Children with Class III Malocclusion: Development of Multivariate Statistical Models to Predict Future Need for Orthognathic Surgery

Transcription

1 Originl Article Children with Clss III Mlocclusion: Development of Multivrite Sttisticl Models to Predict Future Need for Orthognthic Surgery Gbriele Schuster, DDS ; Christopher J. Lux, DDS b ; Angelik Stellzig-Eisenhuer, DDS, PhD c Abstrct: Until now, the literture does not provide n ccurte model to predict the future need for orthognthic surgery in prepubertl ptients with clss III mlocclusion. Becuse not ll of these ptients re cndidtes for lter surgicl correction, ptient ssessment nd selection remin rbitrry with respect to dignosis nd tretment plnning. The purpose of the present investigtion ws to nlyze the vlue of clssifying clss III children before puberty into ptients who cn be effectively treted by orthopedic/ orthodontic therpy lone nd those who require orthognthic surgery. To obtin robust model, the study design ws multicentric (University Orthodontic Deprtments of Frnkfurt, Heidelberg, nd Würzburg). A totl of 88 ptients with clss III mlocclusion were grouped into orthopedic/orthodontic (n 65) nd surgery ptients (n 23), ccording to their records fter puberty (men ge, 17 yers three months). Discriminnt nlysis (DA) nd logistic regression (LogR) were pplied to 20 lndmrks of the ptients cephlogrms before puberty (men ge, nine yers eight months) to identify the dentoskeletl vribles tht provide the best group seprtion nd the best predictbility of group membership, respectively. Both models were highly significnt (P.001), clssifying 93.3% (DA) nd 94.3% (LogR) of the ptients correctly. The extrcted vribles were identicl for both procedures: Wits pprisl, pltl plne ngle, nd individulized inclintion of the lower incisors. The resulting eqution of LogR ws individul score Wits 0.363NL-L 0.153[180 (L1-ML) (L1-ML ind )]. We concluded tht by mens of multivrite sttistics, prepubertl children with clss III mlocclusions my be clssified into nonsurgery nd surgery ptients with high ccurcy. (Angle Orthod 2003;73: ) Key Words: Clss III mlocclusion; Crniofcil growth; Prediction; Surgery; Discriminnt nlysis; Logistic regression; Multivrite sttistics INTRODUCTION Clss III mlocclusion is one of the most severe dentofcil nomlies. Individuls with clss III mlocclusion frequently show combintions of skeletl nd dentolveolr components. 1 Moreover, there re complex interctions of genetic nd environmentl fctors, which my ct synergisticlly or in isoltion, or my cncel ech other out. 2 Assistnt Professor, Deprtment of Orthodontics, University of Frnkfurt, Frnkfurt, Germny. b Assistnt Professor, Deprtment of Orthodontics, University of Heidelberg, Heidelberg, Germny. c Hed, Deprtment of Orthodontics, University of Würzburg, Würzburg, Germny. d Dr Schuster nd Dr Stellzig-Eisenhuer hve contributed eqully to the pper. Corresponding uthor: Gbriele Schuster, DDS, Deprtment of Orthodontics, J.W. Goethe University, Theodor-Stern-Ki 7 (ZZMK, Hus 29), Frnkfurt m Min, Germny (e-mil: g.schuster@em.uni-frnkfurt.de). Accepted: August Submitted: October by The EH Angle Eduction nd Reserch Foundtion, Inc. Compred with clss I subjects, severl berrnt cephlometric mesurements hve been reported in clss III mlocclusion ptients, such s shorter nterior crnil bse length, more cute crnil bse ngle, shorter nd more retrusive mxill, more proclined mxillry incisors, more retroclined mndibulr incisors, n excess of lower nterior fce height, nd more obtuse gonil ngle. 2 8 Becuse no single morphologic feture is indictive of clss III development, tretment outcome is extremely difficult to predict in clss III children. 9 Ricketts 10 introduced the computer-ssisted growth prognosis the so-clled visul tretment objective for prediction of individul tretment outcome. This method is bsed on empiriclly obtined men growth increments, nticipting the influence of orthodontic tretment. However, the prognostic power of dentl reltionships, dentoskeletl reltions, or soft-tissue configurtions t the end of tretment ws limited. 11,12 In prticulr, overestimtion of tretment influences ws considered to be responsible for the low predictbility of this method. 13 Moreover, ccurte individ- 136

2 STATISTICAL MODELS PREDICTING NEED FOR FUTURE SURGERY ulized growth prediction ws regrded s nerly impossible becuse of the diversity nd vribility of fcil growth Becuse of the complexity of clss III mlocclusion, univrite sttisticl techniques turned out to be insufficient for dignosis, tretment plnning, nd outcome prognosis. 17 Insted, recent studies suggested tht the reltions between crniofcil structure nd occlusion would be nlyzed best by using multivrite pproch Logistic regression (LogR) is one multivrite procedure tht estimtes the likelihood of certin event occurring or group membership In orthodontic literture most of the studies using multivrite sttistics explored the potentil of discriminnt nlysis (DA) DA is specilly designed to seprte two groups of individuls tken from the sme popultion. Until now, it hs been successfully pplied to seprte clss III ptients from clss I subjects. 18,29,30 Furthermore, DA ws used to predict tretment outcome nd relpse of orthodonticlly treted clss III ptients. 