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Treatment of adult Class III malocclusions with orthodontic therapy or orthognathic surgery: Receiver operating characteristic analysis
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Treatment of adult Class III malocclusions with orthodontic therapy or orthognathic surgery: Receiver operating characteristic analysis Yu-Chuan Tseng,a Chin-Yun Pan,a Szu-Ting Chou,a Chen-Yi Liao,b Sheng-Tsung Lai,c Chun-Ming Chen,c Hong-Po Chang,d and Yi-Hsin Yange Kaohsiung, Taiwan
Introduction: The aim of this study was to distinguish between orthodontic patients with skeletal Class III malocclusions requiring surgery and those not requiring surgery by conducting a receiver operating characteristic analysis of cephalometric variables. Methods: We used lateral cephalometric radiographs of 80 subjects (40 nonsurgical and 40 surgical patients) with Class III malocclusions and obtain 25 cephalometric measurements using computerized cephalometry. Of these, 14 measurements showed statistically significant differences between the 2 groups. Receiver operating characteristic analysis was used to determine the ability of the 14 cephalometric measurements in distinguishing between the 2 groups. Six statistically validated and clinically relevant measurements were used to obtain the optimum discriminant effectiveness. Results: For a Class III malocclusion patient with any 4 of these 6 measurement criteria, the sensitivity was 88% and the specificity was 90% in determining the need for surgical treatment: overjet, #–4.73 mm; Wits appraisal, #–11.18 mm; L1-MP angle, #80.8 ; Mx/Mn ratio, #65.9%; overbite, #–0.18 mm; and gonial angle, $120.8 . Conclusions: We selected 6 cephalometric measurements as the minimum number of discriminators required to obtain the optimum discriminant effectiveness of diagnosis between surgical and nonsurgical treatment of skeletal Class III malocclusions. (Am J Orthod Dentofacial Orthop 2011;139:e485-e493)
A
Class III malocclusion is a difficult anomaly to correct, especially with only orthodontic means. This class of malocclusion is a common clinical
a Lecturer, Faculty of Dentistry, College of Dental Medicine, Kaoshiung Medical University; Department of Orthodontics, Kaoshiung Medical University Hospital, Kaohsiung, Taiwan. b Former graduate student, Faculty of Dentistry, College of Dental Medicine, Kaohsiung Medical University, Kaohsiung, Taiwan. c Associate professor, Faculty of Dentistry, College of Dental Medicine, Kaoshiung Medical University; Department of Oral and Maxillofacial Surgery, Kaoshiung Medical University Hospital, Kaohsiung, Taiwan. d Professor and chair, Department of Orthodontics, Faculty of Dentistry, College of Dental Medicine, Kaoshiung Medical University; Department of Orthodontics, Kaoshiung Medical University Hospital, Kaohsiung, Taiwan. e Associate professor, Department of Oral Hygiene, College of Dental Medicine, Kaoshiung Medical University; Department of Medical Research, Kaoshiung Medical University Hospital, Kaohsiung, Taiwan. Partially funded by the Taiwan Association of Orthodontists (97-TAORP-9704) and the Kaohsiung Medical University Hospital, Taiwan (KMUH 95-5D13). The authors report no commercial, proprietary, or financial interest in the products or companies described in this article. Reprint requests to: Hong-Po Chang, Department of Orthodontics, Kaoshiung Medical University, 100 Shih-Chuan 1st Road, Kaohsiung 80708, Taiwan; e-mail, [email protected]; Yi-Hsin Yang, Department of Oral Hygiene, College of Dental Medicine, Kaohsiung Medical University, 100 Shih-Chuan 1st Road, Kaohsiung 80708, Taiwan; e-mail, [email protected]. Submitted, February 2010; revised and accepted, December 2010. 0889-5406/$36.00 Copyright Ó 2011 by the American Association of Orthodontists. doi:10.1016/j.ajodo.2010.12.014
problem in orthodontic patients of Asian or Mongoloid descent.1-5 A Class III malocclusion is largely a skeletal type of occlusal variation (63%-81%).2,6-8 These skeletal abnormalities result from growth disharmony between the maxilla and the mandible, and thus produce a concave facial profile. Patients with skeletal Class III malocclusions exhibit maxillary retrusion, mandibular protrusion, or a combination of both.9,10 There are 3 main treatment options for skeletal Class III malocclusions: growth modification, orthodontic therapy, and orthognathic surgery combined with orthodontic treatment.11,12 Maxillofacial growth modification with dentofacial orthopedic appliances is an effective method for resolving skeletal Class III jaw discrepancies in children.9,13-15 Correcting this problem in adults requires orthognathic surgery in conjunction with orthodontic treatment.11,12 Receiver operating characteristic (ROC) analysis is an excellent method for evaluating and comparing the performance of diagnostic tests.16,17 Wardlaw et al18 used ROC analysis to evaluate the relationships between several cephalometric measurements and anterior open bite. They found that the overbite depth indicator had the highest diagnostic value in discriminating between patients with and without open bite.19 e485
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Not all adult Class III patients are candidates for surgical correction. Patient assessment and selection are the main issues in diagnosis and treatment planning.20 The purpose of this study was to distinguish between surgery candidates (surgical group) and nonsurgery candidates (nonsurgical group) with skeletal Class III malocclusions by using ROC analysis of cephalometric variables. MATERIAL AND METHODS
The subjects included 40 men and 40 women with Class III malocclusions, whose mean age before treatment was 23 years (range, 18-34 years). The criteria for inclusion in the study were a Class III molar relationship, a negative overjet, an ANB angle less than 0 , and a Wits appraisal less than –1 mm. Consecutive patients were selected and divided into 2 groups, each with 20 men and 20 women. Those who had received orthodontic therapy alone made up the nonsurgical group; those who had required orthognathic surgery of mandibular setback combined with orthodontic treatment comprised the surgical group. Some patients were excluded from the study because complete records were lacking. We also excluded subjects with craniofacial syndromes, cleft lip or palate, and trauma history. The goals of orthodontic treatment, with or without orthognathic surgery, are to achieve harmonious facial esthetics and a functional occlusion, but soft-tissue changes also play an important role in evaluating treatment effects. The Taiwan Board of Orthodontics introduced an objective grading system for assessing posttreatment dental casts and panoramic radiographs similar to that of the American Board of Orthodontics and supplemented by lateral cephalographs.21 The Taiwan Board of Orthodontics objective grading system evaluates 20 criteria. In this retrospective study with this grading system, we evaluated orthodontic and orthognathic surgical patients who were consecutively completed in 2006 to 2009. The mean scores for orthodontic patients were 78%. There were 1 patient in the “slightly improved” category and no patients in the “worse" or "no improvement” categories. The mean scores for orthognathic surgical patients were 74%. There were no patients in the “worse," "no improvement," or "slightly improved” categories. A mean score of more than 70% represents a high standard of treatment in the “greatly improved” category. The mean scores of this study indicate excellent-to-good treatment results for both groups. In this study, we used lateral cephalometric radiographs obtained before treatment. A correction of 10% was made for the magnification of the linear measurements from each cephalogram. Thirty cephalometric
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landmarks on the craniofacial complex were identified and digitized (Fig 1). A computerized cephalometric system, Winceph (version 8.0, Rise, Sendai, Japan), was used to obtain 25 cephalometric measurements, including 12 angular, 9 linear, and 4 ratio variables (Table I). Descriptive statistics, including means, standard deviations, and Student t tests results, were computed for each measurement (Table II). We selected 25 cephalometric measurements that were used in previous studies. The Bonferroni adjustment with an alpha level of 0.002 (0.05/25) was applied as a multiple-comparison correction when several statistical tests were performed simultaneously. The most suitable measurements were statistically validated and clinically relevant.22 Measurements that were statistically different between the 2 groups with the 2-sample t test and the Bonferroni adjustment were further analyzed by the ROC curve analysis. Systematic measurement errors were estimated by means of paired Student t tests, and the random method error (ME) was quantified with Dahlberg’s formula, ME 5 OSd2/2n, where d is the difference between duplicate measurements and n is the number of double measurements.23,24 We study used the ROC analysis and the area under the curve (AUC) to determine the set of cephalometric measurements for the best discrimination between orthodontic therapy and orthognathic surgery. The ROC curve is a plot of sensitivity (true positive rate) on the y-axis and 1−specificity (false positive rate) on the xaxis. The different points on the curve correspond to different cutoff points used to designate the surgery group.25 The AUC is generally considered a reasonable summary of the overall diagnostic accuracy of the continuous variables. In general, for 2 variables, the variable with higher AUC is considered a better indicator for the surgery group. For each ROC curve, a cutoff point that yields the best combination of sensitivity and specificity can be identified to provide a recommendation for surgery. All data analyses were performed by using SAS software (version 9, SAS Institute, Cary, NC). RESULTS
To assess errors in the cephalometric digitizing, 1 investigator (C.Y.L.) digitized 20 randomly selected lateral cephalographs. The same investigator redigitized the same cephalographs after an interval of 2 weeks. The method errors between the double measurements were analyzed. No significant differences appeared between the 2 sets of repeated measurements. The method errors were between 0.16 and 0.29 mm for linear measurements, between 0.26 and 0.60 for angular measurements, and between 0.14% and 0.30% for ratios. The intraclass correlation coefficients were from 0.973 to
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Table I. Variables of cephalometric analysis used in
this study Linear variables (mm) S-N A–Nv B–Nv Pg–Nv Symphysis width Wits appraisal Overjet Overbite Si–(Li–Pg')
Fig 1. Cephalometric landmarks: 1, N, nasion; 2, S, sella; 3, Po, porion; 4, Or, orbitale; 5, ANS, anterior nasal spine; 6, PNS, posterior nasal spine; 7, A, Point A; 8, U1E, maxillary central incisor edge; 9, U1A, maxillary central incisor apex; 10, B, Point B; 11, Pg, pogonion; 12, Gn, gnathion; 13, Me, menton; 14, Cd, condylion; 15, Go, gonion; 16, GoI, gonial intersection; 17, L1E, mandibular incisor edge; 18, L1A, mandibular incisor apex; 19, BL, lingual Point B; 20, G, glabella; 21, N', soft-tissue nasion; 22, Sn, subnasale; 23, Pg', soft-tissue pogonion; 24, Ls, labrale superius; 25, Li, labrale inferius; 26, Stoms, stomion superius; 27, Stomi, stomion inferius; 28, Si, mentolabial sulcus; 29, Gn', soft-tissue gnathion; 30, Me', soft-tissue menton.
