predictive variable for the outcome of early functional treatment of class iii maloclussion

7
CONTINUING EDUCATION Predictive treatment variables for the outcome of Class III malocclusion of early functional Lorenzo Franchi, DDS, a Tiziano Baccetti, DDS, PhD, b and Isabella Tollaro, MD, DDS c Firenze, Italy The aim of this study was to select a model of cephalometric and occlusal predictive variables for the results of early treatment of Class III malocclusion, due to mandibular protrusion in the deciduous dentition. Lateral cephalograms and dental casts of 45 subjects (22 boys and 23 girls) with Class III malocclusion in the deciduous dentition were analyzed at the start of treatment (mean age 5.57 _+ 0.85 years). The patients were treated with a functional appliance (removable mandibular retractor). All subjects were reevaluated after a mean period of 9.54 _ 2.28 years comprising active treatment plus retention. At this time, the sample was divided into two groups according to occlusal criteria: successful group (23 subjects) and unsuccessful group (22 subjects). Stepwise variable selection on the measurements at the time of first observation identified three predictive variables: the inclination of the condylar axis in relation to the stable basicranial line (CondAx-SBL), the inclination of the nasal line to the mandibular line (NL-ML), and the transverse width of the mandibular arch measured at the first deciduous molars. Discriminant analysis assigned a classificative power of 95.55% to the predictive model. On the basis of the equation generated by the multivariate statistical method, outcome of early treatment for each new case with Class III malocclusion in the deciduous dentition can be accordingly predicted. The important role of both vertical and transverse relationships in Class III prognosis was emphasized. (Am J Orthod Dentofac Orthop 1997;112:80-6.) Prognosis of Class III malocclusion still represents one of the major challenges in contem- porary orthodontics. Two intimately interconnected facets of this clinical problem are (1) the appraisal of long-term results of early treatment, and (2) the early identification of "surgical" cases. Adequate statistical methods on samples of sub- jects starting treatment in the very early ages have to be implemented to predict success or failure of interceptive therapy of developing Class III maloc- clusion. Multivariate approach to cephalometric data for predictive purposes has been recommended by Johnston 1 and used for differential diagnosis by Kowalski.2,3 Discriminant analysis was used by Bat- tagel 4 to forecast relapse in subjects with Class III malocclusion treated by nonextraction techniques in the mixed and permanent dentitions. Stensland et al.5 used the same statistical method to predict short-term outcome of early orthopedic therapy of Class III malocclusion. Different kinds of functional or orthopedic ap- From the Department of Orthodontics, The University of Florence. aPhD program in Preventive Orthodontics. bPost-Doctoral Fellow. CProfessor, Head and Chairman. Reprint requests to: Dr. Lorenzo Franchi, Istituto di Odonto-Gnato- Stomatologia, Universit~ degli Studi di Firenze, Via del Ponte di Mezzo, 46-48, 50127, Firenze, Italy. Copyright © 1997 by the American Association of Orthodontists. 0889-5406/97/$5.00 + 0 8/1/72686 pliances are available for treatment of Class III malocclusion associated with mandibular protrusion in the early developmental phases? -11 Our previous studies showed significant favorable craniofacial changes induced by a functional appliance (remov- able mandibular retractor, RMR) in children with Class III malocclusion, treated in the deciduous dentition.12, a3 The aim of the current study was to investigate whether any dentoskeletal characteristics in the deciduous dentition can be used as predictive vari- ables for long-term results of early functional treat- ment of Class III malocclusion because of mandib- ular protrusion. SUBJECTS AND METHODS A sample of 45 subjects, 22 boys and 23 girls, with Class III malocclusion, was selected from the files of the Department of Orthodontics at the University of Flo- rence. At the time of first observation, the subjects presented with Class III malocclusion in the deciduous dentition (concomitant presence of anterior crossbite, Class III deciduous canine relationship, and mesial step deciduous molar relationship). Class III malocclusion was due to mandibular protrusion in all the subjects, as revealed by cephalometric floating norms. 14,a5Functional analysis16 showed a postural rest position anterior to the occlusal position in all the patients. Mean age at the time of first observation was 5.57 -+ 0.85 years. 80

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Page 1: Predictive Variable for the Outcome of Early Functional Treatment of Class III Maloclussion