20,28,31 36 Recently, formul ws developed to clssify dult clss III ptients into group tht is tretble solely orthodonticlly nd group tht requires orthognthic surgery. 37 However, to dte the literture does not provide n ccurte multivrite model to distinguish between growing clss III ptients who cn be treted successfully by orthodontics/orthopedics lone nd clss III ptients who require surgicl tretment fter termintion of dentofcil growth. Becuse most of the clss III mlocclusion ptients lredy hve undergone orthodontic/orthopedic tretment in erly infncy, prediction of future crniofcil growth is n essentil issue in clinicl orthodontics. Therefore, the purpose of the present investigtion ws to develop sttisticl model clssifying clss III children before puberty into ptients who cn be effectively treted by orthodontic/orthopedic therpy lone nd those who require future orthognthic surgery. MATERIALS AND METHODS Subjects For sufficiently stble model tht is lso pplicble to ptients outside the study, lrge smple size is prerequisite. For this reson, the present nlysis ws bsed on the dt of three different orthodontic centers (Deprtment of Orthodontics, University Dentl School of Frnkfurt, Heidelberg, nd Würzburg). The three prticipting universities re locted in the sme region in the middle prt of Germny. The concept nd modlity of tretment of clss III children were similr. In ll three centers, tretment of clss III mlocclusion strts s soon s the mlocclusion is detected. Besides chin-cps nd reverse hedgers, functionl pplinces re used s rule, followed by fixed pplince t the end of pubertl growth. Becuse of this convergence, pooling of the records ws pplicble. 137 Ptients with crniofcil disorders such s cleft plte or crniosynostosis were excluded. The ptients were ll Cucsins nd met the following criteri for inclusion into the retrospective study: I. Initil records (plster csts, cephlogrms, extrorl pictures) before pubertl growth spurt (men ge, nine yers eight months; stndrd devition [SD], one yer six months): presence of clss III molr reltionship; negtive overjet; Wits pprisl 1 mm; negtive difference between ANB ngle nd individulized ANB ngle. 38 II. Finl records (plster csts, cephlogrms, extrorl pictures) fter puberty (men ge, 17 yers three months; t lest four yers fter the initil records). Three experienced orthodontists grouped the finl records into nonsurgery nd surgery group. For lloction to the nonsurgery group, the following tretment outcome criteri hd to be fulfilled: stble occlusion in sgittl, trnsversl, nd verticl dimension; correct overjet nd overbite; proper incisl inclintion; stisfying fcil esthetics; long-term stbility. Accordingly, the mteril for the study comprised the cephlometric rdiogrphs of 88 clss III mlocclusion ptients, 39 boys nd 49 girls. The orthodontic group consisted of 65 ptients nd the surgery group, 23 ptients. Methods Becuse the lterl cephlogrms were tken with different X-ry devices, ll liner mesurements were corrected by their respective mgnifiction fctors. The sme investigtor trced ll films with 20 lndmrks (Figure 1) nd digitized the dt using pproprite softwre (WinCeph, Dentev Compudent, Koblenz, Germny). The following liner, proportionl, nd ngulr mesurements were clculted (Figure 2 e) S-N: nteroposterior length of the crnil bse; PoOr-NB ( ): crnil deflection; ML-L ( ): divergence of the mndibulr plne reltive to the nterior crnil bse; Ar ( ): sddle ngle; ArGoMe ( ): gonil ngle; Go upper ( ): upper gonil ngle; Go lower ( ): lower gonil ngle; SNB ( ): nteroposterior mndibulr position to the nterior crnil plne; L1-ML ( ): xis of the lower incisor to the mndibulr plne; individulized inclintion of the lower incisors ( ) [180 (L1-ML) (L1-ML ind )]: difference between 180 minus xis of the lower incisor to the mndibulr plne nd individulized L1-ML ngle, ccording to the formul L1-

3 138 SCHUSTER, LUX, STELLZIG-EISENHAUER Rndom errors rnged from 0.02 to 0.81 mm for the liner mesurements nd from 0.38 to 1.93 for the ngulr vribles. Systemtic error ws tested t the 10% level of significnce, s recommended by Houston, 41 nd no systemtic errors were found. Sttisticl nlysis FIGURE 1. Hrd-tissue lndmrks used in the study: S indictes Sell; Po, porion; B, bsion; Ar, rticulre; Go, gonil intersection; Me, menton; Pog, pogonion; B, point B; L1 pex, pex of the lower centrl incisor; L1 tip, tip of the lower centrl incisor; U1 tip, tip of the upper centrl incisor; U1 pex, pex of the upper centrl incisor; A, point A; Ans, nterior nsl spine; Pns, posterior nsl spine; Ptm, pterygomxillry fissure; Or, orbitle; N, nsion; ERP, ethmoid registrtion point; PocP, posterior point of the occlusl plne; nd AocP, nterior point of the occlusl plne. ML ind ML-NL; 39 Wits pprisl: length of the distnce AO-BO (AO, intersection between perpendiculr line dropped from point A nd the occlusl plne; BO, intersection between perpendiculr line dropped from point A nd the occlusl plne); ANB ( ): nteroposterior reltion of the mxill nd the mndible; ANB-ANB ind ( ): difference between ANB ngle nd individulized ANB ngle ccording to formul 7, ANB ind SNA 0.2ML-L; 38 M/M rtio: rtio of the nteroposterior length of the mxill to the nteroposterior length of the mndible; NAPog ( ): ngle of convexity; 1/1 ( ): ngle between the xis of the upper nd the lower incisor; SNA ( ): nteroposterior mxillry position to the nterior crnil plne; NL-L ( ): inclintion of the pltl plne in reltion to the nterior crnil bse; U1-L ( ): xis of the upper incisor to the nterior crnil bse; [(U1-NL) (U1-NL ind )] ( ): difference between the xis of the upper incisor to the pltl plne mesured outside nd the individulized U1-NL ngle, ccording to the formul U1-NL ind ML-NL. 39 Fifteen films were selected rndomly, retrced, nd redigitized on two seprte occsions two weeks prt. The method error ws clculted s recommended by Dhlberg. 