Regression Equations for Determining Mesiodistal Crown Diameters of Canines and Premolars

Transcription

1 Originl Artile Regression Equtions for Determining Mesiodistl Crown Dimeters of Cnines nd Premolrs Mrio Legović, DDS, MS, PhD ; Andrej Novosel, DDS, MS ; Asj Legović, DDS Astrt: In this study, regression equtions (predition equtions) were estlished for the purpose of urtely prediting the widths of the rowns of unerupted nines (C) nd premolrs (P 1 nd P 2 )onthe sis of the mesured mesiodistl dimeter (MDD) nd vestiuloorl dimeter (VOD) of the rowns of the erupted entrl nd lterl inisors (I 1,I 2 ) nd first permnent molrs (M l ). On the plster sts of 120 sujets (60 oys nd 60 girls), MDD nd VOD of the rowns of I 1,I 2, C, oth P 1 nd P 2, nd M l on oth sides in oth jws were mesured twie, with time distne etween mesurements. Grdul regression equtions were derived on the sis of the mesurement results, y whih the sums of the widths of rowns of C, P 1, nd P 2 n e predited using three to five preditors. The oeffiients of multiple orreltions regrding the sex nd the jw vried from 0.79 to (Angle Orthod 2003;73: ) Key Words: Regression eqution; Mesiodistl rown dimeters; Cnine; Premolrs INTRODUCTION The determintion of the mesiodistl dimeters (MDD) of rowns of unerupted nines nd premolrs (C, P 1, nd P 2 ) hs gret importne in determining the hoie of therpy during the mixed dentition. There re three si methods of prediting MDD of the C, P 1, nd P 2 pplition of middle vlues, 1 3 orreltion-sttistil methods, 4 15 nd omintion of X-ry nd orreltion-sttistil methods Beuse of their simpliity, orreltion-sttistil methods re most frequently pplied. However, severl uthors hve pointed out tht the predited vlues re too high The im of this study ws to estlish regression equtions, ie, predition equtions, whih would give the gretest orreltion oeffiient for the sum of MDD of the C, P 1, nd P 2 for oth jws y using three to five preditors, mesured MDD, nd vestiuloorl dimeters (VOD) of rowns of the permnent entrl nd lterl inisors (I 1,I 2 ) nd the first permnent molrs (M l ). Professor of Orthodontis t the Deprtment of Orthodontis nd Deprtment of Peditri Dentistry, Shool of Dentistry, University of Rijek, Croti. Clinil Hospitl Center, nd the Shool of Dentl Mediine, University of Zgre, Croti. Deprtment of Orthodontis, Shool of Dentistry, University of Rijek, Croti. Corresponding uthor: Mrio Legović, DDS, MS, PhD, I. G. Kovčić 3, Poreč, Croti (e-mil: mrio.legovi@pu.tel.hr). Aepted: Otoer Sumitted: My y The EH Angle Edution nd Reserh Foundtion, In. MATERIALS AND METHODS A totl of 120 plster sts (60 oys nd 60 girls) were hosen from the plster st rhives of the orthodonti linis in the ity of Zgre. All sts met the following riteri: permnent dentition in oth jws (ge rnged from 14 to 18 yers); teeth without nomlies in numer, form, size, nd struture; intt mesiodistl nd vestiuloorl surfes of the rowns of the teeth I 1,I 2,C,P 1,P 2, nd M 1 ; nd hildren without syndrome diseses. The MDD nd VOD of I 1,I 2,C,P 1,P 2, nd M 1 were mesured on the plster sts in ll four segments. The mesurements were mde ording to the method of Seipel 30 using eletroni digitl liper, 150 mm HS/R3/lA, from Knuth GmH Co., Werkzeugmshinen KG, with n ury of 0.01 mm. To gin n esier pproh to interdentl spes, the mesuring surfes of the digitl liper were nrrowed. Before the mesurement, the liper ws set t the Fulty of Mhine Engineering nd Ship Building of the