic approach.
Eur J Orthod
1988
.
10
:
39
51
.
32
Battagel
,
J. M.
Discriminant analysis: a model for the prediction of relapse in Class III children treated orthodontically by a non-extraction technique.
Eur J Orthod
1993
.
15
:
199
209
.
33
Battagel
,
J. M.
Predictors of relapse in orthodontically-treated Class III malocclusions.
Br J Orthod
1994
.
21
:
1
13
.
34
Tollaro
,
I.
,
T.
Baccetti
, and
L.
Franchi
.
Craniofacial changes induced by early functional treatment of Class III malocclusion.
Am J Orthod Dentofacial Orthop
1996
.
109
:
310
318
.
35
Ishikawa
,
H.
,
S.
Nakamura
,
C.
Kim
,
H.
Iwasaki
,
Y.
Satoh
, and
S.
Yoshida
.
Individual growth in Class III malocclusions and its relationship to the chin cap effects.
Am J Orthod Dentofacial Orthop
1998
.
114
:
337
346
.
36
Baccetti
,
T.
,
J. S.
McGill
,
L.
Franchi
,
J. A.
McNamara
Jr
, and
I.
Tollaro
.
Skeletal effects of early treatment of Class III malocclusion with maxillary expansion and face-mask therapy.
Am J Orthod Dentofacial Orthop
1998
.
113
:
333
343
.
37
Stellzig-Eisenhauer
,
A.
,
C. J.
Lux
, and
G.
Schuster
.
Treatment decision in adult patients with Class III malocclusion: orthodontic therapy or orthognatic surgery?
Am J Orthod Dentofacial Orthop
2002
.
122
:
27
38
.
38
Panagiotidis
,
G.
and
E.
Witt
.
Der individualisierte ANB.
Fortschr Kieferorthop
1977
.
38
:
408
416
.
39
Schopf
,
P.
Kephalometrische “Normwerte” für die Stellung der Inzisivi—eine mögliche Ursache für den Misserfolg kieferorthopädischer Behandlungen?
Fortschr Kieferorthop
1988
.
49
:
37
47
.
40
Dahlberg
,
G.
Statistical for Medical and Psychological Students.
New York, NY: Interscience; 1940
.
41
Houston
,
W. J. B.
The analysis of errors in orthodontic measurements.
Am J Orthod
1983
.
83
:
382
390
.
42
Jacobson
,
A.
Growth and its relation to orthodontic treatment.
J Oral Surg
1981
.
39
:
817
826
.
43
Hixon
,
E. H.
Prediction of facial growth.
Trans Eur Orthod Soc. 1968;127–139
.
44
Baumrind
,
S.
and
R. C.
Frantz
.
The reliability of head film measurements. 1. Landmark identification.
Am J Orthod
1971
.
60
:
111
127
.
45
Freisfeld
,
M.
Fehlerquellen an Einzeichenserien kephalometrischer Bezugspunkte.
Fortschr Kieferorthop
1973
.
34
:
296
306
.
46
Allen
,
R. A.
,
I. H.
Connolly
, and
A.
Richardson
.
Early treatment of Class III incisor relationship using the chin cap appliance.
Eur J Orthod
1993
.
15
:
371
376
.
47
Proffit
,
W. R.
and
J. L.
Ackerman
.
A systematic approach to orthodontic diagnosis and treatment planning.
In: Graber TM, Swain BF, eds. Current Orthodontic Concept and Techniques. 3rd ed. St Louis, Mo: CV Mosby; 1985:15–148
.
48
Kerr
,
W. J. S.
,
S.
Miller
, and
J. E.
Dawber
.
Class III malocclusion: surgery or orthodontics?
Br J Orthod
1992
.
19
:
21
24
.
49
Björk
,
A.
Prediction of mandibular growth rotation.
Am J Orthod
1969
.
55
:
585
599
.
50
Riedel
,
R. A.
The relation of the maxillary structures to the cranium in malocclusion and normal occlusion.
Angle Orthod
1952
.
22
:
140
145
.
51
Moore
,
A. W.
Observations on facial growth and its clinical significance.