40 The method error in locting nd mesuring ws clculted by the formul: ME 2 d /2n where d is the difference between two registrtions of pir nd n the number of double registrtions. Dt nlysis ws performed using SPSS PC (version 9.0), the Sttisticl Pckge for the Socil Sciences. The rithmetic mens (men), SDs, medins (medin), minim (min), nd mxim (mx) were clculted for ech vrible nd group before tretment (T1). To ssess differences between the crniofcil fetures of both groups t the strt of tretment, the dt were compred using Mnn- Whitney U-test for independent smples (Tble 2). For multivrite sttistics two procedures were pplied to the set of dt: 1. Discriminnt nlysis DA ws used to identify those dento-skeletl vribles tht best seprte the ptients who need orthognthic surgery for correcting the mlocclusion from those who do not. To void redundncy mong the vrious vribles, stepwise vrible selection ws performed to obtin model with the smllest possible set of significnt cephlometric prmeters. The independent vribles were included in the model ccording to the 5% level of significnce. The first vrible selected ws the one with the smllest vlue of Wilks lmbd, where lmbd is the rtio of the withingroup sum of squres divided by the totl sum of squres. We chose the subsequent vribles by reclculting lmbd for ech of the vribles, nd the vrible with the next lowest vlue ws selected. For ech stge, test ws done to scertin whether the inclusion of the respective vrible in the model would significntly improve prediction. Unstndrdized discriminnt function coefficients were clculted for ech selected vrible together with constnt. This leds to n eqution tht ssigns score to ech ptient. For ech group, DA results in men score over ll known cses in the relevnt group. The dividing line hlfwy between these scores shows to which of the two groups n individul cse belongs (criticl score: men vlue of group centroids of the two groups). 2. Logistic regression LogR is vrition of ordinry regression, pplicble when the observed outcome is restricted to two vlues, which represent the occurrence (where surgicl intervention is necessry for correction of the clss III nomly) or nonoccurrence (where no surgicl intervention is necessry for correction) of n outcome event. It produces formul tht predicts the probbility of the occurrence of n event s function of the independent vribles. The globl P-vlue of the finl model ws bsed on the likelihood rtio test, evluting the totl influence of ll vribles in the model. The P-vlues of the single vr-

4 STATISTICAL MODELS PREDICTING NEED FOR FUTURE SURGERY 139 FIGURE 2. Liner nd ngulr cephlometric mesurements used in the study: S-N (mm) indictes nteroposterior length of the crnil bse; PoOr-NB ( ), crnil deflection; ML-L ( ), divergence of the mndibulr plne reltive to the nterior crnil bse; Ar ( ), sddle ngle; ArGoMe ( ), gonil ngle; Go upper ( ), upper gonil ngle; Go lower ( ), lower gonil ngle; SNB ( ), nteroposterior mndibulr position to the nterior crnil plne; L1-ML ( ), xis of the lower incisor to the mndibulr plne; Wits (mm), length of the distnce AO-BO (AO, intersection between perpendiculr line dropped from point A nd the occlusl plne; BO, intersection between perpendiculr line dropped from point A nd the occlusl plne); ANB ( ), nteroposterior reltion of the mxill nd the mndible; M/M rtio, rtio of the nteroposterior length of the mxill to the nteroposterior length of the mndible; NAPog ( ), ngle of convexity; U1/L1 1/1 ( ), ngle between the xis of the upper nd the lower incisors; SNA ( ), nteroposterior mxillry position to the nterior crnil plne; NL-L ( ), inclintion of the pltl plne in reltion to the nterior crnil bse; U1-L ( ), xis of the upper incisor to the nterior crnil bse; nd U1-NL ( ), xis of the upper incisor to the pltl plne mesured outside. ibles tht entered the model were clculted by the Wld test. Becuse the study ws bsed on lterl cephlometric lndmrks only, the skeletl trnsverse component of clss III mlocclusion ws not considered. RESULTS Univrite cephlometric nlysis Descriptive sttistics for ll cephlometric vribles for both ptient groups t T1 re listed in Tble 1. The levels of significnce t P-vlues of *P.05, **P.01, nd P.001 between the no surgery nd the surgery groups re given in Tble 2. Significnt intergroup differences were found for prmeters representing the sgittl mxillo-mndibulr reltionship s indicted by ANB, ANB-ANB ind, nd Wits pprisl. In ddition, significnt differences were given for length of the nterior crnil bse, nteroposterior position of the mndible, rtio between length of the mxill nd length of the mndible nd ngle of convexity, lower gonil ngle, individulized xis of the lower centrl incisors, nd interincisl ngle. In contrst, there were no significnt differences in the position nd inclintion of the upper jw, the xis of the mxillry centrl incisors, the crnil deflection, s well s the prmeters describing the direction of crniofcil growth (NL-L, ML-L, Ar, Go upper ) (Tble 2). Multivrite cephlometric nlysis Discriminnt nlysis. Stepwise vrible selection of DA resulted in significnt model of three vribles. The vribles selected were Wits pprisl (F likelihood to remove