University in Zgre. To determine the onsisteny in the mesurements of MDD nd VOD of the I 1,I 2,C,P 1,P 2, nd M 1 rowns, the mesurements were onduted twie within 10-dy period (test-retest reliility). The repeted mesurement ws entered twie to prevent the results of the previous mesurement from influening the seond mesurement. The vriles for the nlyses of regression equtions were otined y determining the rithmeti men of two mesurements. The vriles were divided into groups of preditor vriles (MDD nd VOD of I 1,I 2, nd M l ) nd riteri vriles (sum of MDD of C, P 1, nd P 2 ) in ll four segments. The onsisteny in mesurement ws determined y Person s orreltion oeffiients. The disrepnies in 314

2 REGRESSION EQUATIONS TABLE 1. Mesiodistl nd Vestiuloorl Dimeters of Crowns of Inisors nd the Anlysis of the Vrint with Independent Sex Vrile Vriles MDD 11 VOD 11 MDD 12 VOD 12 MDD 21 VOD 21 VOD 22 MDD 31 VOD 31 MDD 41 VOD 41 MDD 42 VOD F Rtio P **.0170** ** ** **.2786 indites rithmeti men;, stndrd devition; MDD, mesiodistl dimeter; nd VOD, vestiuloorl dimeter. MDD nd VOD of teeth etween oys nd girls were verified y the t-test proedure, the im eing the need to lulte seprte optiml liner omintion for eh sex. Beuse the reserh showed exeptionlly high mesures of onnetions etween the different tooth size mesures on the left nd right sides of the jw, the justifition of determining the liner regression for only one side of the jw ws verified y Person s orreltion oeffiient. -ponders for three to five preditors, MDD nd VOD of I 1,I 2, nd M l, in ll segments were determined y the liner regression nlysis, in grdul regression nlysis for the predition of the sum of MDD, C, P 1, nd P 2 with the highest oeffiient of multiple orreltions. The riterion for exluding the preditors from the grdul regression nlysis ws determined in dvne to e 10%. RESULTS Beuse the im of this study ws to determine optiml liner omintions of preditors (I 1,I 2, nd M l ) for prediting the riteri C, P 1, nd P 2, it ws importnt to determine in dvne whether the dimension of teeth of oys nd girls vry (Tles 1 through 4). It n e seen from the tles tht there is sttistilly signifint sex disrepny, whih neessittes division of the sujets ording to sex when determining optiml liner omintions of preditors. Correltion oeffiients etween homologous teeth of the left nd right side of the sme jw were exeptionlly positive nd vried from 0.72 to 0.97 (girls, mxill ; oys, mxill ; girls, mndile ; oys, mndile ). 315 TABLE 2. Mesiodistl nd Vestiuloorl Dimeters of Crowns of Cnines nd the Anlysis of the Vrint with Independent Sex Vrile Vriles MDD 13 VOD 13 MDD 23 VOD 23 MDD 33 VOD 33 MDD 43 VOD F Rtio P **.0125** indites rithmeti men;, stndrd devition; MDD, mesiodistl dimeter; nd VOD, vestiuloorl dimeter. TABLE 3. Mesiodistl nd Vestiuloorl Dimeters of Crowns of Premolrs nd the Anlysis of the Vrint with Independent Sex Vrile Vriles MDD 14 VOD 14 MDD 15 VOD 15 MDD 24 VOD 24 MDD 25 VOD 25 MDD 34 VOD 34 MDD 35 VOD 35 MDD 44 VOD 44 MDD 45 VOD F Rtio P **.0050**.0021*.0097**.0073**.0165**.0013*.0217**.0126** * indites rithmeti men;, stndrd devition; MDD, mesiodistl dimeter; nd VOD, vestiuloorl dimeter. TABLE 4. Mesiodistl nd Vestiuloorl Dimeters of Crowns of Molrs nd the Anlysis of the Vrint with Independent Sex Vrile Vriles MDD 16 VOD 16 MDD 26 VOD 36 MDD 46 VOD F Rtio P *.0003*.0008* indites rithmeti men;, stndrd devition; MDD, mesiodistl dimeter; nd VOD, vestiuloorl dimeter.