0.990. The reliability was high for all values. Table II shows the means and standard deviations of the 25 cephalometric measurements of both groups. Of these, 14 measurements were significantly different between the surgical and nonsurgical groups (overjet, Wits appraisal, L1-MP, Mx/Mn ratio (Cd-A/Cd-Gn), gonial angle, overbite, Si-(Li-Pg'), PP-MP, G-Sn/Sn-Me', symphysis width, H-angle, PFH/AFH, SN-MP, Pg-Nv) (P \0.002 [0.05/25]), based on the Bonferroni multiple-comparisons procedure. Table III shows the results of further computing the AUCs based on these 14 original measurements (range, 0.694-0.908). Their corresponding cutoff points, which yielded the highest values of sensitivity 1 specificity, were determined. The 14 cephalometric measurements were dichotomized into 2 parts based on the cutoff points. Depending on the clinical criteria, the part with a tendency to surgery
Angular variables ( ) SNA SNB ANB NAPg SN-MP PP-MP Gonial angle U1-PP L1-MP U1–L1 G–Sn–Pg' H–angle
Ratio variables (%) PFH/AFH Mx/Mn ratio G-Sn/Sn-Me Sn-Stoms/Stomi-Me'
was given a score of 1 and the other was given a score of 0. For example, in the overjet measurement, participants with a measure of less than or equal to –4.73 mm were considered to have a tendency for surgery and were given a score of 1. Hence, each of the 14 measurements was transferred into a new score of 1 and 0. The next step was to determine the optimal number of dichotomized measurements for inclusion in the final scoring system. The 14 dichotomized measurements were added 1 by 1 from the measurements with highest to lowest AUC values. Table IV shows the score systems with measurements 2 through 14 with their corresponding AUC values. Although higher AUCs would have better diagnostic accuracy, the AUCs after 6 dichotomized measurements were not greatly changed (0.96 to 0.97). Hence, a scoring system based on 6 dichotomized measurements (overjet, Wits appraisal, L1-MP, Mx/Mn ratio, overbite, and gonial angle) provided an acceptable AUC (0.96) and a feasible number (6) of measurements for the scoring system. For the scoring system of 6 dichotomized measurements, the possible scores of 0 to 6 corresponded to 0 to 6 measurements with values within the part of score 1 (tendency for surgery) in Table III. Using the cutoff points in Table III to dichotomize each of the 14 cephalometric measurements, the optimal combination of sensitivities and specificities is shown in Table III. Since no single measurement can have satisfactory classification performance, a scoring system that combined cephalometric measurements was then compared and analyzed (Table IV and Fig 2). Table V shows the sensitivity and specificity of scores 0 to 6. A score of 4 with the highest value of sensitivity 1 specificity appeared to be the cutoff point, indicating the best combination of sensitivity (88%) and specificity (90%), of the requirement for surgical treatment (Fig 2). The scores of 6 dichotomized measurements were computed for all patients. Table VI lists the 6 measurements in
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Table II. Cephalometric measurements of Class III malocclusion patients treated with and without surgery Nonsurgical group Mean 6 SD 66.06 6 4.17 81.57 6 3.44 85.44 6 3.96 3.87 6 2.18 7.91 6 4.88 68.70 6 3.33 0.56 6 3.88 5.21 6 5.77 6.05 6 5.94 7.50 6 1.46 30.91 6 6.38 21.37 6 5.91 119.55 6 7.39 68.24 6 5.26 122.58 6 6.11 86.94 6 6.82 129.30 6 7.87 9.67 6 2.76 3.55 6 1.20 2.95 6 2.09 4.03 6 2.96 101.20 6 9.08 44.55 6 5.57 3.28 6 0.81 11.26 6 3.06
Variable S-N (mm) SNA ( ) SNB ( ) ANB ( ) NAPg ( ) Mx/Mn ratio (%) A–Nv (mm) B–Nv (mm) Pg–Nv (mm) Symphysis width (mm) SN–MP ( ) PP–MP ( ) Gonial angle ( ) PFH/AFH (%) U1–PP ( ) L1–MP ( ) U1–L1 ( ) Wits appraisal (mm) Overjet (mm) Overbite (mm) G–Sn–Pg' ( ) G–Sn/Sn–Me' (%) Sn–Stoms/Stomi–Me' (%) Si–(Li–Pg') (mm) H–angle ( )
Surgical group Mean 6 SD 65.17 6 3.74 82.57 6 4.03 87.65 6 3.78 5.29 6 3.05 11.05 6 6.43 64.03 6 3.15 0.10 6 3.41 9.25 6 6.27 11.10 6 7.47 6.05 6 1.17 35.92 6 6.03 27.38 6 5.42 127.67 6 6.11 64.14 6 4.81 121.61 6 7.33 77.07 6 7.07 134.12 6 11.44 15.27 6 4.25 7.02 6 2.45 0.37 6 2.70 6.05 6 4.07 92.89 6 7.98 41.30 6 4.22 2.26 6 1.04 7.69 6 4.13
Mean Difference 0.89 1.00 2.21 1.43 3.14 4.67 0.47 4.03 5.50 1.45 5.01 6.01 8.13 4.10 0.97 9.87 4.82 5.06 3.47 2.58 2.03 8.31 3.25 1.03 3.57
t test P value 0.3167 0.2349 0.0126 0.0185 0.0162 \0.0001 0.5643 0.0037 0.0012 \0.0001 0.0005 \0.0001 \0.0001 0.0005 0.5245 \0.0001 0.0313 \0.0001 \0.0001 \0.0001 0.0130 \0.0001 0.0042 \0.0001 \0.0001
P \0.002 (0.05/25) was considered significant based on the Bonferroni multiple-comparisons procedure.
Table III. AUC of 14 significant measurements from Table II Variable Overjet (mm) Wits appraisal L1-MP Mx/Mn ratio Overbite Gonial angle Si-(Li-Pg') G-Sn/Sn-Me' Symphysis width PP-MP H–angle PFH/AFH Pg-Nv SN-MP
AUC 0.908 0.857 0.848 0.840 0.799 0.791 0.776 0.772 0.771 0.769 0.746 0.710 0.696 0.694
Cutoff point 4.73 mm 11.18 mm 80.80 65.90% 0.18 mm 120.80 2.73 mm 97.50% 6.55 mm 25.70 7.60 66.00% 10.09 mm 30.90
Score 1 # 4.73 mm # 11.18 mm #80.80 #65.90% # 0.18 mm $120.80 # 2.73 mm #97.50% #6.55 mm $25.70 #7.60 #66.00% $10.09 mm $30.90
patients with different scores. Thirteen patients had values of 1, and 46.2% (n 5 6) of them were in the gonial angle. Patients with scores of 4, 5, and 6 were mostly in the measurements of gonial angle, Wits appraisal, Mx/Mn ratio, and L1-MP. Overjet and overbite appeared to be the final added measurements in the scores of the 6 measurements. Most patients (23 of 25, or 92%) with overbite problems
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Score 0 . 4.73 mm . 11.18 mm .80.80 .65.90% . 0.18 mm \120.80 . 2.73 mm .97.50% .6.55 mm \25.70 .7.60 .66.00% \10.09 mm \30.90
Sensitivity 0.825 0.850 0.750 0.750 0.600 0.925 0.675 0.800 0.675 0.700 0.525 0.675 0.600 0.875
Specificity 0.850 0.725 0.825 0.775 0.975 0.600 0.725 0.675 0.750 0.750 0.875 0.650 0.800 0.525
had scores of 4 or higher, implying that those with an overbite problem also had other variables. DISCUSSION
This study had several limitations. It was a retrospective study sampled from a university orthodontic practice. The main skeletal anomalies were mandibular
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Table IV. ROC analysis of prediction results in the cumulated top-ranked cephalometric measurements (cumulative
scores) Number of cumulated top–ranked cephalometric measurements 2 3 4 5 6 7 8 9 10 11 12 13 14
Measurements Overjet and Wits appraisal Above measurements plus L1–MP Above measurements plus Mx/Mn ratio Above measurements plus overbite Above measurements plus gonial angle Above measurements plus Si–(Li–Pg') Above measurements plus PP–MP Above measurements plus G–Sn/Sn–Me' Above measurements plus symphysis width Above measurements plus H–angle Above measurements plus PFH/AFH Above measurements plus Pg-Nv Above measurements plus SN-MP
Fig 2. The ROC curve of the final 6-measurement scoring system with the best cutoff point.