5 140 SCHUSTER, LUX, STELLZIG-EISENHAUER TABLE 1. Mens (men), Stndrd Devitions (SDs), Medins (medin), Minim (min), nd Mxim (mx) of the Nonsurgery nd Surgery Groups t the Beginning of Tretment Cephlometric Vribles S-N (mm) SNA ( ) SNB ( ) ANB ( ) ANB-ANB ind ( ) Wits (mm) M/M rtio (%) PoOr-NB ( ) NAPog ( ) ML-L ( ) Ar ( ) ArGoMe ( ) Go upper ( ) Go lower ( ) NL-L ( ) U1-L ( ) (L1-NL) (L1-NL ind )( ) L1-ML ( ) 180 (L1-ML) (L1-ML ind )( ) 1/1 ( ) Nonsurgery Group (n 65) Men SD Medin Min Mx Surgery Group (n 23) Men SD Medin Min Mx TABLE 2. Significnt Differences Between the Ptients of the Nonsurgery nd the Surgery Groups t the Beginning of Tretment Cephlometric Vribles S-N (mm) SNA ( ) SNB ( ) ANB ( ) ANB-ANB ind ( ) Wits (mm) M/M rtio (%) PoOr-NB ( ) NAPog ( ) ML-L ( ) Ar ( ) ArGoMe ( ) Go upper ( ) Go lower ( ) NL-L ( ) U1 L ( ) (U1 NL) (1 NL ind )( ) L1 ML ( ) (180 (L1-ML)) (L1-ML ind )( ) 1/1 ( ) indictes not significnt. * P.05; ** P.01; P.001. Mnn-Whitney Test Z P * * * **.000), NL-L (F likelihood to remove.010), nd [180 (L1-ML) (L1-ML ind )] (F likelihood to remove.020). Unstndrdized discriminnt function coefficients of the selected vribles, long with clculted constnt (Tble 3), led to the following eqution tht provides individul scores for the ssignment of new cse to the nonsurgery or the surgery group: individul score Wits 0.116NL-L 0.058[(180 (L1-ML) (L1-ML ind)]. The criticl score ws 0.653, which is the men vlue of group centroids of the two groups (Tble 3). Ech new cse with clss III mlocclusion tht will show n individul score higher thn the criticl score will probbly be treted successfully by orthodontics/orthopedics lone. On the other hnd, new clss III ptient with more negtive individul score thn the criticl score should be treted by combined orthodontic-orthognthic therpy fter termintion of crniofcil growth. The percentge of correctly clssified cses ws 93.2% (Tble 4). Only 4.6% of the ptients in the nonsurgery group nd 13.0% of those in the surgery group, respectively, were misclssified. Then, sensitivity mounted to 0.87, nd the specificity scored ws (Tble 4). Liner regression. Forwrd conditionl stepwise procedure ws run for LogR. Agin, the vribles Wits pprisl, NLL, nd [180 (L1-ML) (L1-ML ind )] entered the model, resulting in the following eqution (Tble 5): individul score Wits 0.363NL-L 0.153[180 (L1-ML) (L1-MLind)]. The overll percentge of correctly clssified cses ws Only one ptient of the nonsurgery group ws misclssified, wheres four ptients of the surgery group were wrongly clssified.

6 STATISTICAL MODELS PREDICTING NEED FOR FUTURE SURGERY 141 TABLE 3. Discriminnt Anlysis Cnonicl Discriminnt Function Coefficients Predictive Vribles Wits pprisl NL-L [180 (L1-ML) (L1-ML ind )] Constnt Unstndrdized Stndrdized Individul score Wits 0.116NL-L 0.058[180 (L1-ML) (L1-ML ind )]. Discriminnt scores for group mens (group centroids): nonsurgery group, 0.715; surgery group, 2.020; criticl score, 0.653; nd significnce of the model, TABLE 4. Clssifiction Results of the Discriminnt Anlysis Predicted Group Alloction Originl group membership Nonsurgery group Surgery group Nonsurgery Group, % 95.4 (n 62) 13.0 (n 3) Surgery Group, % 4.6 (n 3) 87.0 (n 20) Sensitivity (need for lter surgicl intervention) 0.87; specificity (conservtive tretment dequte for correction of the mlocclusion) 0.954; nd overll ccurcy (correctly clssified ptients in totl) TABLE 5. Logistic Regression Predictive Vribles Wits NL-L [180 (L1-ML) (L1-ML ind )] Constnt Logistic Regression Stndrd Coefficients Error Significnce Individul score Wits 0.363NL-L 0.153[180 (L1-ML) (L1-ML ind )]. Significnce of the model.001. TABLE 6. Clssifiction Results of Logistic Regression Originl group membership Nonsurgery group Surgery group Predicted Group Alloction Nonsurgery Group, % 98.5 (n 64) 17.4 (n 4) Surgery Group, % 1.5 (n 1) 82.6 (n 19) Sensitivity (need of lter surgicl intervention) 0.826; specificity (conservtive tretment dequte for correction of the mlocclusion) 0.985; nd overll ccurcy (correctly clssified ptients in totl) The grouping of the smple ccording to LogR is shown for Wits pprisl in Figure 3. The sensitivity mounted to 0.985, nd the specificity ws (Tble 6). FIGURE 3. Box plots of Wits pprisl of correctly clssified nonsurgery ptients (n 64) nd surgery ptients (n 19), nd misclssified surgery ptients (n 3) in pplied DA. DISCUSSION Prediction of crniofcil growth is one of the most relevnt objectives in orthodontic dignosis nd tretment plnning. Prticulrly in growing individuls, it is necessry to determine whether the dentofcil dysplsi cn be corrected by orthodontic/orthopedic mens lone or whether surgicl procedures hve to be pplied. 