CONTINUING EDUCATION

Predictive treatment

variables for the outcome of Class III malocclusion

of early functional

Lorenzo Franchi, DDS, a Tiziano Baccetti, DDS, PhD, b and Isabella Tollaro, MD, DDS c Firenze, Italy

The aim of this study was to select a model of cephalometric and occlusal predictive variables for the results of early treatment of Class III malocclusion, due to mandibular protrusion in the deciduous dentition. Lateral cephalograms and dental casts of 45 subjects (22 boys and 23 girls) with Class III malocclusion in the deciduous dentition were analyzed at the start of treatment (mean age 5.57 _+ 0.85 years). The patients were treated with a functional appliance (removable mandibular retractor). All subjects were reevaluated after a mean period of 9.54 _ 2.28 years comprising active treatment plus retention. At this time, the sample was divided into two groups according to occlusal criteria: successful group (23 subjects) and unsuccessful group (22 subjects). Stepwise variable selection on the measurements at the time of first observation identified three predictive variables: the inclination of the condylar axis in relation to the stable basicranial line (CondAx-SBL), the inclination of the nasal line to the mandibular line (NL-ML), and the transverse width of the mandibular arch measured at the first deciduous molars. Discriminant analysis assigned a classificative power of 95.55% to the predictive model. On the basis of the equation generated by the multivariate statistical method, outcome of early treatment for each new case with Class III malocclusion in the deciduous dentition can be accordingly predicted. The important role of both vertical and transverse relationships in Class III prognosis was emphasized. (Am J Orthod Dentofac Orthop 1997;112:80-6.)

Prognosis of Class III malocclusion still represents one of the major challenges in contem- porary orthodontics. Two intimately interconnected facets of this clinical problem are (1) the appraisal of long-term results of early treatment, and (2) the early identification of "surgical" cases.

Adequate statistical methods on samples of sub- jects starting treatment in the very early ages have to be implemented to predict success or failure of interceptive therapy of developing Class III maloc- clusion. Multivariate approach to cephalometric data for predictive purposes has been recommended by Johnston 1 and used for differential diagnosis by Kowalski. 2,3 Discriminant analysis was used by Bat- tagel 4 to forecast relapse in subjects with Class III malocclusion treated by nonextraction techniques in the mixed and permanent dentitions. Stensland et al.5 used the same statistical method to predict short-term outcome of early orthopedic therapy of Class III malocclusion.

Different kinds of functional or orthopedic ap-

From the Department of Orthodontics, The University of Florence. aPhD program in Preventive Orthodontics. bPost-Doctoral Fellow. CProfessor, Head and Chairman. Reprint requests to: Dr. Lorenzo Franchi, Istituto di Odonto-Gnato- Stomatologia, Universit~ degli Studi di Firenze, Via del Ponte di Mezzo, 46-48, 50127, Firenze, Italy. Copyright © 1997 by the American Association of Orthodontists. 0889-5406/97/$5.00 + 0 8/1/72686

pliances are available for treatment of Class III malocclusion associated with mandibular protrusion in the early developmental phases? -11 Our previous studies showed significant favorable craniofacial changes induced by a functional appliance (remov- able mandibular retractor, RMR) in children with Class III malocclusion, treated in the deciduous dentition.12, a3

The aim of the current study was to investigate whether any dentoskeletal characteristics in the deciduous dentition can be used as predictive vari- ables for long-term results of early functional treat- ment of Class III malocclusion because of mandib- ular protrusion.

SUBJECTS AND METHODS

A sample of 45 subjects, 22 boys and 23 girls, with Class III malocclusion, was selected from the files of the Department of Orthodontics at the University of Flo- rence. At the time of first observation, the subjects presented with Class III malocclusion in the deciduous dentition (concomitant presence of anterior crossbite, Class III deciduous canine relationship, and mesial step deciduous molar relationship). Class III malocclusion was due to mandibular protrusion in all the subjects, as revealed by cephalometric floating norms. 14,a5 Functional analysis 16 showed a postural rest position anterior to the occlusal position in all the patients. Mean age at the time of first observation was 5.57 -+ 0.85 years.

80

Page 2: Predictive Variable for the Outcome of Early Functional Treatment of Class III Maloclussion

American Journal of Orthodontics and Dentofacial Orthopedics Franchi, Baccetti, and Tollaro 81 Volume 112, No. 1

Fig. 1. Removable mandibular retractor.