3 316 LEGOVIĆ, NOVOSEL, LEGOVIĆ TABLE 5. Results of Grdul Regression Anlysis for the Sum of Preditle Mesiodistl Dimeters of Crowns of C, P 1, nd P 2 for Both Sexes Grdul Regression Anlysis Mxill.79 F SEE.61 Mndile.78 F SEE.63 SEE indites stndrd error of the estimte..84 F SEE F SEE.53 TABLE 6. Grdul Regression Eqution for the Predition of the Sum of Mesiodistl Dimeters of Crowns of C, P 1, nd P 2 in the Upper Jw for the Preditors Bet Ponder t P VOD MDD indites mesiodistl dimeter; VOD, vestiuloorl dimeter. Constnt C, P 1,P () 0.386() 0.398(VOD 31) 0.725() 0.277() The oeffiients of noni orreltion etween the oserved six teeth of the right nd left sides of oth jws were lso determined. The first pir of noni orreltions ws greter thn 0.97 in ll ses. These findings justify the use of liner equtions for oth sides of the jw regrdless of the side for whih they were determined. In this study, we opted for the left side. The orreltions etween the first nd seond mesurement of MDD nd VOD lie in the intervl from 0.85 to Beuse the reliility etween the first nd the seond mesurement on ll vriles ws extremely high, we deided to determine the verge of the first nd seond mesurements. Tle 5 illustrtes the oeffiients of multiple orreltions resulting from grdul regression nlysis y kwrd method for oth susmples. Tles 6 through 9 show the results of grdul regression nlysis for the predition of sums of MDD of C, P 1, nd P 2 with regrd to the jw nd sex. Regression equtions for the predition of sums of MDD of C, P 1, nd P 2 for girls, eh jw seprtely, re estlished from Tles 6 nd 7. Regression equtions for the predition of the sums of MDD of C, P 1, nd P 2 for oys, eh jw seprtely, re estlished from Tles 8 nd 9. TABLE 7. Grdul Regression Eqution for the Predition of the Sum of Mesiodistl Dimeters of Crowns of C, P 1, nd P 2 in the Lower Jw for the Preditors Bet Ponder t P MDD indites mesiodistl dimeter; VOD, vestiuloorl dimeter. Constnt C, P 1,P () 0() 0.414(VOD 26) TABLE 8. Grdul Regression Eqution for the Predition of the Sum of Mesiodistl Dimeters of Crowns of C, P 1, nd P 2 in the Upper Jw for the Preditors Bet Ponder t P MDD MDD indites mesiodistl dimeter; VOD, vestiuloorl dimeter. Constnt C, P 1,P () 4C,P 1,P 2 () 0(MDD 26) 0.385() TABLE 9. Grdul Regression Eqution for the Predition of the Sum of Mesiodistl Dimeters of Crowns of C, P 1, nd P 2 in the Lower Jw for the Preditors Bet Ponder t P MDD indites mesiodistl dimeter; VOD, vestiuloorl dimeter. Constnt C, P 1,P () 0() 7(VOD 32) 0.611() In grdul regression nlysis, only three to five preditors were mintined. Bets nd -ponders re given in those tles, s well s the onstnt for determining MDD of C, P 1, nd P 2. DISCUSSION The im of this study ws to estlish regression equtions with whih, y the use of the preditors MDD nd VOD, I 1,I 2, nd M 1, the sums of MDD of C, P 1, nd P 2 in oth jws would e predited, nd these predited vlues would e the most uthenti representtion of the mesured vlues. Out of ll the proposed methods so fr for the predition of the sums of MDD of C, P 1, nd P 2, Moyer s method is