42 To dte, informtion bout crniofcil growth pttern is primrily bsed on cephlometric nlysis. Although generl growth rtes, increments, nd directions cn be predicted with some degree of ccurcy, individul growth prognosis is limited becuse of the wide rnge of vribility, which is minly relted to heredity, gender, nd ethnic bckground. 15,42 Most ttempts t the prediction of tretment-relted chnges nd outcome in orthodontics relied on single biometric prmeters. However, ppliction of multivrite sttistics ws the exception. Despite its dvntges over the use of univrite procedures, the following limittions of this multivrite technique hve to be kept in mind: (1) multivrite models bsed on cephlometric nlysis re hmpered by the difficulties of precise lndmrk identifiction, 9,43 45 (2) the selected mesurements might not comprise ll the vribles needed to seprte the groups ccurtely, 9,14,18,25 (3) the smple sizes re too smll for sufficiently robust discriminnt model tht is pplicble to ptients outside the study, 18 nd (4) the differences between both groups might be too smll to llow cler group seprtion. 18 Most of the studies exploring the potentil of DA in orthodontics hve been concerned with the fcil chrcteristics of different rces Multivrite technique hs been successfully pplied to seprte clss III ptients from clss I subjects. 18,29,30 Furthermore, it hs been useful for predic-

7 142 SCHUSTER, LUX, STELLZIG-EISENHAUER tion of tretment outcome nd relpse in clss III ptients treted with singulr pplinces like the chin-cup or specil tretment modlity like tooth extrction. 20,28,31 36 The im of the present study ws to predict the need for surgicl intervention in dolescent children with clss III mlocclusion. For this reson, multivrite techniques were pplied, the DA nd the LogR. The decision s to wht kind of tretment is indicted usully is bsed on degree of nteroposterior nd verticl skeletl discrepncy, inclintion nd position of the incisors, nd dentofcil ppernce. Severl lterl cephlometric studies hve been conducted to elucidte the growth pttern in clss III subjects when compred with eugnthic subjects nd to show up the effects of orthopedic therpy nd the stbility of tretment outcome. 3 8,32,33,46 However, only few studies hve been undertken to estblish some threshold vlues for pretretment identifiction of ptients for whom orthognthic correction would be necessry. The three envelopes of discrepncies from Proffit nd Ackermn 47 represent guideline for differentition between orthodontic nd combined orthodontic-surgicl tretment. Criticl limittion for orthodontic tretment ws seen in n upper incisor protrusion of two mm combined with lower retrusion of three mm. Kerr et l 48 tried to estblish cephlometric yrdsticks to objectify tretment decision. The most importnt fctors tht differentited between the surgery nd the orthodontic ptients in this study were size of the nteroposterior discrepncy, inclintion of the lower incisors, nd ppernce of the soft-tissue profile. The verticl dimensions, eg, gonil ngle nd y-xis, were of limited relevnce for tretment decisions. Bsed on the overlps of box-nd-whisker plots, the following criticl vlues were set up: ANB: 4 ; M/M rtio: 0.84; lower incisor inclintion: 83 ; nd Holdwy ngle: 3.5. However, univrite sttistics re not insufficient to reflect complex crniofcil reltionships. 9,22,49 For these resons, multivrite sttistics were used in the present study to seprte the ptients into the nonsurgery nd the surgery groups. The prerequisite for powerful model is reltively lrge smple. Thus, when n unknown ptient hs to be clssified, his mesurements will not fll outside those used in generting the model. 33 On this ccount, multicentric study design ws chosen. Stepwise vrible selection of both DA nd LogR generted three-vrible model producing the most efficient seprtion between the nonsurgery nd the surgery groups. The vribles chosen were identicl: (1) Wits pprisl, (2) NL-L, nd (3) individulized inclintion of the lower incisors. The clssifiction power of the model ws 93.2% for DA nd 94.3% for LogR. Since its introduction by Riedel, 50 ANB ngle is the most commonly used cephlometric mesurement to describe skeletl reltionships between the mxill nd the mndible. However, its vlidity s true indictor of the nteroposterior jw reltionships hs been questioned by the fct tht Nsion is not fixed point nd ny chnge in its nteroposterior position consequently ffects ANB In ddition, the mgnitude of the ANB ngle is ffected by rottion of the jws reltive to the crnil bse. 50,52,53 The individulized ANB, ccording to Pngiotidis nd Witt, 38 tkes the ngle between the mndibulr plnum nd the Sell- Nsion line into ccount nd by this, the verticl dimension. To uncouple the nteroposterior jw reltionships completely from the crniofcil reference, Jcobson 42 introduced Wits pprisl. Here, the functionl occlusl plne is used s reference plne for defining the reltion of the jws. Thus, rottion of the jws reltive to the crnil reference plne does not ffect the severity of jw dishrmony. Vrious uthors hve investigted the degree of correltion between Wits pprisl nd ANB ngle, showing only wek correltion between both vribles When nlyzing the geometricl reltionship between ANB ngle nd Wits pprisl, Jrvinen 60 found tht it is difficult to compre mesurements bsed on different reference plnes. Therefore, the conjunctive use of ANB ngle nd Wits pprisl ws recommended s n pproprite method for clinicl ssessment of jw reltionships. 