Am J Orthod
1959
.
42
:
399
423
.
52
Enlow
,
D. H.
A morphogenetic analysis of facial growth.
Am J Orthod
1966
.
52
:
283
299
.
53
Taylor
,
C. M.
Changes in the relationship of nasion, point A and B and the effect upon ANB.
Am J Orthod
1969
.
56
:
143
163
.
54
Jacobson
,
A.
The “Wits” appraisal of jaw disharmony.
Am J Orthod
1975
.
67
:
125
138
.
55
Ferrazzini
,
G.
Critical evaluation of the ANB angle.
Am J Orthod
1976
.
69
:
620
626
.
56
Roth
,
R.
The “Wits” appraisal—its skeletal and dento-alveolar background.
Eur J Orthod
1982
.
4
:
21
28
.
57
Rotberg
,
S.
,
N.
Fried
,
J.
Kane
, and
E.
Shapiro
.
Predicting the “Wits” appraisal from the ANB angle.
Am J Orthod
1980
.
77
:
636
642
.
58
Bishara
,
S. E.
,
J. A.
Fahl
, and
L. C.
Peterson
.
Longitudinal changes in the ANB angle and Wits appraisal: clinical implications.
Am J Orthod
1983
.
84
:
133
139
.
59
Rushton
,
R.
,
A. M.
Cohen
, and
A. D.
Linney
.
The relationship and reproducibility of angle ANB and the Wits appraisal.
Br J Orthod
1991
.
18
:
225
231
.
60
Jarvinen
,
S.
The relation of the Wits appraisal to the ANB angle: a statistical appraisal.
Am J Orthod Dentofacial Orthop
1988
.
94
:
432
435
.
61
Hurmerinta
,
K.
,
A.
Rahkamo
, and
K.
Haavikko
.
Comparison between cephalometric classification methods for sagittal jaw relationships.
Eur J Oral Sci
1997
.
105
:
221
227
.
62
Ferrario
,
V. F.
,
C.
Sforza
,
A.
Miani
Jr
, and
G. M.
Tartaglia
.
The use of linear and angular measurements of maxillo-mandibular anteroposterior discrepancies.
Clin Orthod Res
1999
.
2
:
34
41
.
63
Haynes
,
S.
and
M. N.
Chau
.
The reproducibility and repeatability of the Wits analysis.
Am J Orthod Dentofacial Orthop
1995
.
107
:
640
647
.
64
Sherman
,
S. L.
,
M.
Woods
,
R. S.
Nanda
, and
G. F.
Currier
.
The longitudinal effects of growth on the Wits appraisal.
Am J Orthod Dentofacial Orthop
1988
.
93
:
429
436
.
65
Nanda
,
R. S.
and
R. M.
Merrill
.
Cephalometric assessment of sagittal relationship between maxilla and mandible.
Am J Orthod Dentofacial Orthop
1994
.
105
:
328
344
.
66
Tsang
,
W. M.
,
L. K.
Cheung
, and
N.
Samman
.
Cephalometric parameters affecting severity of anterior open bite.
Int J Oral Maxillofac Surg
1997
.
26
:
321
326
.
67
Ishikawa
,
H.
,
S.
Nakamura
,
H.
Iwasaki
,
S.
Kitazawa
,
H.
Tsukada
, and
Y.
Sato
.
Dentoalveolar compensation related to variations in sagittal jaw relationships.
Angle Orthod
1999
.
69
:
534
538
.
68
Hirschfeld
,
W. J.
and
R. E.
Moyers
.
Prediction of craniofacial growth: the state of the art.
Am J Orthod
1971
.
60
:
435
444
.
69
Press
,
J. S.
and
S.
Wilson
.
Choosing between logistic regression and discriminant analysis.
J Am Stat Assoc
1978
.
73
:
699
705
.

Author notes

Corresponding author: Gabriele Schuster, DDS, Department of Orthodontics, J.W. Goethe University, Theodor-Stern-Kai 7 (ZZMK, Haus 29), 60590 Frankfurt am Main, Germany ([email protected])