4 REGRESSION EQUATIONS most frequently pplied Proffit nd Akermn 31 find Moyer s method stisftory, wheres mny others hve indited tht the predited vlues were too high when this method is used with different popultion. 13,15,23 Moyer s predited vlues re too high for the Crotin popultion s well Another method tht is frequently used is the Tnk nd Johnston 8 method. This method lso hs een reported y severl uthors to e impreise. 24,25,28 The predited vlues re, s with Moyer s, too high. X-ry orreltion methods proposed y severl uthors hve turned out to e very relile ,32 35 However, when the reliility of orreltion methods nd X-ry methods were ompred, mny uthors found tht the ltter ws muh more preise. 24,28,33,34,36 In this study, using three to five preditors (MDD nd VOD of I 1,I 2, nd M 1 ), orreltion oeffiients with the sums of MDD of C, P 1, nd P 2 mounted to: for the oys, 0.84 in the mxill nd 0.85 in the mndile; nd for the girls, 0.79 in the mxill nd 0.78 in the mndile. A more omprehensive reserh in future studies will surely hek the stility of ponder, prediting mesiodistl dimeters of the C, P 1, nd P 2 rowns. For the requirements of this work, we ross-vlidted in the following wy: rndomly hosen testees of oth sexes were divided into hlves. For eh hlf, ponders were lulted for the group of preditor vriles otined in the grdul regression nlysis. The ponder otined in the first susmple ws pplied to the testees vriles from the seond susmple nd vie vers. Wht we got were very high oeffiients of orreltion (etween 0.93 nd 0.96) mong the riteri vriles lulted in tht wy. Sums of MDD of C, P 1, nd P 2 in oth jws predited y this method were more preise in oys. Stley et l 34 hve mde similr oservtions. Aording to Stley et l, 34 the predition of the width of the rowns of teeth is more relile on the left thn on the right side of the jw. Aording to our reserh, the hoie of the side is not importnt. Bhmnn 15 nd Gross nd Hsund 13 used three preditors in their regression equtions for prediting the sums of MDD of C, P 1, nd P 2. Bhmnn 15 otined orreltion oeffiients from 0.83 in the mxill to 0.85 in the mndile without dividing the smple ording to sex, nd Gross nd Hsund, 13 depending on the side of the jw, got orreltion oeffiients from 0.72 to The VOD of the M l rown is used s preditor in this study. Their use showed greter orreltion with C, P 1, nd P 2 thn the use of MDD s indited y Gross nd Hsund 13 nd Ingerwl nd Lennrtsson. 32 They used the VOD of the M 1 in their predition methods. Aording to Potter, 37 the VOD of the teeth in the mxill re more strongly ontrolled thn the geneti system of MDD. Aording to Stley et l, 34 omintions of three preditors, two of whih re determined y mesuring MDD of rowns on rdiogrphs nd the third y mesuring MDD 317 of rowns on the plster st, give the gretest orreltion oeffiient ( ). The study elortes regression equtions seprtely for eh sex. The MDD nd VOD of lmost ll teeth were sttistilly signifintly higher in oys. Other uthors hve lso pointed t sex dimorphism of dimensions of MDD of C, P 1, nd P 2. 29,38,39 All of them find tht the methods of determining the sums of MDD of C, P 1, nd P 2 hve to e different ording to sex. CONCLUSION On the sis of the estlished im of this reserh nd nlysis of the results, it is onluded tht with orreltion oeffiients from 0.84 to 0.85 in oys nd 0.78 to 0.79 in girls, the sums of MDD of C, P 1, nd P 2 n e predited y regression eqution with the use of three to five preditors. REFERENCES 1. Pnherz H, Shffer C. Individul-sed predition of size of the supporting zones in the permnent dentition. A omprison of the Moyers method with unitry predition vlue. J Orof Orthop. 1999;60: Bishr SE, Hoppens BJ, Jkosen JR, et l. Chnges in the molr reltionship etween the deiduous nd permnent dentitions: longitudinl study. Am J Orthod Dentofil Orthop. 1988;93: Moorrees CFA, Thomsen S, Jensen E, et l. 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