30,61,62 The vlidity of precise lndmrk identifiction of Wits pprisl hs been questioned becuse the functionl occlusl plne ws considered s mjor source of error. However, no sttisticlly significnt differences were found for repeted introbserver mesurements. 63 In contrst, interobserver reproducibility ws low. In the present study the sme investigtor trced ll rdiogrphs. Therefore, systemtic error bsed on interobserver vrince ws eliminted. The question of the stbility of the occlusl plne during crniofcil growth hs lso been rised. Shermn et l 64 ssumed tht Wits pprisl is ffected by chnges in the ngultion of the occlusl plne during eruption of the permnent teeth. In contrst, Nnd nd Merrill 65 found tht the inclintion of the pltl plne ws stble throughout the growth period nd tht the distnce between the projections from points A nd B on the pltl plne ws the best indictor of the sgittl jw reltionship. In the present study, ANB ngle, ANB-ANB ind ngle, nd Wits pprisl showed highly significnt differences between the nonsurgery nd the surgery groups. However, of these vribles, only Wits pprisl entered the DA s well s the LogR models. This nd the fct tht Wits pprisl ws the first vrible in both models point to its prepondernce in seprting both ptient groups. In comprble study with group of 175 dult clss III ptients, Stellzig-Eisenhuer et l 37 could lso show the decisive chrcter of Wits pprisl in clssifying the ptients into group needing either surgery or nonsurgicl tretment pproch. The second vrible tht ws extrcted into the models ws the inclintion of the pltl plne reltive to the nterior crnil bse. Children in the surgery group showed less steep inclintion of the pltl plne thn did those in the nonsurgery group. Although this vrible did not show significnt

8 STATISTICAL MODELS PREDICTING NEED FOR FUTURE SURGERY 143 difference in both ptient groups in the univrite comprison, it becme importnt for ptient selection in multivrite nlysis. In the literture to dte, no rticle discusses the inclintion of the pltl plne for further development of clss III mlocclusion. However, less steep mxillry occlusl plne in combintion with posterior verticl excess of the mxill ws described in dult clss III mlocclusion ptients with n nterior open bite. 6 Consistently, Tsng et l 66 found tht the pltl plne inclintion correltes significntly with the severity of the nterior open bite. With respect to these findings, the less steep pltl plne before puberty, s seen in surgery ptients, possibly constitutes n unfvorble condition for chievement of stble overbite during dolescence. The third vlue tht entered the models ws the lower inclintion of the front teeth fter correction for the interbse ngle ccording to Schopf. 39 As mentioned bove, Proffit nd Ackermn 47 nd Kerr et l 48 lredy considered lower incisor inclintion s one of the most decisive fctors in the choice of orthodontics/orthopedics lone or orthognthic surgery. In the univrite nlysis both the inclintion of the lower front teeth to the mndibulr plne nd its individuliztion to the interbse ngle tested highly significnt. Moreover, Ishikw et l 30 found tht mong the compenstory dentolveolr chnges in clss III mlocclusion, lower incisor inclintion ws strongly relted to the sgittl jw reltionship. The predictive power of the discriminnt model for identifiction of those clss III ptients for whom orthodontic tretment ws sufficient ws high. Only 4.6% of the nonsurgery ptients were misclssified. In contrst, the percentge of misjudgment in ptients who needed orthognthic surgery ws 13.0%. For the LogR the overll clssifiction ws even slightly higher. Over 98% of the nonsurgery ptients were correctly clssified, which is 3.1% higher thn for DA. In contrst, the grouping of the surgery ptients worsened by 4.4% to 82.6%. Limittion of growth prediction is bsed on the fct tht huge vrition exists in timing, durtion, nd mount of growth in different components of the fce. 15,16 Also, individul response to orthodontic/orthopedic procedures is different in growing ptients. There re cses tht do not respond stisfctorily to tretment becuse of bizrre or unnticipted growth ptterns or insufficient ptient complince. 42 Consequently individul growth prediction is limited. A further explntion for misjudgment of ptients is tht the cephlometric mesurements used here did not encompss ll the fctors tht cliniclly contribute to tretment outcome. Especilly in borderline surgicl ptients, dditionl fctors hve to be considered, such s incisl guidnce, soft tissue fetures, nd dentofcil esthetics. 