protrusion in both the surgical and nonsurgical groups of Class III malocclusions. When we correct an anterior crossbite in the treatment of Class III malocclusions, an inevitable side effect is opening of the mandibular plane. A nonsurgical orthodontic approach or a mandibular setback surgical procedure for skeletal Class III correction often results in backward repositioning of the mandible; this increases the lower anterior face height. Therefore, the indication of nonsurgical orthodontic or surgical treatment for an adult Class III malocclusion is hypodivergent, orthodivergent, or slightly hyperdivergent, whereas the contraindication is moderately and severely hyperdivergent. For orthognathic surgical
AUC 0.876 0.924 0.930 0.956 0.964 0.964 0.968 0.968 0.963 0.976 0.972 0.977 0.973
patients treated with mandibular setback, the vertical relationship can be improved by vertical chin reduction and genioplasty.26 However, we excluded moderately and severely hyperdivergent subjects from the nonsurgical and surgical groups. When used appropriately within their limitations, conventional methods of surgical prediction with cephalometric analysis can provide the objective evidence needed to guide treatment planning and assess treatment outcomes.27 For patients who have developmental dentofacial jaw deformities, predictions for orthognathic surgery are more accurate than for those with underlying cleft or syndromic craniofacial conditions. Since its introduction in the context of electronic signal detection, the ROC curve has become the method of choice for quantification of the accuracy of medical diagnostic tests. The ROC curve analysis is widely applied in measuring the discriminatory ability of diagnostic or prognostic tests. It is an excellent method for evaluating and comparing the performance of diagnostic tests.16,17 ROC curve analysis has substantial value for evaluating the diagnostic information of cephalometric measurements. A Class III malocclusion is difficult to treat optimally.20 Using ROC curve analysis, we found incisal overjet, L1-MP angle (anteroposterior dental relationships), Wits appraisal, and Mx/Mn ratio (anteroposterior jaw relationships), gonial angle (vertical jaw dimension), and incisal overbite (vertical dental relationship) to be the best diagnostic parameters for determining treatment modalities for Class III malocclusion patients. All these parameters showed highly significant differences between the orthodontic nonsurgical and surgical groups.
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Table V. Identifying the cutoff point Number of dichotomized measurements 6 5 4 3 2 1 0
Probability for requiring surgical treatment 0.99 0.95 0.81 0.46 0.15 0.04 0.01
Sensitivity 1 specificity 1.225 1.675 1.750 1.750 1.675 1.350 1.000
Sensitivity Specificity 0.225 1.000 0.675 1.000 0.875 0.900 0.925 0.825 1.000 0.675 1.000 0.350 1.000 0.000
True True False positive negative positive 9 40 0 27 40 0 35 36 4 37 33 7 40 27 13 40 14 26 40 0 40
False negative 30 13 5 3 0 0 0
Table VI. Relationship of scores with variables
Score Total 1 2 3 4 5 6
Total number of participants 80 13 9 6 11 18 9
Gonial angle
Wits appraisal
Mx/Mn ratio
n 53 6 7 4 10 17 10
n 45 1 3 6 9 17 9
n 39 3 1 2 9 15 9
% 46.2 77.8 66.7 90.9 94.4 100.0
In Class III malocclusions, the mandibular incisors are relatively retroclined, and the maxillary incisors are relatively proclined to compensate for skeletal dysplasia. A patient with a skeletal Class III malocclusion generally has a negative overjet in incisor relationships, despite the compensatory inclination of the maxillary and mandibular incisors.28 Ishikawa et al29 reported a close relationship between the inclination of the mandibular incisors and the sagittal jaw relationship. We found highly significant lingual inclinations of the mandibular incisors and largely negative overjets in the surgical group (L1-MP angle, 86.94 6 6.82 in the nonsurgical group and 77.07 6 7.07 in the surgical group; 96 6 7.0 is the Taiwanese norm). The ANB angle has been the most commonly used cephalometric measurement to describe the skeletal discrepancies between the maxilla and the mandible. However, the validity of the ANB angle as an indicator of sagittal jaw relationships has been criticized.30,31 Various investigations showed a low correlation between the Wits appraisal and the ANB angle.32-34 Choi and Chang35 used ROC analysis to evaluate the usefulness of various cephalometric measurements for identifying patients with Class III malocclusions. They found that the Wits appraisal was highly effective for this purpose. Later, Murakami et al36 examined the morphologic differences in the craniofacial complex between surgical and orthodontic patients with skeletal Class III malocclusion. They found that the Wits appraisal was
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% 7.7 33.3 100.0 81.8 94.4 100.0
% 23.1 11.1 33.3 81.8 83.3 100.0
Overjet n 38 2 2 4 5 16 9
% 15.4 22.2 66.7 45.5 88.9 100.0
L1–MP n 37 1 4 1 9 13 9
% 7.7 44.4 16.7 81.8 72.2 100.0
Overbite n 25 0 1 1 2 12 9
% 0.0 11.1 16.7 18.2 66.7 100.0
significantly smaller and the gonial angle was significantly larger in the surgical group than in the orthodontic group. In addition, they observed no values below –15 mm in the orthodontic group in the Wits appraisal. Therefore, the Wits appraisal and the gonial angle might be useful for distinguishing between the 2 groups. Stellzig-Eisenhauer et al20 applied stepwise discriminant analysis to identify the dentoskeletal variables that best distinguish the nonsurgical and surgical groups among adult patients with Class III malocclusion. Of all the variables, the Wits appraisal was the most useful parameter. Similar to the Wits appraisal, we also used the Mx/Mn ratio to analyze the sagittal discrepancy between the maxilla and mandible. This sagittal jaw relationship seems to be a more decisive factor for treatment decisions than morphometric parameters of the mandible alone. We found significant intergroup differences for the parameters representing the sagittal maxillomandibular relationship as indicated by the Mx/ Mn ratio and the Wits appraisal. In addition, the incisal overbite was highly significantly smaller in the surgical group than in the orthodontic group. Furthermore, the patients in the surgical group with smaller overbites also had other variables. Variations in the dentofacial complex are rarely produced by a single factor. As stated by Han and Kim,37 there is no widely accepted cephalometric measurement that shows the dentofacial configuration of a malocclusion. The ROC method of multivariable analysis is far
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more useful in discriminating the diagnostic value of cephalometric measurements. We selected 6 statistically validated variables as the minimum number of discriminators required to obtain the optimum discriminant effectiveness. Hence, if a Class III malocclusion patient has at least 4 of the 6 conditions (overjet, #–4.73 mm; Wits appraisal, #–11.18 mm; L1-MP angle, #80.8 ; Mx/Mn ratio, #65.9%; overbite, #–0.18 mm; and gonial angle, $120.8 ), then the patient would be recommended to have surgical treatment. Using the scoring system based on 6 dichotomized measurements, a higher score indicates the tendency to have surgery. The suggested diagnostic cutoff point of 4 had the best combination of sensitivity (88%) and specificity (90%); for those who had surgical treatment, 88% had scores of 4 or higher, and for those who did not have surgical treatment, 90% had scores of 3 or less. Several methods can be used to identify the important cephalometric measurements for a clinical decision on surgery. The major advantages of the ROC curve in determining cephalometric measurements include the following: (1) it is insensitive to the changes of measurement distribution, since the calculation was based on ranks; (2) although in our study we used the equal classification error costs (the cost for a false positive is equal to the cost of a false negative), ultimately one can specify unequal classification error costs when identifying cutoff points; and (3) it is a relatively easy scoring system, because the score applies only to the dichotomized measurements according to the cutoff points, and it sums the number of items in the surgical regions. The same research methods with lateral cephalometric radiographs with ROC analysis seem suitable, but the most important variables could differ relative to the ethnic population concerned.35,37 Although the discriminant analysis was also a common strategy for selecting important measurements, measurements with skewed distributions can result in optimistically biased estimates and, hence, have less sensitivity.38,39 Even though dental specialists (orthodontists or oral-maxillofacial surgeons) might recommend, and cephalometric measurements might indicate, surgical treatment, self-perceptions of the profile could be more important factors affecting the patient’s decision for surgical correction.40 CONCLUSIONS
In this study, we identified 6 cephalometric measurements as the minimum number of discriminators required to obtain the optimum discriminant effectiveness of diagnosis between surgical and nonsurgical treatment for patients with skeletal Class III malocclusions.