Early treatment of the malocclusion was accomplished by means of a functional appliance, removable mandibu- lar retractor (RMR) (Fig. 1). Mean active treatment period was 2.79 _+ 1.24 years. During this period, the children wore RMR at least 14 hours a day (nighttime included). The degree of cooperation was acceptable in all the patients. Active treatment was discontinued when anterior crossbite had been completely corrected. There- after, all patients underwent a retention period by means of RMR, which was applied only during the night. Con- struction features and mode of action of RMR have been extensively reported elsewhere. 12

At the time of first observation lateral cephalograms and dental casts of all patients were analyzed. Lateral cephalograms of the 45 children with Class III malocclu- sion were taken with the same x-ray device and by a single technician. Focus-median plane distance was 152 cm and film-median plane distance was 10 cm, with an enlarge- ment of 7%.

Cephalometric analysis was based on a previously described basicranial reference system comprising two lines perpendicular to each other12:

• Stable Basicranial Line, SBL (passing through the most superior point of the anterior wall of the sella turcica at the junction with tuberculum sellae, point T, 17 and tangent to the lamina cribrosa of the ethmoid);

• Vertical T, VertT (perpendicular to SBL and passing through point T).

The following landmarks were used: point A (A); point B (B); prosthion (Pr); infradentale (Id); pogonion (Pg); menton (Me); gonial intersection (Goi); articulare (At); condylion (Co); center of the condyle (Cs), i.e., a

T SBL.

G ~ b

Fig. 2. Cephalometric linear measurements.

point equidistant from the anterior, posterior, and supe- rior borders of the condylar head; basion (Ba); anterior nasal spine (ANS); and posterior nasal spine (PNS). The definitions of all these landmarks correspond to those given by Bj6rk, 18 ~degaard, 19 and Riolo et al. 2°

The following measurements were performed:

Linear measurements for the assessment of sagittal rela- tionships (Fig. 2): A-VertT, B-VertT, Pr-VertT, Id- VertT, Pg-VertT, Goi-VertT, Co-VertT.

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82 Franchi, Baccetti, and Tollaro American Journal of Orthodontics and Dentofacial Orthopedics July 1997

NL

ANS

Fig. 3. Cephalometdc angular measurements .

Linear measurements for the assessment of mandibular dimensions (Fig. 2): Co-Pg, Co-Goi, Goi-Pg.

Angular measurements for the assessment of cranial base angulation (Fig. 3): Ba-T-VertT, Ar-T-VertT.

Angular measurements for the assessment of vertical relationships (Fig. 3): Nasal line (NL)-SBL, man- dibular line (ML)-SBL, nasal line-mandibular line (NL-ML), gonial angle (Ar-Goi-Me).

Angular measurement for the assessment of condyle inclination (Fig. 3): Condylar axis (CondAx)-SBL. Condylar axis is a line passing through point condylion and point Cs.

The assessment of the method error for the cephalo- metric measurements was performed with the Dahlberg's formula 21 on 20 repeated measurements randomly se- lected from the total of the observations. The error ranged between 0.13 and 0.81 mm for the linear measurements, and between 0.19 ° and 0.93 ° for the angular measure- ments.

On the dental casts of all the subjects at the time of the first observation, the following measurements for the assessment of interarch transverse relationships were car- ried out:

• Maxillary deciduous intermolar width, intended as the distance between the central fossae of right and left first maxillary deciduous molars (measurement 1 in Fig. 4).

• Mandibular deciduous intermolar width, intended as the distance between the tips of the distobuccal cusps of right and left first mandibular deciduous molars (measurement 2 in Fig. 4).

• Transverse discrepancy (TD), i.e., the difference between maxillary and mandibular deciduous inter-

Fig, 4. Transverse measurements on dental casts (see text for explanations).

molar widths (measurement 1 subtracted from mea- surement 2 in Fig. 4).

Method error for dental cast measurements 21 on 20 repeated measurements randomly selected from the total of the observations was of 0.14 mm.

The subjects were revaluated after a mean period of 9.54 + 2.28 years (mean age: 15.76 _+ 1.67 years) on the basis of their postretention occlusions. At this time, failure of treatment was defined as "the concomitant presence of Class III permanent molar relationship, Class I l l perma- nent canine relationship and anterior crossbite (of at least one incisor)." According to this rationale, the sample was divided into two groups: successful group (SG) and unsuc- cessful group (USG). The SG consisted of 23 subjects, 12 boys and 11 girls, mean age at the time of first observation 5.5 -+ 0.8 years; the USG comprised 22 subjects, 10 boys and 12 girls, mean age at the time of first observation 5.65 + 0.91 years. Reevaluation occurred 9.32 -+ 2.43 years after first observation for SG, and 9.78 -+ 2.14 years after first observation for USG.