9,14,20,25,26,67,68 Becuse clss III ptients lso frequently show skeletl deficiencies in the trnsverse dimension, nteroposterior cephlogrms re necessry to nlyze this spect of crniofcil development. If trnsverse components s well s the forementioned fctors could be included into the nlysis, the predictive power of the multivrite model might increse. Both multivrite sttisticl procedures yielded nerly the sme result. The extrcted vribles were not only the sme but were even selected in the sme order. According to Press nd Wilson, 69 the two methods do not differ mrkedly in their results, which lso is demonstrted by the dt presented. The predictive power of the LogR model ws slightly higher (94.3%) thn the percentge of correct clssifiction by DA (93.2%). The better result of the LogR procedure ws due to higher sensitivity (0.985). In contrst, the specificity of the LogR model ws lesser (0.826) thn the specificity resulting from DA (0.87). Becuse of the more serious consequences, misclssifiction of nonsurgicl ptients should be prevented primrily. For tht reson the predictive model with the highest sensitivity hs to be preferred, which in this study is the model of LogR. CONCLUSIO Both, the LogR nd the discriminnt models were highly significnt (P.0001), clssifying 94.3% nd 93.2%, respectively, of the prepubertl clss III mlocclusion children correctly into ptients who cn be dequtely treted by orthopedic/orthodontic therpy lone nd those who require orthognthic surgery. The following three cephlometric vribles were concordntly selected: Wits pprisl, inclintion of the pltl plne, nd individulized inclintion of the lower incisors. However, individul growth prediction bsed on multivrite models is limited becuse of the diversity nd vribility of fcil growth nd the individul response on orthodontic/orthopedic procedures. Moreover, dditionl fctors tht might lso contribute to clinicl tretment outcome, such s trnsverse components nd fcil esthetics, hve not been considered in the present study. ACKNOWLEDGMENT This study required lrge number of ptients. We express our grtitude to Prof Dr Witt for providing ccess to the records of the Deprtment of Orthodontics, Würzburg University, nd for his kind support. REFERENCES 1. Ngn P, Hgg U, Yiu C, Merwin D, Wie SH. Cephlometric comprisons of Chinese nd Cucsin surgicl Clss III ptients. Int J Adult Orthod Orthognth Surg. 1997;12: Bttgel JM. The etiologicl fctors in Clss III mlocclusion. Eur J Orthod. 1993;15: Snborn RT. Differences between the fcil skeletl ptterns of Clss III mlocclusion nd norml occlusion. Angle Orthod. 1955;25: Jcobson A, Evns WG, Preston CG, Sdowsky PL. Mndibulr prognthism. Am J Orthod. 1974;66:

9 144 SCHUSTER, LUX, STELLZIG-EISENHAUER 5. Schulhof RJ, Nkmur S, Willimson WV. Prediction of bnorml growth in Clss III mlocclusions. Am J Orthod. 1977;71: Ellis E, McNmr JA. Components of dult Clss III mlocclusion. J Orl Mxillofc Surg. 1984;42: Guyer EC, Ellis EE, McNmr JA Jr, Behrents RG. Components of Clss III mlocclusion in juveniles nd dolescents. Angle Orthod. 1986;56: Willims S, Andersen CE. The morphology of the potentil Clss III skeletl pttern in the growing child. Am J Orthod. 1986;89: Johnston LE. A sttisticl evlution of cephlometric prediction. Angle Orthod. 1968;38: Ricketts RM. Plnning tretment on the bsis of the fcil pttern nd n estimte of its growth. Angle Orthod. 1957;27: Greenberg LZ, Johnston LE. Computerized prediction: the ccurcy of contemporry long-rnge forecst. Am J Orthod. 1975; 67: Toepel-Sievers C, Fischer-Brndies H. Vlidity of the computerssisted cephlometric growth prognosis VTO (visul tretment objective) ccording to Ricketts. J Orofc Orthop. 1999;60: Witt E, Körn I. Studies on the vlidity of computer growth predictions. Fortschr Kieferorthop. 1982;43: Skieller V, Björk A, Linde-Hnson T. Prediction of mndibulr growth rottion evluted from longitudinl implnt smple. Am J Orthod. 1984;86: Nnd RS. The contributions of crniofcil growth to clinicl orthodontics. Am J Orthod Dentofcil Orthop. 2000;117: Bishr SM. Fcil nd dentl chnges in dolescents nd their clinicl impliction. Angle Orthod. 2000;70: Keeling SD, Riolo ML, Mrtin RE, Ten Hve TR. A multivrite pproch to nlyzing the reltion between occlusion nd crniofcil morphology. Am J Orthod Dentofcil Orthop. 1989;95: Bttgel JM. The identifiction of Clss III mlocclusions by discriminnt nlysis. Eur J Orthod. 1994;16: Jäger A, Zittlu O, Luhr HG. Zur differentildignostischen Wertigkeit von skelettlen, dentlen und Weichteilnlysen bei der Plnung der kieferorthopädisch-kieferchirurgischen Therpie. Fortschr Kieferorthop. 1994;55: Frnchi L, Bccetti T, Tollro I. Predictive vribles for the outcome of erly functionl tretment of Clss III mlocclusion. Am J Orthod Dentofcil Orthop. 1997;11: Norusis MJ. Spss/PC Advnced Sttistics V2.0. Chicgo, Ill: SPSS; 1988: Richmond S, Aylott NA, Pnhei ME, Rolfe B, Tusche EA. 2- Center comprison of orthodontist s perceptions of orthodontic tretment difficulty. Angle Orthod. 2001;71: Mrcin JP, Slonim AD, Pollck MM, Ruttimnn UE. Long-sty ptients in the peditric intensive cre unit. Crit Cre Med. 2001; 29: Stewrt SH, Silverstein MD. Rcil nd ethnic disprity in blood pressure nd cholesterol mesurement. J Gen Intern Med. 2002; 17: Kowlski CJ, Nsjleti CE, Wlker GF. Differentil dignosis of dult mle blck nd white popultions. Angle Orthod. 1974;44: Kowlski CJ, Nsjleti CE, Wlker GF. Dentofcil vritions within nd between four groups of dult Americn mles. Angle Orthod. 