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We thank Yi-Ching Poon for her help with the preparation of the manuscript. REFERENCES 1. Kameda A. The Begg technique in Japan. Am J Orthod 1982;81: 209-27. 2. Chang HP. Components of Class III malocclusion in Taiwanese. Kaohsiung J Med Sci 1985;1:144-55. 3. Yang WS. The study on the orthodontic patients who visited Department of Orthodontics, Seoul National University Hospital. J Korean Dent Assoc 1990;28:811-21. 4. Fu M, Zhang D, Wang B, Deng Y, Wang F, Ye X. The prevalence of malocclusion in China—an investigation of 25392 children. Chin J Orthod 2002;9:151-3. 5. Graber TM, Vanarsdall RL, Vig KWL. Orthodontics: current principles and techniques. 4th ed. St Louis: Mosby; 2005. p. 565. 6. Susami R. A cephalometric study of dentofacial growth in Class III subjects with anterior crossbite. J Jpn Orthod Soc 1967;26: 1-34. 7. Kim SC, Lee KS. The cephalometric study of facial types in Class III malocclusion. Korean J Orthod 1990;20:569-89. 8. Zeng XL. A study of skeletal types of Class III malocclusion. Chin J Stomatol 1993;28:170-3, 191. 9. Chang HP, Lin HC, Liu PH, Chang CH. Geometric morphometric assessment of treatment effects of maxillary protraction combined with chin cup appliance on the maxillofacial complex. J Oral Rehabil 2005;32:720-8. 10. Staudt CB, Kiliaridis S. Different skeletal types underlying Class III malocclusion in a random population. Am J Orthod Dentofacial Orthop 2009;136:715-21. 11. Proffit WR, White RP Jr, Sarver DM. Contemporary treatment of dentofacial deformity. St Louis: Mosby; 2003. p. 507-73. 12. Chang HP, Tseng YC, Chang HF. Treatment of mandibular prognathism. J Formosa Med Assoc 2006;105:781-90. 13. Chang HP, Liu PH, Chang HF, Chang CH. Thin-plate spline (TPS) graphical analysis of the mandible on cephalometric radiographs. Dentomaxillofac Radiol 2002;31:137-41. 14. Chang ZC, Chang HP, Chen YJ, Yao CC, Liu PH, Chang HF. The treatment effects of the face mask therapy in the midfacial configurations in skeletal Class III growing patients by means of morphometric techniques. J Formosa Med Assoc 2005;104:935-41. 15. Lin HC, Chang HP, Chang HF. Treatment effects of occipito-mental anchorage appliance of maxillary protraction combined with chincup traction in children with Class III malocclusion. J Formosa Med Assoc 2007;106:380-91. 16. Swets JA. Measuring the accuracy of diagnostic systems. Science 1988;240:1285-93. 17. Gu J, Ghosal S, Roy A. Bayesian bootstrap estimation of ROC curve. Stat Med 2008;27:5407-20. 18. Wardlaw DW, Smith RJ, Hertweck DW, Hildebolt CF. Cephalometrics of anterior open bite: a receiver operating characteristic (ROC) analysis. Am J Orthod Dentofacial Orthop 1992;101:234-43. 19. Kim YH. Overbite depth indicator with particular reference to anterior open-bite. Am J Orthod 1974;65:586-611. 20. Stellzig-Eisenhauer A, Lux CJ, Schuster G. Treatment decision in adult patients with Class III malocclusion: orthodontic therapy or orthognathic surgery? Am J Orthod Dentofacial Orthop 2002; 122:27-38. 21. Casko JS, Vaden JL, Kokich VG, Damone J, James RD, Cangialosi TJ, et al. Objective grading system for dental casts and panoramic radiographs. American Board of Orthodontics. Am J Orthod Dentofacial Orthop 1998;114:589-99.
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22. Chang HP. Evaluation of cephalometric analysis. J Formosa Dent Assoc 1985;8:2-13. 23. Dahlberg G. Statistical methods for medical and biological students. New York: Interscience Publications; 1940. p. 100-40. 24. Houston WJB. The analysis of errors in orthodontic measurements. Am J Orthod 1983;83:382-90. 25. Rosner B. ROC curves. In: Rosner B, editor. Fundamentals of biostatistics. Belmont, Calif: Thomson Brooks/Cole; 2006. p. 64-6. 26. Bailey LJ, Sarver DM, Turvey TA, Proffit WR. Class III problems. In: Proffit WR, White RP, Sarver DM, editors. Contemporary treatment of dentofacial deformity. St Louis: Mosby; 2003. 27. Jacobson A. How reliable is cephalometric prediction? In: Jacobson A, Jacobson R, editors. Radiographic cephalometry: from basics to videoimaging. 2nd ed. Chicago: Quintessence; 2006. p. 293-300. 28. Ishikawa H, Nakamura S, Iwasaki H, Kitazawa S, Tsukada H, Chu S. Dentoalveolar compensation in negative overjet cases. Angle Orthod 2000;70:145-8. 29. Ishikawa H, Nakamura S, Iwasaki H, Kitazawa S, Tsukada H, Sato Y. Dentoalveolar compensation related to variations in sagittal jaw relationships. Angle Orthod 1999;69:534-8. 30. Jacobson A. The “Wits” appraisal of jaw disharmony. Am J Orthod 1975;67:125-38. 31. Chang HP. Assessment of anteroposterior jaw relationship. Am J Orthod Dentofacial Orthop 1987;92:117-22.
32. Rotberg S, Fried N, Kane J, Shapiro E. Predicting the “Wits” appraisal from the ANB angle. Am J Orthod 1980;77:636-42. 33. Bishara SE, Fahl JA, Peterson LC. Longitudinal changes in the ANB angle and Wits appraisal: clinical implications. Am J Orthod 1983; 84:133-9. 34. Rushton R, Cohen AM, Linney AD. The relationship and reproducibility of angle ANB and the Wits appraisal. Br J Orthod 1991;18: 225-31. 35. Choi HY, Chang YI. Comparative study on the horizontal measurements of skeletal Class III malocclusion using the ROC analysis. Korean J Orthod 1995;25:153-63. 36. Murakami C, Hiyama S, Ohyama K. Craniofacial morphology of skeletal Class III patients before treatment and growth-related changes during treatment with a maxillary protraction appliance: a comparison of orthodontic and surgical cases. World J Orthod 2005;6:51-60. 37. Han UK, Kim YH. Determination of Class II and Class III skeletal patterns: receiver operating characteristic (ROC) analysis on various cephalometric measurements. Am J Orthod Dentofacial Orthop 1998;113:538-45. 38. McLachlan GJ. Discriminant analysis and statistical recognition. New York: Wiley; 2004. 39. Morrison DF. Multivariate statistical methods. 4th ed. Belmont, Calif: Brooks/Cole Thomson Learning; 2005. 40. Bell R, Kiyak HA, Joondeph DR, McNeill RW, Wallen TR. Perceptions of facial profile and their influence on the decision to undergo orthognathic surgery. Am J Orthod 1985;88:323-32.
APPENDIX
y-axis. Some sample values are shown in Table A and marked on Figure A1. The lower left point of the ROC curve (0, 0) means that all patients were classified into the nonsurgical group. Hence, there would be no false positives but, at the same time, no true positives. Similarly, the point of 1, 1 means that all patients were classified into the surgical group. Hence, there would be no false negatives but, at the same time, no true negatives. The area under the connected line is considered the AUC, and any point with the largest sum of sensitivity and specificity is the best cutoff point (a threshold of the ROC curve). For the 14 cephalometric measurements with significant differences between the surgical and nonsurgical groups, their ROC curves are shown in Figure A2. The best cutoff point for each cephalometric measurement is indicated by a small circle on the corresponding ROC curve (Fig A2).
The ROC curve for each measurement was generated from the computed sensitivities and specificities of all possible values in the measurement. For example, the values of overjet of the 80 subjects ranged from –12.73 (mm) to –1.55 (mm). Starting by using the smallest value (–12.73) as the cutoff point for indicating surgery (#–12.73), since only 1 subject in the surgery group had a value of –12.73, and all subjects in the nonsurgery group were all larger than –12.73, the corresponding sensitivity is 2.5% and the corresponding specificity is 100%. The corresponding point of (1-specificity, sensitivity) 5 (0, 0.025) is marked as point 1 in the ROC curve (Fig A1). Similarly, we computed from all the values of overjet the corresponding sensitivities and specificities, and a series of points can be plotted with 1-specificity as the x-axis and sensitivity as the
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Table A. Corresponding sensitivities and specificities from the values of overjet marked on Figure A1 Number of participants Point 1 2 3 4 5 6 7
Overjet 12.73 11.73 6.00 5.91 4.73 3.55 3.27 1.55
Sensitivity 0.025 0.050 0.625 0.650 0.825 0.900 1.000 1.000
Specificity 1.000 1.000 1.000 0.925 0.850 0.575 0.400 0.000
Sensitivity 1 specificity 1.025 1.050 1.625 1.575 1.675 1.475 1.400 1.000
Fig A1. The ROC curve for overjet measurement. The corresponding points marked by 1 through 7 are shown in Table A.
True positive 1 2 25 26 33 36 40 40
True negative 40 40 40 37 34 23 16 0
False positive 0 0 0 3 6 17 24 40
True negative 39 38 15 14 7 4 0 0
Fig A2. The ROC curves for the 14 measurements and their corresponding cutoff points.
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Treatment of adult Class III malocclusions with orthodontic therapy or orthognathic surgery: Receiver operating characteristic analysis Yu-Chuan Tseng,a Chin-Yun Pan,a Szu-Ting Chou,a Chen-Yi Liao,b Sheng-Tsung Lai,c Chun-Ming Chen,c Hong-Po Chang,d and Yi-Hsin Yange Kaohsiung, Taiwan
Introduction: The aim of this study was to distinguish between orthodontic patients with skeletal Class III malocclusions requiring surgery and those not requiring surgery by conducting a receiver operating characteristic analysis of cephalometric variables. Methods: We used lateral cephalometric radiographs of 80 subjects (40 nonsurgical and 40 surgical patients) with Class III malocclusions and obtain 25 cephalometric measurements using computerized cephalometry. Of these, 14 measurements showed statistically significant differences between the 2 groups. Receiver operating characteristic analysis was used to determine the ability of the 14 cephalometric measurements in distinguishing between the 2 groups. Six statistically validated and clinically relevant measurements were used to obtain the optimum discriminant effectiveness. Results: For a Class III malocclusion patient with any 4 of these 6 measurement criteria, the sensitivity was 88% and the specificity was 90% in determining the need for surgical treatment: overjet, #–4.73 mm; Wits appraisal, #–11.18 mm; L1-MP angle, #80.8 ; Mx/Mn ratio, #65.9%; overbite, #–0.18 mm; and gonial angle, $120.8 . Conclusions: We selected 6 cephalometric measurements as the minimum number of discriminators required to obtain the optimum discriminant effectiveness of diagnosis between surgical and nonsurgical treatment of skeletal Class III malocclusions. (Am J Orthod Dentofacial Orthop 2011;139:e485-e493)
A
Class III malocclusion is a difficult anomaly to correct, especially with only orthodontic means. This class of malocclusion is a common clinical
a Lecturer, Faculty of Dentistry, College of Dental Medicine, Kaoshiung Medical University; Department of Orthodontics, Kaoshiung Medical University Hospital, Kaohsiung, Taiwan. b Former graduate student, Faculty of Dentistry, College of Dental Medicine, Kaohsiung Medical University, Kaohsiung, Taiwan. c Associate professor, Faculty of Dentistry, College of Dental Medicine, Kaoshiung Medical University; Department of Oral and Maxillofacial Surgery, Kaoshiung Medical University Hospital, Kaohsiung, Taiwan. d Professor and chair, Department of Orthodontics, Faculty of Dentistry, College of Dental Medicine, Kaoshiung Medical University; Department of Orthodontics, Kaoshiung Medical University Hospital, Kaohsiung, Taiwan. e Associate professor, Department of Oral Hygiene, College of Dental Medicine, Kaoshiung Medical University; Department of Medical Research, Kaoshiung Medical University Hospital, Kaohsiung, Taiwan. Partially funded by the Taiwan Association of Orthodontists (97-TAORP-9704) and the Kaohsiung Medical University Hospital, Taiwan (KMUH 95-5D13). The authors report no commercial, proprietary, or financial interest in the products or companies described in this article. Reprint requests to: Hong-Po Chang, Department of Orthodontics, Kaoshiung Medical University, 100 Shih-Chuan 1st Road, Kaohsiung 80708, Taiwan; e-mail, [email protected]; Yi-Hsin Yang, Department of Oral Hygiene, College of Dental Medicine, Kaohsiung Medical University, 100 Shih-Chuan 1st Road, Kaohsiung 80708, Taiwan; e-mail, [email protected]. Submitted, February 2010; revised and accepted, December 2010. 0889-5406/$36.00 Copyright Ó 2011 by the American Association of Orthodontists. doi:10.1016/j.ajodo.2010.12.014
problem in orthodontic patients of Asian or Mongoloid descent.1-5 A Class III malocclusion is largely a skeletal type of occlusal variation (63%-81%).2,6-8 These skeletal abnormalities result from growth disharmony between the maxilla and the mandible, and thus produce a concave facial profile. Patients with skeletal Class III malocclusions exhibit maxillary retrusion, mandibular protrusion, or a combination of both.9,10 There are 3 main treatment options for skeletal Class III malocclusions: growth modification, orthodontic therapy, and orthognathic surgery combined with orthodontic treatment.11,12 Maxillofacial growth modification with dentofacial orthopedic appliances is an effective method for resolving skeletal Class III jaw discrepancies in children.9,13-15 Correcting this problem in adults requires orthognathic surgery in conjunction with orthodontic treatment.11,12 Receiver operating characteristic (ROC) analysis is an excellent method for evaluating and comparing the performance of diagnostic tests.16,17 Wardlaw et al18 used ROC analysis to evaluate the relationships between several cephalometric measurements and anterior open bite. They found that the overbite depth indicator had the highest diagnostic value in discriminating between patients with and without open bite.19 e485
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Not all adult Class III patients are candidates for surgical correction. Patient assessment and selection are the main issues in diagnosis and treatment planning.20 The purpose of this study was to distinguish between surgery candidates (surgical group) and nonsurgery candidates (nonsurgical group) with skeletal Class III malocclusions by using ROC analysis of cephalometric variables. MATERIAL AND METHODS
The subjects included 40 men and 40 women with Class III malocclusions, whose mean age before treatment was 23 years (range, 18-34 years). The criteria for inclusion in the study were a Class III molar relationship, a negative overjet, an ANB angle less than 0 , and a Wits appraisal less than –1 mm. Consecutive patients were selected and divided into 2 groups, each with 20 men and 20 women. Those who had received orthodontic therapy alone made up the nonsurgical group; those who had required orthognathic surgery of mandibular setback combined with orthodontic treatment comprised the surgical group. Some patients were excluded from the study because complete records were lacking. We also excluded subjects with craniofacial syndromes, cleft lip or palate, and trauma history. The goals of orthodontic treatment, with or without orthognathic surgery, are to achieve harmonious facial esthetics and a functional occlusion, but soft-tissue changes also play an important role in evaluating treatment effects. The Taiwan Board of Orthodontics introduced an objective grading system for assessing posttreatment dental casts and panoramic radiographs similar to that of the American Board of Orthodontics and supplemented by lateral cephalographs.21 The Taiwan Board of Orthodontics objective grading system evaluates 20 criteria. In this retrospective study with this grading system, we evaluated orthodontic and orthognathic surgical patients who were consecutively completed in 2006 to 2009. The mean scores for orthodontic patients were 78%. There were 1 patient in the “slightly improved” category and no patients in the “worse" or "no improvement” categories. The mean scores for orthognathic surgical patients were 74%. There were no patients in the “worse," "no improvement," or "slightly improved” categories. A mean score of more than 70% represents a high standard of treatment in the “greatly improved” category. The mean scores of this study indicate excellent-to-good treatment results for both groups. In this study, we used lateral cephalometric radiographs obtained before treatment. A correction of 10% was made for the magnification of the linear measurements from each cephalogram. Thirty cephalometric
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landmarks on the craniofacial complex were identified and digitized (Fig 1). A computerized cephalometric system, Winceph (version 8.0, Rise, Sendai, Japan), was used to obtain 25 cephalometric measurements, including 12 angular, 9 linear, and 4 ratio variables (Table I). Descriptive statistics, including means, standard deviations, and Student t tests results, were computed for each measurement (Table II). We selected 25 cephalometric measurements that were used in previous studies. The Bonferroni adjustment with an alpha level of 0.002 (0.05/25) was applied as a multiple-comparison correction when several statistical tests were performed simultaneously. The most suitable measurements were statistically validated and clinically relevant.22 Measurements that were statistically different between the 2 groups with the 2-sample t test and the Bonferroni adjustment were further analyzed by the ROC curve analysis. Systematic measurement errors were estimated by means of paired Student t tests, and the random method error (ME) was quantified with Dahlberg’s formula, ME 5 OSd2/2n, where d is the difference between duplicate measurements and n is the number of double measurements.23,24 We study used the ROC analysis and the area under the curve (AUC) to determine the set of cephalometric measurements for the best discrimination between orthodontic therapy and orthognathic surgery. The ROC curve is a plot of sensitivity (true positive rate) on the y-axis and 1−specificity (false positive rate) on the xaxis. The different points on the curve correspond to different cutoff points used to designate the surgery group.25 The AUC is generally considered a reasonable summary of the overall diagnostic accuracy of the continuous variables. In general, for 2 variables, the variable with higher AUC is considered a better indicator for the surgery group. For each ROC curve, a cutoff point that yields the best combination of sensitivity and specificity can be identified to provide a recommendation for surgery. All data analyses were performed by using SAS software (version 9, SAS Institute, Cary, NC). RESULTS
To assess errors in the cephalometric digitizing, 1 investigator (C.Y.L.) digitized 20 randomly selected lateral cephalographs. The same investigator redigitized the same cephalographs after an interval of 2 weeks. The method errors between the double measurements were analyzed. No significant differences appeared between the 2 sets of repeated measurements. The method errors were between 0.16 and 0.29 mm for linear measurements, between 0.26 and 0.60 for angular measurements, and between 0.14% and 0.30% for ratios. The intraclass correlation coefficients were from 0.973 to
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Table I. Variables of cephalometric analysis used in
this study Linear variables (mm) S-N A–Nv B–Nv Pg–Nv Symphysis width Wits appraisal Overjet Overbite Si–(Li–Pg')
Fig 1. Cephalometric landmarks: 1, N, nasion; 2, S, sella; 3, Po, porion; 4, Or, orbitale; 5, ANS, anterior nasal spine; 6, PNS, posterior nasal spine; 7, A, Point A; 8, U1E, maxillary central incisor edge; 9, U1A, maxillary central incisor apex; 10, B, Point B; 11, Pg, pogonion; 12, Gn, gnathion; 13, Me, menton; 14, Cd, condylion; 15, Go, gonion; 16, GoI, gonial intersection; 17, L1E, mandibular incisor edge; 18, L1A, mandibular incisor apex; 19, BL, lingual Point B; 20, G, glabella; 21, N', soft-tissue nasion; 22, Sn, subnasale; 23, Pg', soft-tissue pogonion; 24, Ls, labrale superius; 25, Li, labrale inferius; 26, Stoms, stomion superius; 27, Stomi, stomion inferius; 28, Si, mentolabial sulcus; 29, Gn', soft-tissue gnathion; 30, Me', soft-tissue menton.
0.990. The reliability was high for all values. Table II shows the means and standard deviations of the 25 cephalometric measurements of both groups. Of these, 14 measurements were significantly different between the surgical and nonsurgical groups (overjet, Wits appraisal, L1-MP, Mx/Mn ratio (Cd-A/Cd-Gn), gonial angle, overbite, Si-(Li-Pg'), PP-MP, G-Sn/Sn-Me', symphysis width, H-angle, PFH/AFH, SN-MP, Pg-Nv) (P \0.002 [0.05/25]), based on the Bonferroni multiple-comparisons procedure. Table III shows the results of further computing the AUCs based on these 14 original measurements (range, 0.694-0.908). Their corresponding cutoff points, which yielded the highest values of sensitivity 1 specificity, were determined. The 14 cephalometric measurements were dichotomized into 2 parts based on the cutoff points. Depending on the clinical criteria, the part with a tendency to surgery
Angular variables ( ) SNA SNB ANB NAPg SN-MP PP-MP Gonial angle U1-PP L1-MP U1–L1 G–Sn–Pg' H–angle
Ratio variables (%) PFH/AFH Mx/Mn ratio G-Sn/Sn-Me Sn-Stoms/Stomi-Me'
was given a score of 1 and the other was given a score of 0. For example, in the overjet measurement, participants with a measure of less than or equal to –4.73 mm were considered to have a tendency for surgery and were given a score of 1. Hence, each of the 14 measurements was transferred into a new score of 1 and 0. The next step was to determine the optimal number of dichotomized measurements for inclusion in the final scoring system. The 14 dichotomized measurements were added 1 by 1 from the measurements with highest to lowest AUC values. Table IV shows the score systems with measurements 2 through 14 with their corresponding AUC values. Although higher AUCs would have better diagnostic accuracy, the AUCs after 6 dichotomized measurements were not greatly changed (0.96 to 0.97). Hence, a scoring system based on 6 dichotomized measurements (overjet, Wits appraisal, L1-MP, Mx/Mn ratio, overbite, and gonial angle) provided an acceptable AUC (0.96) and a feasible number (6) of measurements for the scoring system. For the scoring system of 6 dichotomized measurements, the possible scores of 0 to 6 corresponded to 0 to 6 measurements with values within the part of score 1 (tendency for surgery) in Table III. Using the cutoff points in Table III to dichotomize each of the 14 cephalometric measurements, the optimal combination of sensitivities and specificities is shown in Table III. Since no single measurement can have satisfactory classification performance, a scoring system that combined cephalometric measurements was then compared and analyzed (Table IV and Fig 2). Table V shows the sensitivity and specificity of scores 0 to 6. A score of 4 with the highest value of sensitivity 1 specificity appeared to be the cutoff point, indicating the best combination of sensitivity (88%) and specificity (90%), of the requirement for surgical treatment (Fig 2). The scores of 6 dichotomized measurements were computed for all patients. Table VI lists the 6 measurements in
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Table II. Cephalometric measurements of Class III malocclusion patients treated with and without surgery Nonsurgical group Mean 6 SD 66.06 6 4.17 81.57 6 3.44 85.44 6 3.96 3.87 6 2.18 7.91 6 4.88 68.70 6 3.33 0.56 6 3.88 5.21 6 5.77 6.05 6 5.94 7.50 6 1.46 30.91 6 6.38 21.37 6 5.91 119.55 6 7.39 68.24 6 5.26 122.58 6 6.11 86.94 6 6.82 129.30 6 7.87 9.67 6 2.76 3.55 6 1.20 2.95 6 2.09 4.03 6 2.96 101.20 6 9.08 44.55 6 5.57 3.28 6 0.81 11.26 6 3.06
Variable S-N (mm) SNA ( ) SNB ( ) ANB ( ) NAPg ( ) Mx/Mn ratio (%) A–Nv (mm) B–Nv (mm) Pg–Nv (mm) Symphysis width (mm) SN–MP ( ) PP–MP ( ) Gonial angle ( ) PFH/AFH (%) U1–PP ( ) L1–MP ( ) U1–L1 ( ) Wits appraisal (mm) Overjet (mm) Overbite (mm) G–Sn–Pg' ( ) G–Sn/Sn–Me' (%) Sn–Stoms/Stomi–Me' (%) Si–(Li–Pg') (mm) H–angle ( )
Surgical group Mean 6 SD 65.17 6 3.74 82.57 6 4.03 87.65 6 3.78 5.29 6 3.05 11.05 6 6.43 64.03 6 3.15 0.10 6 3.41 9.25 6 6.27 11.10 6 7.47 6.05 6 1.17 35.92 6 6.03 27.38 6 5.42 127.67 6 6.11 64.14 6 4.81 121.61 6 7.33 77.07 6 7.07 134.12 6 11.44 15.27 6 4.25 7.02 6 2.45 0.37 6 2.70 6.05 6 4.07 92.89 6 7.98 41.30 6 4.22 2.26 6 1.04 7.69 6 4.13
Mean Difference 0.89 1.00 2.21 1.43 3.14 4.67 0.47 4.03 5.50 1.45 5.01 6.01 8.13 4.10 0.97 9.87 4.82 5.06 3.47 2.58 2.03 8.31 3.25 1.03 3.57
t test P value 0.3167 0.2349 0.0126 0.0185 0.0162 \0.0001 0.5643 0.0037 0.0012 \0.0001 0.0005 \0.0001 \0.0001 0.0005 0.5245 \0.0001 0.0313 \0.0001 \0.0001 \0.0001 0.0130 \0.0001 0.0042 \0.0001 \0.0001
P \0.002 (0.05/25) was considered significant based on the Bonferroni multiple-comparisons procedure.
Table III. AUC of 14 significant measurements from Table II Variable Overjet (mm) Wits appraisal L1-MP Mx/Mn ratio Overbite Gonial angle Si-(Li-Pg') G-Sn/Sn-Me' Symphysis width PP-MP H–angle PFH/AFH Pg-Nv SN-MP
AUC 0.908 0.857 0.848 0.840 0.799 0.791 0.776 0.772 0.771 0.769 0.746 0.710 0.696 0.694
Cutoff point 4.73 mm 11.18 mm 80.80 65.90% 0.18 mm 120.80 2.73 mm 97.50% 6.55 mm 25.70 7.60 66.00% 10.09 mm 30.90
Score 1 # 4.73 mm # 11.18 mm #80.80 #65.90% # 0.18 mm $120.80 # 2.73 mm #97.50% #6.55 mm $25.70 #7.60 #66.00% $10.09 mm $30.90
patients with different scores. Thirteen patients had values of 1, and 46.2% (n 5 6) of them were in the gonial angle. Patients with scores of 4, 5, and 6 were mostly in the measurements of gonial angle, Wits appraisal, Mx/Mn ratio, and L1-MP. Overjet and overbite appeared to be the final added measurements in the scores of the 6 measurements. Most patients (23 of 25, or 92%) with overbite problems
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Score 0 . 4.73 mm . 11.18 mm .80.80 .65.90% . 0.18 mm \120.80 . 2.73 mm .97.50% .6.55 mm \25.70 .7.60 .66.00% \10.09 mm \30.90
Sensitivity 0.825 0.850 0.750 0.750 0.600 0.925 0.675 0.800 0.675 0.700 0.525 0.675 0.600 0.875
Specificity 0.850 0.725 0.825 0.775 0.975 0.600 0.725 0.675 0.750 0.750 0.875 0.650 0.800 0.525
had scores of 4 or higher, implying that those with an overbite problem also had other variables. DISCUSSION
This study had several limitations. It was a retrospective study sampled from a university orthodontic practice. The main skeletal anomalies were mandibular
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Table IV. ROC analysis of prediction results in the cumulated top-ranked cephalometric measurements (cumulative
scores) Number of cumulated top–ranked cephalometric measurements 2 3 4 5 6 7 8 9 10 11 12 13 14
Measurements Overjet and Wits appraisal Above measurements plus L1–MP Above measurements plus Mx/Mn ratio Above measurements plus overbite Above measurements plus gonial angle Above measurements plus Si–(Li–Pg') Above measurements plus PP–MP Above measurements plus G–Sn/Sn–Me' Above measurements plus symphysis width Above measurements plus H–angle Above measurements plus PFH/AFH Above measurements plus Pg-Nv Above measurements plus SN-MP
Fig 2. The ROC curve of the final 6-measurement scoring system with the best cutoff point.
protrusion in both the surgical and nonsurgical groups of Class III malocclusions. When we correct an anterior crossbite in the treatment of Class III malocclusions, an inevitable side effect is opening of the mandibular plane. A nonsurgical orthodontic approach or a mandibular setback surgical procedure for skeletal Class III correction often results in backward repositioning of the mandible; this increases the lower anterior face height. Therefore, the indication of nonsurgical orthodontic or surgical treatment for an adult Class III malocclusion is hypodivergent, orthodivergent, or slightly hyperdivergent, whereas the contraindication is moderately and severely hyperdivergent. For orthognathic surgical
AUC 0.876 0.924 0.930 0.956 0.964 0.964 0.968 0.968 0.963 0.976 0.972 0.977 0.973
patients treated with mandibular setback, the vertical relationship can be improved by vertical chin reduction and genioplasty.26 However, we excluded moderately and severely hyperdivergent subjects from the nonsurgical and surgical groups. When used appropriately within their limitations, conventional methods of surgical prediction with cephalometric analysis can provide the objective evidence needed to guide treatment planning and assess treatment outcomes.27 For patients who have developmental dentofacial jaw deformities, predictions for orthognathic surgery are more accurate than for those with underlying cleft or syndromic craniofacial conditions. Since its introduction in the context of electronic signal detection, the ROC curve has become the method of choice for quantification of the accuracy of medical diagnostic tests. The ROC curve analysis is widely applied in measuring the discriminatory ability of diagnostic or prognostic tests. It is an excellent method for evaluating and comparing the performance of diagnostic tests.16,17 ROC curve analysis has substantial value for evaluating the diagnostic information of cephalometric measurements. A Class III malocclusion is difficult to treat optimally.20 Using ROC curve analysis, we found incisal overjet, L1-MP angle (anteroposterior dental relationships), Wits appraisal, and Mx/Mn ratio (anteroposterior jaw relationships), gonial angle (vertical jaw dimension), and incisal overbite (vertical dental relationship) to be the best diagnostic parameters for determining treatment modalities for Class III malocclusion patients. All these parameters showed highly significant differences between the orthodontic nonsurgical and surgical groups.
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Table V. Identifying the cutoff point Number of dichotomized measurements 6 5 4 3 2 1 0
Probability for requiring surgical treatment 0.99 0.95 0.81 0.46 0.15 0.04 0.01
Sensitivity 1 specificity 1.225 1.675 1.750 1.750 1.675 1.350 1.000
Sensitivity Specificity 0.225 1.000 0.675 1.000 0.875 0.900 0.925 0.825 1.000 0.675 1.000 0.350 1.000 0.000
True True False positive negative positive 9 40 0 27 40 0 35 36 4 37 33 7 40 27 13 40 14 26 40 0 40
False negative 30 13 5 3 0 0 0
Table VI. Relationship of scores with variables
Score Total 1 2 3 4 5 6
Total number of participants 80 13 9 6 11 18 9
Gonial angle
Wits appraisal
Mx/Mn ratio
n 53 6 7 4 10 17 10
n 45 1 3 6 9 17 9
n 39 3 1 2 9 15 9
% 46.2 77.8 66.7 90.9 94.4 100.0
In Class III malocclusions, the mandibular incisors are relatively retroclined, and the maxillary incisors are relatively proclined to compensate for skeletal dysplasia. A patient with a skeletal Class III malocclusion generally has a negative overjet in incisor relationships, despite the compensatory inclination of the maxillary and mandibular incisors.28 Ishikawa et al29 reported a close relationship between the inclination of the mandibular incisors and the sagittal jaw relationship. We found highly significant lingual inclinations of the mandibular incisors and largely negative overjets in the surgical group (L1-MP angle, 86.94 6 6.82 in the nonsurgical group and 77.07 6 7.07 in the surgical group; 96 6 7.0 is the Taiwanese norm). The ANB angle has been the most commonly used cephalometric measurement to describe the skeletal discrepancies between the maxilla and the mandible. However, the validity of the ANB angle as an indicator of sagittal jaw relationships has been criticized.30,31 Various investigations showed a low correlation between the Wits appraisal and the ANB angle.32-34 Choi and Chang35 used ROC analysis to evaluate the usefulness of various cephalometric measurements for identifying patients with Class III malocclusions. They found that the Wits appraisal was highly effective for this purpose. Later, Murakami et al36 examined the morphologic differences in the craniofacial complex between surgical and orthodontic patients with skeletal Class III malocclusion. They found that the Wits appraisal was
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% 7.7 33.3 100.0 81.8 94.4 100.0
% 23.1 11.1 33.3 81.8 83.3 100.0
Overjet n 38 2 2 4 5 16 9
% 15.4 22.2 66.7 45.5 88.9 100.0
L1–MP n 37 1 4 1 9 13 9
% 7.7 44.4 16.7 81.8 72.2 100.0
Overbite n 25 0 1 1 2 12 9
% 0.0 11.1 16.7 18.2 66.7 100.0
significantly smaller and the gonial angle was significantly larger in the surgical group than in the orthodontic group. In addition, they observed no values below –15 mm in the orthodontic group in the Wits appraisal. Therefore, the Wits appraisal and the gonial angle might be useful for distinguishing between the 2 groups. Stellzig-Eisenhauer et al20 applied stepwise discriminant analysis to identify the dentoskeletal variables that best distinguish the nonsurgical and surgical groups among adult patients with Class III malocclusion. Of all the variables, the Wits appraisal was the most useful parameter. Similar to the Wits appraisal, we also used the Mx/Mn ratio to analyze the sagittal discrepancy between the maxilla and mandible. This sagittal jaw relationship seems to be a more decisive factor for treatment decisions than morphometric parameters of the mandible alone. We found significant intergroup differences for the parameters representing the sagittal maxillomandibular relationship as indicated by the Mx/ Mn ratio and the Wits appraisal. In addition, the incisal overbite was highly significantly smaller in the surgical group than in the orthodontic group. Furthermore, the patients in the surgical group with smaller overbites also had other variables. Variations in the dentofacial complex are rarely produced by a single factor. As stated by Han and Kim,37 there is no widely accepted cephalometric measurement that shows the dentofacial configuration of a malocclusion. The ROC method of multivariable analysis is far
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more useful in discriminating the diagnostic value of cephalometric measurements. We selected 6 statistically validated variables as the minimum number of discriminators required to obtain the optimum discriminant effectiveness. Hence, if a Class III malocclusion patient has at least 4 of the 6 conditions (overjet, #–4.73 mm; Wits appraisal, #–11.18 mm; L1-MP angle, #80.8 ; Mx/Mn ratio, #65.9%; overbite, #–0.18 mm; and gonial angle, $120.8 ), then the patient would be recommended to have surgical treatment. Using the scoring system based on 6 dichotomized measurements, a higher score indicates the tendency to have surgery. The suggested diagnostic cutoff point of 4 had the best combination of sensitivity (88%) and specificity (90%); for those who had surgical treatment, 88% had scores of 4 or higher, and for those who did not have surgical treatment, 90% had scores of 3 or less. Several methods can be used to identify the important cephalometric measurements for a clinical decision on surgery. The major advantages of the ROC curve in determining cephalometric measurements include the following: (1) it is insensitive to the changes of measurement distribution, since the calculation was based on ranks; (2) although in our study we used the equal classification error costs (the cost for a false positive is equal to the cost of a false negative), ultimately one can specify unequal classification error costs when identifying cutoff points; and (3) it is a relatively easy scoring system, because the score applies only to the dichotomized measurements according to the cutoff points, and it sums the number of items in the surgical regions. The same research methods with lateral cephalometric radiographs with ROC analysis seem suitable, but the most important variables could differ relative to the ethnic population concerned.35,37 Although the discriminant analysis was also a common strategy for selecting important measurements, measurements with skewed distributions can result in optimistically biased estimates and, hence, have less sensitivity.38,39 Even though dental specialists (orthodontists or oral-maxillofacial surgeons) might recommend, and cephalometric measurements might indicate, surgical treatment, self-perceptions of the profile could be more important factors affecting the patient’s decision for surgical correction.40 CONCLUSIONS
In this study, we identified 6 cephalometric measurements as the minimum number of discriminators required to obtain the optimum discriminant effectiveness of diagnosis between surgical and nonsurgical treatment for patients with skeletal Class III malocclusions.
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We thank Yi-Ching Poon for her help with the preparation of the manuscript. REFERENCES 1. Kameda A. The Begg technique in Japan. Am J Orthod 1982;81: 209-27. 2. Chang HP. Components of Class III malocclusion in Taiwanese. Kaohsiung J Med Sci 1985;1:144-55. 3. Yang WS. The study on the orthodontic patients who visited Department of Orthodontics, Seoul National University Hospital. J Korean Dent Assoc 1990;28:811-21. 4. Fu M, Zhang D, Wang B, Deng Y, Wang F, Ye X. The prevalence of malocclusion in China—an investigation of 25392 children. Chin J Orthod 2002;9:151-3. 5. Graber TM, Vanarsdall RL, Vig KWL. Orthodontics: current principles and techniques. 4th ed. St Louis: Mosby; 2005. p. 565. 6. Susami R. A cephalometric study of dentofacial growth in Class III subjects with anterior crossbite. J Jpn Orthod Soc 1967;26: 1-34. 7. Kim SC, Lee KS. The cephalometric study of facial types in Class III malocclusion. Korean J Orthod 1990;20:569-89. 8. Zeng XL. A study of skeletal types of Class III malocclusion. Chin J Stomatol 1993;28:170-3, 191. 9. Chang HP, Lin HC, Liu PH, Chang CH. Geometric morphometric assessment of treatment effects of maxillary protraction combined with chin cup appliance on the maxillofacial complex. J Oral Rehabil 2005;32:720-8. 10. Staudt CB, Kiliaridis S. Different skeletal types underlying Class III malocclusion in a random population. Am J Orthod Dentofacial Orthop 2009;136:715-21. 11. Proffit WR, White RP Jr, Sarver DM. Contemporary treatment of dentofacial deformity. St Louis: Mosby; 2003. p. 507-73. 12. Chang HP, Tseng YC, Chang HF. Treatment of mandibular prognathism. J Formosa Med Assoc 2006;105:781-90. 13. Chang HP, Liu PH, Chang HF, Chang CH. Thin-plate spline (TPS) graphical analysis of the mandible on cephalometric radiographs. Dentomaxillofac Radiol 2002;31:137-41. 14. Chang ZC, Chang HP, Chen YJ, Yao CC, Liu PH, Chang HF. The treatment effects of the face mask therapy in the midfacial configurations in skeletal Class III growing patients by means of morphometric techniques. J Formosa Med Assoc 2005;104:935-41. 15. Lin HC, Chang HP, Chang HF. Treatment effects of occipito-mental anchorage appliance of maxillary protraction combined with chincup traction in children with Class III malocclusion. J Formosa Med Assoc 2007;106:380-91. 16. Swets JA. Measuring the accuracy of diagnostic systems. Science 1988;240:1285-93. 17. Gu J, Ghosal S, Roy A. Bayesian bootstrap estimation of ROC curve. Stat Med 2008;27:5407-20. 18. Wardlaw DW, Smith RJ, Hertweck DW, Hildebolt CF. Cephalometrics of anterior open bite: a receiver operating characteristic (ROC) analysis. Am J Orthod Dentofacial Orthop 1992;101:234-43. 19. Kim YH. Overbite depth indicator with particular reference to anterior open-bite. Am J Orthod 1974;65:586-611. 20. Stellzig-Eisenhauer A, Lux CJ, Schuster G. Treatment decision in adult patients with Class III malocclusion: orthodontic therapy or orthognathic surgery? Am J Orthod Dentofacial Orthop 2002; 122:27-38. 21. Casko JS, Vaden JL, Kokich VG, Damone J, James RD, Cangialosi TJ, et al. Objective grading system for dental casts and panoramic radiographs. American Board of Orthodontics. Am J Orthod Dentofacial Orthop 1998;114:589-99.
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22. Chang HP. Evaluation of cephalometric analysis. J Formosa Dent Assoc 1985;8:2-13. 23. Dahlberg G. Statistical methods for medical and biological students. New York: Interscience Publications; 1940. p. 100-40. 24. Houston WJB. The analysis of errors in orthodontic measurements. Am J Orthod 1983;83:382-90. 25. Rosner B. ROC curves. In: Rosner B, editor. Fundamentals of biostatistics. Belmont, Calif: Thomson Brooks/Cole; 2006. p. 64-6. 26. Bailey LJ, Sarver DM, Turvey TA, Proffit WR. Class III problems. In: Proffit WR, White RP, Sarver DM, editors. Contemporary treatment of dentofacial deformity. St Louis: Mosby; 2003. 27. Jacobson A. How reliable is cephalometric prediction? In: Jacobson A, Jacobson R, editors. Radiographic cephalometry: from basics to videoimaging. 2nd ed. Chicago: Quintessence; 2006. p. 293-300. 28. Ishikawa H, Nakamura S, Iwasaki H, Kitazawa S, Tsukada H, Chu S. Dentoalveolar compensation in negative overjet cases. Angle Orthod 2000;70:145-8. 29. Ishikawa H, Nakamura S, Iwasaki H, Kitazawa S, Tsukada H, Sato Y. Dentoalveolar compensation related to variations in sagittal jaw relationships. Angle Orthod 1999;69:534-8. 30. Jacobson A. The “Wits” appraisal of jaw disharmony. Am J Orthod 1975;67:125-38. 31. Chang HP. Assessment of anteroposterior jaw relationship. Am J Orthod Dentofacial Orthop 1987;92:117-22.
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APPENDIX
y-axis. Some sample values are shown in Table A and marked on Figure A1. The lower left point of the ROC curve (0, 0) means that all patients were classified into the nonsurgical group. Hence, there would be no false positives but, at the same time, no true positives. Similarly, the point of 1, 1 means that all patients were classified into the surgical group. Hence, there would be no false negatives but, at the same time, no true negatives. The area under the connected line is considered the AUC, and any point with the largest sum of sensitivity and specificity is the best cutoff point (a threshold of the ROC curve). For the 14 cephalometric measurements with significant differences between the surgical and nonsurgical groups, their ROC curves are shown in Figure A2. The best cutoff point for each cephalometric measurement is indicated by a small circle on the corresponding ROC curve (Fig A2).
The ROC curve for each measurement was generated from the computed sensitivities and specificities of all possible values in the measurement. For example, the values of overjet of the 80 subjects ranged from –12.73 (mm) to –1.55 (mm). Starting by using the smallest value (–12.73) as the cutoff point for indicating surgery (#–12.73), since only 1 subject in the surgery group had a value of –12.73, and all subjects in the nonsurgery group were all larger than –12.73, the corresponding sensitivity is 2.5% and the corresponding specificity is 100%. The corresponding point of (1-specificity, sensitivity) 5 (0, 0.025) is marked as point 1 in the ROC curve (Fig A1). Similarly, we computed from all the values of overjet the corresponding sensitivities and specificities, and a series of points can be plotted with 1-specificity as the x-axis and sensitivity as the
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Table A. Corresponding sensitivities and specificities from the values of overjet marked on Figure A1 Number of participants Point 1 2 3 4 5 6 7
Overjet 12.73 11.73 6.00 5.91 4.73 3.55 3.27 1.55
Sensitivity 0.025 0.050 0.625 0.650 0.825 0.900 1.000 1.000
Specificity 1.000 1.000 1.000 0.925 0.850 0.575 0.400 0.000
Sensitivity 1 specificity 1.025 1.050 1.625 1.575 1.675 1.475 1.400 1.000
Fig A1. The ROC curve for overjet measurement. The corresponding points marked by 1 through 7 are shown in Table A.
True positive 1 2 25 26 33 36 40 40
True negative 40 40 40 37 34 23 16 0
False positive 0 0 0 3 6 17 24 40
True negative 39 38 15 14 7 4 0 0
Fig A2. The ROC curves for the 14 measurements and their corresponding cutoff points.
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