Data Analysis

Discriminant analysis was applied to cephalometric and dental cast values of the 45 subjects at the time of first observation. Discriminant analysis is a multivariate statistical technique that is specifically designed to separate as widely as possible two groups of subjects taken from the same population. 22 In the current study, this statistical procedure was used to identify those

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American Journal o f Orthodontics and Dentofacial Orthopedics Franchi, Baccetti , a n d T o l l a r o 83 Volume 112, No. 1

Table I. Descriptive statistics for all cephalometric and dental cast variables

Total sample n = 45 Cephalometric

variables Mean SD SE Max Min

A-VertT (mm) 54.05 3.50 0.52 61 43 B-VertT (mm) 49.94 5.34 0.79 60 36 Pr-VertT (mm) 53.14 4.30 0.64 61 40 Id-VertT (mm) 52.46 5.04 0.75 63 41 Pg-VertT (ram) 46.76 6.77 1.00 63 29 Goi-VertT (mm) 12.31 4.46 0.66 20 2 Co-VertT (mm) 16.49 2.46 0.37 21 9 Co-Pg (mm) 97.75 5.04 0.75 108 85 Co-Goi (ram) 45.98 2.89 0.43 52 40.5 Goi-Pg (ram) 65.25 3.80 0.57 73 57 Ba-T-VertT (°) 40.58 4.70 0.70 49 27 Ar-T-VertT (°) 35.34 5.22 0.78 46 21 NL-SBL (°) 5.23 4.25 0.63 16 -2 .5 ML-SBL (°) 31.37 6.20 0.92 44 19.5 NL-ML (°) 26.13 5.85 0.87 39 12 Ar-Goi-Me (°) 130.58 5.36 0.80 143 119 CondAx-SBL (°) 67.87 5.03 0.75 79 58

Dental casts measurements Maxillary deciduous

intermolar width (ram) 33.59 1.8i 0.27 37.3 Mandibular deciduous

intermolar width (mm) 35.24 2.42 0.36 40.8 TD (mm) -1 .62 2.00 0.29 3.5

Successful groupn = 2 3 Unsuccessfulgroupn = 22

Mean SD SE Max Min Mean SD SE Max Min

53.87 2.96 0.62 59 49 54.25 4.04 0.86 61 43 49.98 4.67 0.97 60 40 49.91 6.07 1.29 58 36 52.87 3.92 0.82 61 44 53.43 4.73 1.00 60 40 52.32 4.76 0.99 63 42 52.61 5.43 1.16 60 41 47.32 5.77 1.20 63 36 46.18 7.78 1.66 58 29 12.65 3.84 0.80 18 3 11.95 5.10 1.09 20 2 16.78 2.06 0.43 12 20 16.18 2.83 0.60 21 9 97.24 4.43 0.92 108 89 98.29 5.65 1.20 108 85 46.26 2.47 0.51 50.5 41 45.68 3.31 0.70 52 40.5 65.54 3.34 0.69 73 60 64.95 4.30 0.91 71.5 57 40.80 4.00 0.83 48 34 40.34 5.42 1.15 49 27 35.84 4.66 0.97 45 2 6 34.81 5.81 1.24 46 21

6.06 3.70 0.77 13 - 2 4.36 4.68 1.00 16 -2 .5 29.06 4.41 0.92 37 21 33.77 6.96 1.48 44 19.5 23.00 4.14 0.86 31.5 12 29.41 5.63 1.20 39 18

128.39 4.80 1.00 136 119 133.32 4.76 1.01 143 122 71.27 4.01 0.84 79 65 64.32 3.21 0.68 69.5 58

30 33.37

30 33.71 - 6 -0 .34

1.81 0.38 37.3 30 33.83 1.83 0.39 37.2 30

1.75 0.36 37.3 30 36.84 1.97 0.42 40.8 33.2 1.50 0.31 3.5 - 3 -2 .96 1.55 0.33 0 - 6

Max, Maximum; Min, minimum.

dentoskeletal variables in the deciduous dentition most responsible for the prediction of success or failure of early Class III treatment. This multivariate approach was allowed by exploratory comparison between the values for all variables in SG and in USG with one-way analysis of variance at the time of first observation. 22'23 Null hypothesis that all group means were equal was rejected at the significant level o f p < 0.01.

To arrive at the best model for discrimination, the first phase of the analysis was to select those variables which were most important for group separation be- tween SG and USG. Therefore stepwise variable selec- tion was used to identify "good" predictor variables. Forward selection procedure with F-to-enter and F-to

remove equal to 4 was chosen. 23 When the smallest set of significant discriminant variables was selected, pre- dictive power (classificative power) of the model was tested with discriminant analysis.

The aim of this last procedure is to provide a method to forecast which group a new case is most likely to fall into. Unstandardized discriminant function coefficients are calculated for each previously selected variable, along with a constant. 23 This leads to an equation that will assign a score to each patient. A "mean score" for each of the two groups is given. Halfway between these scores is the dividing value (critical score), which establishes to which of the two groups an individual case belongs. 4

Table II, Stepwise variable selection procedure

Variables in model F-Remove Variables not

CondAx-SBL 26.9855

Mandibular Intermolar Width 14.3599

ML-NL 12.7936

in model F-Enter

Ar-Goi-Me 1.5067

NL-SBL 1.1273

ML-SBL 1.1273 A-VertT 0.5584

Ba-T-VertT 0.5296 Co-Pg 0.2139

Co-VertT 0.1311

B-VertT 0.1217 TD 0.0951

Id-VertT 0.0639 Pg-VertT 0.0585 Pr-VertT 0.0520

Step # 3. Stepwise variable selection R-squared = 0.7395, F-to-enter = 4, F-to-remove = 4, d.f. = 41.

RESULTS

Descr ipt ive statistics for all cepha lometr ic and dental cast variables both for total sample and for successful and unsuccessful groups at the t ime of first observat ion (dec iduous denti t ion) are l isted in Table I.

Stepwise variable se lect ion generated a three- variable m o d e l that produced the m o s t efficient separation b e t w e e n the two groups (SG vs U S G ) .

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8 4 Franchi , Baccett i , a n d Tollaro American Journal of Orthodontics and Dentofacial Orthopedics July 1997

Table IlL D i s c r i m i n a n t ana lys i s

Actual group Number of cases No.

Group 1 (success) 23 22 Group 2 (failure) 22 1

Percentage of cases correctly classified: 95.55%

Classification results

Predicted group membership

1 2

% No: %

95.65 1 4.35 4.55 21 95.45

Predictive variables Unstandardized canonical discriminant

function coefficients

CondAx-SBL 0.20809 ML-NL -0.11904 Mandibular arch width -0.31604 Constant 0.10603

Individual score = 0.20809(CondAx_SBL) -- 0.11904(ML_NL ) -- 0.31604(Mand. Dec. Interrnolar Width) ~1- 0.10603. Discriminant scores for group means (group centroids): Successful Group = 1.61094. Unsuccessful Group = - 1.68416. Critical score = - 0.03651.

The variables selected were the inclination of the condylar axis, in relation to the stable basicranial line (CondAx-SBL), the inclination of the nasal line to the mandibular line (NL-ML), and the transverse width of the mandibular arch measured at the first deciduous molars (Table II). The classificative power of the selected three-variable model was 95.55% (Table III). Only one case in each group was not correctly classified. Unstandardized discrimi- nant function coefficients of the selected variables, along with a calculated constant (Table III), lead to the following equation that provides individual scores for the assignment of a new case to U G or to USG:

Individual score = 0.20809(CondAx-SBL~ - 0.11904(ML_NL)

-- 0"31604(Mantt.Dec.Int . . . . larWidth) + 0 . 1 0 6 0 3 .

The critical score (i.e., the value dividing SG from USG) was -0.03661, that is the mean value of group centroids of the two groups (Table III). Each new case with Class III malocclusion associated with mandibular protrusion in the deciduous dentition that will show an individual score higher than the critical score will be treated successfully by func- tional appliances. On the contrary, each new case with Class III malocclusion presenting with a more negative individual score than the critical score can be predicted to respond poorly to early treatment. Both predictions can be made with a probability of error of about 5%.

DISCUSSION

The current investigation dealt with the predict- ability of outcome in early functional treatment of

Class III malocclusion. "Outcome" was considered as the result of active treatment plus retention. Therefore the aim of this study was not to assess relapse of early Class III treatment. All patients underwent a long- term evaluation of treatment results about 9.5 years after the start of treatment (around 15.5 years of age), when a great part of active growth had already oc- curred. A certain amount of residual craniofacial growth had still to take place in a few subjects at later ages. For all these reasons, it is not convenient to compare the results of the current work to those of previous investigators. Stensland et al.5 studied the short-term outcome of early treatment of Class III malocclusion; Battagel 4 analyzed a model for predic- tion of relapse in treated children with Class III map occlusion.

Other peculiar features of the current study were as follows:

• Treatment of Class III malocclusion was started in the deciduous dentition.

• All patients presented with mandibular pro- trusion and were accordingly treated with a specific appliance. As a consequence, the pro- posed predictive model is not suitable for children with Class III malocclusion associ- ated with maxillary retrusion and treated with face mask or protraction headgear.

• Definition of failure of early treatment was based on strict criteria, i.e., the same occlusal features that were used as a clinical rationale for the diagnosis of Class III malocclusion at the start of treatment.

As to statistical method, discriminant analysis appears to be one of the most powerful tools for the

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American Journal of Orthodontics and Dentofacial Orthopedics Franchi, Baccetti, and ToUaro 85 Volume 112, No. 1

identification of predictive variables at the time of first observation. Nevertheless, there are likely to be other elements for the final result of treatment (cephalometric variables, heredity, soft tissue fea- tures) that have not been included in the current analysis, but that might improve the model. 1-4,24,25

In the current study, a set of cephalometric and dental cast measurements was chosen as represen- tative of craniofacial and occlusal characteristics in the three dimensions. In fact, our previous research provided evidence that the cephalometric analysis comprising a basicranial reference system and mea- surements for the inclination of the condylar axis was quite efficient in the description of mandibular resizing and reshaping (anterior morphogenetic rotation), in- duced by early functional treatment of Class III mal- occlusion. 12,13 Moreover, experimental studies empha- sized similar mandibular changes produced by retractive forces on the growing mandible. 26-29 The good discriminant power of only three of the chosen measurements witnessed that the analysis was viable for the identification of predictive variables in early treatment of mandibular protrusion.

The three predictive measurements in the decid- uous dentition were (1) the orientation of the con- dylar head, (2) the maxillomandibular vertical rela- tionship, and (3) the transverse size of the mandibular arch. Better prognosis of early treat- ment of Class III malocclusion is associated with a large CondAx-SBL angle, i.e., with an upward- forward inclination of the condyle. It has been demonstrated that the major effect of RMR therapy in children with Class III malocclusion consists of a more upward and forward direction of condylar growth when compared with an untreated control group. 12,13 Therefore it appears that early treatment of Class III malocclusion is more effective when the orientation of the condyle at the start of treatment is concordant with the expected change induced by treatment itself.

The two other predictive factors that were se- lected by multivariate analysis regard facial vertical

relationships and transverse dimensions of the man- dibular arch. These results claim for a more atten- tive evaluation of vertical and transverse relation- ships in early Class III diagnosis and treatment planning. Interestingly enough, no sagittal parame- ter or dimensional measurement of the mandible on the lateral films was actually included in the predic- tive model. Skeletal open bite and excessive width of the mandibular arch are to be considered as unfa- vorable signs in prognosis of Class III malocclusion in the deciduous dentition.

The predictive model that was developed in the current study can identify good or bad responders to early treatment of Class III malocclusion with a functional appliance. This does not necessarily mean that the model is able to automatically recog- nize "surgical versus not-surgical" cases. In bad responders, the possibilities of alternative orthodon- tic therapies should be taken into account in com- prehensive treatment planning.

CONCLUSIONS

The appraisal of long-term results of early treatment of Class III malocclusion associated with mandibular protrusion was performed by means of discriminant anal- ysis, to identify significant predictive variables in the deciduous dentition. Three predictive measurements were selected: the inclination of the condylar axis in relation to the stable basicranial line (CondAx-SBL), the inclination of the nasal line to the mandibular line (NL-ML), and the transverse width of the mandibular arch measured at the first deciduous molars.

The classificative power of the model for the predic- tion of success or failure of early Class III treatment is 95.55% for each new individual case.

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