1975;45: Nksim A, Ichinose M. Role of prentl vribles in predicting fcil growth fter tretment of nterior crossbite. Am J Orthod Dentofcil Orthop. 1986;90: Thmin K, Tnk E, Tnne K. Crniofcil morphology in orthodonticlly treted ptients of Clss III mlocclusion with stble nd unstble tretment outcomes. Am J Orthod Dentofcil Orthop. 2000;117: Miyjim K, McNmr JA Jr, Murt S. A dignostic index of verticl problems for Clss III mlocclusions. Int J Adult Orthod Orthognth Surg. 1997;12: Ishikw H, Nkmur S, Iwski H, Kitzw S, Tsukd H, Chu S. Dentolveolr compenstion in negtive overjet cses. Angle Orthod. 2000;70: Stenslnd A, Wisth PJ, Boe OE. Dentofcil chnges in children with negtive overjet treted by combined orthodontic nd orthopedic pproch. Eur J Orthod. 1988;10: Bttgel JM. Discriminnt nlysis: model for the prediction of relpse in Clss III children treted orthodonticlly by nonextrction technique. Eur J Orthod. 1993;15: Bttgel JM. Predictors of relpse in orthodonticlly-treted Clss III mlocclusions. Br J Orthod. 1994;21: Tollro I, Bccetti T, Frnchi L. Crniofcil chnges induced by erly functionl tretment of Clss III mlocclusion. Am J Orthod Dentofcil Orthop. 1996;109: Ishikw H, Nkmur S, Kim C, Iwski H, Stoh Y, Yoshid S. Individul growth in Clss III mlocclusions nd its reltionship to the chin cp effects. Am J Orthod Dentofcil Orthop. 1998;114: Bccetti T, McGill JS, Frnchi L, McNmr JA Jr, Tollro I. Skeletl effects of erly tretment of Clss III mlocclusion with mxillry expnsion nd fce-msk therpy. Am J Orthod Dentofcil Orthop. 1998;113: Stellzig-Eisenhuer A, Lux CJ, Schuster G. Tretment decision in dult ptients with Clss III mlocclusion: orthodontic therpy or orthogntic surgery? Am J Orthod Dentofcil Orthop. 2002;122: Pngiotidis G, Witt E. Der individulisierte ANB. Fortschr Kieferorthop. 1977;38: Schopf P. Kephlometrische Normwerte für die Stellung der Inzisivi eine mögliche Ursche für den Misserfolg kieferorthopädischer Behndlungen? Fortschr Kieferorthop. 1988;49: Dhlberg G. Sttisticl for Medicl nd Psychologicl Students. New York, NY: Interscience; Houston WJB. The nlysis of errors in orthodontic mesurements. Am J Orthod. 1983;83: Jcobson A. Growth nd its reltion to orthodontic tretment. J Orl Surg. 1981;39: Hixon EH. Prediction of fcil growth. Trns Eur Orthod Soc. 1968; Bumrind S, Frntz RC. The relibility of hed film mesurements. 1. Lndmrk identifiction. Am J Orthod. 1971;60: Freisfeld M. Fehlerquellen n Einzeichenserien kephlometrischer Bezugspunkte. Fortschr Kieferorthop. 1973;34: Allen RA, Connolly IH, Richrdson A. Erly tretment of Clss III incisor reltionship using the chin cp pplince. Eur J Orthod. 1993;15: Proffit WR, Ackermn JL. A systemtic pproch to orthodontic dignosis nd tretment plnning. In: Grber TM, Swin BF, eds. Current Orthodontic Concept nd Techniques. 3rd ed. St Louis, Mo: CV Mosby; 1985: Kerr WJS, Miller S, Dwber JE. Clss III mlocclusion: surgery or orthodontics? Br J Orthod. 1992;19: Björk A. Prediction of mndibulr growth rottion. Am J Orthod. 1969;55: Riedel RA. The reltion of the mxillry structures to the crnium in mlocclusion nd norml occlusion. Angle Orthod. 1952;22: Moore AW. Observtions on fcil growth nd its clinicl significnce. Am J Orthod. 1959;42:

10 STATISTICAL MODELS PREDICTING NEED FOR FUTURE SURGERY 52. Enlow DH. A morphogenetic nlysis of fcil growth. Am J Orthod. 1966;52: Tylor CM. Chnges in the reltionship of nsion, point A nd B nd the effect upon ANB. Am J Orthod. 1969;56: Jcobson A. The Wits pprisl of jw dishrmony. Am J Orthod. 1975;67: Ferrzzini G. Criticl evlution of the ANB ngle. Am J Orthod. 1976;69: Roth R. The Wits pprisl its skeletl nd dento-lveolr bckground. Eur J Orthod. 1982;4: Rotberg S, Fried N, Kne J, Shpiro E. Predicting the Wits pprisl from the ANB ngle. Am J Orthod. 1980;77: Bishr SE, Fhl JA, Peterson LC. Longitudinl chnges in the ANB ngle nd Wits pprisl: clinicl implictions. Am J Orthod. 1983;84: Rushton R, Cohen AM, Linney AD. The reltionship nd reproducibility of ngle ANB nd the Wits pprisl. Br J Orthod. 1991;18: Jrvinen S. The reltion of the Wits pprisl to the ANB ngle: sttisticl pprisl. Am J Orthod Dentofcil Orthop. 1988;94: Hurmerint K, Rhkmo A, Hvikko K. Comprison between 145 cephlometric clssifiction methods for sgittl jw reltionships. Eur J Orl Sci. 1997;105: Ferrrio VF, Sforz C, Mini A Jr, Trtgli GM. The use of liner nd ngulr mesurements of mxillo-mndibulr nteroposterior discrepncies. Clin Orthod Res. 1999;2: Hynes S, Chu MN. The reproducibility nd repetbility of the Wits nlysis. Am J Orthod Dentofcil Orthop. 1995;107: Shermn SL, Woods M, Nnd RS, Currier GF. The longitudinl effects of growth on the Wits pprisl. Am J Orthod Dentofcil Orthop. 1988;93: Nnd RS, Merrill RM. Cephlometric ssessment of sgittl reltionship between mxill nd mndible. Am J Orthod Dentofcil Orthop. 1994;105: Tsng WM, Cheung LK, Smmn N. Cephlometric prmeters ffecting severity of nterior open bite. Int J Orl Mxillofc Surg. 1997;26: Ishikw H, Nkmur S, Iwski H, Kitzw S, Tsukd H, Sto Y. Dentolveolr compenstion relted to vritions in sgittl jw reltionships. Angle Orthod. 1999;69: Hirschfeld WJ, Moyers RE. Prediction of crniofcil growth: the stte of the rt. Am J Orthod. 1971;60: Press JS, Wilson S. Choosing between logistic regression nd discriminnt nlysis. J Am Stt Assoc. 1978;73: