Originl Article Are the Lower Incisors the Best Predictors for the Unerupted Cnine nd Premolrs Sums? An Anlysis of Peruvin Smple Edurdo Bernbé, DDS, MSc, Cert Biostt ; Crlos Flores-Mir, DDS, MSc, Cert Orth, PhD b Abstrct: The lower permnent incisor tooth width sum hs been proposed s the best predictor for the tooth width sums of the unerupted cnine nd premolrs (SPCP) for popultions from different ethnic origins. Only two previous studies hve refuted it. The purpose of the present study ws to determine which sum or combintion of sums of permnent tooth widths presented the best prediction cpbility for the SPCP in Peruvin smple, to clculte specific liner regression eqution for this popultion, nd to evlute the clinicl significnce. A totl of 150 children with complete permnent dentitions were selected. Fifty more children were used s vlidtion smple for the ppliction of multiple liner regression eqution (MLRE). They did not present cliniclly visible dentl cries or proximl restortions nd no ctive or previous orthodontic tretment. Their dentl csts were mesured to 0.1 mm with sliding cliper with Vernier scle. Three-wy nlysis of vrince, Person Correltion Test, Fisher Z vlues nd MLRE were used for the sttisticl nlysis. The combintion of the sums of permnent upper nd lower centrl incisors nd upper first molrs ws the best predictor for the SPCP in this smple. A MLRE ws clculted including sex nd rch s dditionl predictor vribles. The MLRE determintion coefficient ws 60% with stndrd error of 0.8 mm. This new MLRE underestimtes (less thn 1 mm discrepncy) the ctul SPCP in only 7% of the cses on the bsis of vlidtion smple. (Angle Orthod 2005;75: 202 207.) Key Words: Mixed dentition nlysis; Multiple regression; Mesiodistl tooth size INTRODUCTION Mixed dentition nlysis is the prediction of the tooth size of nonerupted permnent cnine nd premolrs to determine the discrepncy between the vilble nd required spce in ech dentl rch. Some bsic principles for mixed dentition nlysis re: (1) known minimum systemic error, (2) ese of use by ny person with bsic trining, (3) fst, (4) no specil equipment required, (5) cn be crried out directly in the mouth, nd (6) cn be used in both dentl rches. 1 Mixed dentition nlysis methods cn be grouped into three ctegories, ie, those which use regression equtions, Assistnt Professor, Deprtment of Socil Dentistry, Universidd Perun Cyetno Heredi, Lim, Peru. b Postdoctorl Fellow, Grdute Orthodontics Progrm, University of Albert, Edmonton, Cnd. Corresponding uthor: Crlos Flores-Mir, DDS, MSc, Cert Orth, PhD, Fculty of Medicine nd Dentistry, Room 4051A, Dentistry/ Phrmcy Centre, University of Albert, Edmonton, Albert, Cnd T6G 2N8 (e-mil: crlosflores@ulbert.c). Accepted: Mrch 2004. Submitted: Jnury 2004. 2005 by The EH Angle Eduction nd Reserch Foundtion, Inc. those which use rdiogrphs, nd those which use combintion of both. Among the different mixed dentition nlysis methods reported in the literture, the regression equtions bsed on the lredy erupted permnent teeth in erly mixed dentition re the most brodly used, especilly the Moyers probbility tbles 1,2 nd the Tnk nd Johnston equtions. 3 Crey 4 reported the existence of significnt liner ssocition between the mesiodistl tooth width sum of the lower permnent incisors nd the sum of the lower or upper permnent cnine nd premolrs (SPCP) in 1949. Since then, severl simple liner regression equtions hve been proposed for popultions of different ethnic origins. 3,5 14 Only two recent studies 15,16 reported tht the lower permnent incisor mesiodistl tooth width sum is not the best predictor. Advnces in sttisticl softwre hve permitted complex clcultions of multiple regression models tht could simultneously evlute severl explntory vribles. Nourllh et l 15 reported tht the sum of the lower centrl incisors nd upper first molrs hd the highest prediction vlue (determintion coefficient between 52% nd 56%) for SPCP. A yer lter, Legovic et l 16 developed multiple liner regression equtions (MLRE) with higher pre- 202
BEST PREDICTORS FOR CUSPID AND BICUSPIDS SUMS diction vlues (determintion coefficient between 62% nd 72%) when they lso considered the buccolingul tooth size. Finlly, Hshim nd Al-Shln 17 hve recently reported the inclusion of the sex fctor s n dditionl predictor vrible for the estimtion of the cnine nd premolrs sum on the bsis of the sexul dimorphism in tooth size tht predominted in their smple, but they did not stte the determintion coefficients for their MLRE. However, Legovic et l 16 nd Hshim nd Al-Shln 17 did not vlidte their findings in new smple. Therefore, the present study ws conducted with the following purposes: (1) to determine in Peruvin smple which sum or combintion of sums of permnent tooth widths presented the best prediction cpbility for the permnent cnine nd premolrs sums, (2) to clculte nd vlidte multiple liner regression eqution tht included sex nd rch s predictor fctors for this popultion, nd (3) to evlute the clinicl significnce of the new prediction eqution. MATERIALS AND METHODS A representtive public school with popultion of 1389 dolescent children (ges 12 16 yers) from Lim, Peru, ws selected for this study. From the pool of 1389 students, 673 consented to prticipte in the study by mens of informed consent letters obtined from the subjects prents. Students were clled in groups from their respective clssrooms to specilly equipped room where clinicl exmintions were conducted. A totl of 321 subjects fulfilled the selection criteri, ie, Peruvin ncestors from t lest one previous genertion, both lst nmes of Hispnic-Americn origin, no previous orthodontic tretment, nd complete permnent dentition without cliniclly visible dentl cries, restortions or ttrition in proximl surfces or ny dentl nomlies. From these 321 subjects, rndom smple of 150 students (75 mle nd 75 femle) ws selected. A vlidtion smple of nother 50 students (25 mle nd 25 femle) ws lso rndomly selected from the sme popultion to clculte the mount of underestimtion of the SPCP using the MLRE. Dentl impressions were tken nd immeditely poured with dentl plster to void ny distortion. Mesiodistl tooth widths were mesured subsequently from dentl csts ccording to the technique proposed by Moorrees et l, 18 using sliding cliper with Vernier scle (Denturum, Pforzheim, Germny) with n ccurcy of 0.1 mm. The intrexminer clibrtion procedure consisted of the primry investigtor (Dr Bernbé) mesuring five pirs of models two times, seprted by 24 hours. The interexminer clibrtion ws done ginst n experienced orthodontist (Dr Flores-Mir), who lso mesured the five pirs of models two times, seprted by 24 hours. Concordnce between the three groups of mesurements ws high (intrclss correltion coefficient, 0.987 nd 0.981 for intr- nd 203 interexminer clibrtion) nd sttisticlly different from zero in both cses (P.001). Using the one smple t-test the intr- nd interexminer mesurement errors were 0.08 mm (CI 95% [ 0.24; 0.08]; P.316) nd 0.11 mm (CI 95% [ 0.09; 0.31]; P.256), respectively. For the min study, the primry investigtor nlyzed up to 10 pirs of models ech dy to void eye ftigue. 15,19,20 Ech tooth ws mesured twice, from the right first molr to the left first molr in ech rch; if the difference between both mesurements ws less thn 0.2 mm, then the first mesurement ws registered. 19,20 If the second mesurement differed more thn 0.2 mm from the first mesurement, then the tooth ws remesured, 14,19 22 nd only the new mesurement ws then registered. 19,20 RESULTS Eight groups divided ccording to the mesiodistl tooth width SPCP were gthered ccording to rch side, rch, nd sex. All groups fulfilled normlity (Shpiro-Wilks test, P.134) nd homogeneity of vrinces (Levene test, P.993) criteri; therefter, prmetric tests were used. A three-wy univrite nlysis of vrince (ANOVA) test (ccording to rch side, rch, nd sex) found sttisticlly significnt difference mong sex (P.001) nd rch (P.001) but not for rch side (P.338). Therefore, only four groups (upper nd lower rch from femle nd mle) were used for the clcultion of the regression eqution. Vlues for ech rch side were mintined without verging both mesurements per rch. The liner ssocition between different tooth-type combintions nd the SPCP for the four groups estblished ws evluted by Person correltion coefficient (Tble 1), once normlity criterion ws corroborted in ll the groups (Shpiro-Wilks test, P.240). The force of the ssocition incresed s the number of pirs of teeth incresed following this pttern, ie, if only pir hs to be chosen s predictor, it should be the upper first molrs; if two pirs hve to be chosen, lower centrl incisors should be dded; nd if three pirs hve to be chosen, the upper centrl incisors should be dded. The inclusion of more pirs did not produce notble increses in the correltion vlues. The comprison by pirs of the correltion coefficients mong the three groups with higher correltion vlues ccording the number of teeth included in the tooth-type combintion (groups 3, 8, nd 13, respectively) ws done using Fisher Z vlues. No sttisticlly significnt differences mong the three groups were found, even if nlyzed s totl correltions or grouped by sex (P.092 nd P.082, respectively). On the bsis of group 13 (sum of permnent upper first molr, upper nd lower centrl incisors), new MLRE (Y 3.763 0.37 X 0 1.057 X 1 0.366 X 2, where X 0 is the sum of permnent upper nd lower centrl incisors nd upper first molrs, X 1 is 0 for the mndible nd 1 for
204 BERNABÉ, FLORES-MIR TABLE 1. Group 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Person Correltion Coefficients for Different Teeth Groups According to Arch nd Sex Tooth Combintions b 11, 21 41, 31 16, 26 42, 32 11, 21, 41, 31 42, 41, 31, 32 11, 21, 16, 26 41, 31, 16, 26 42, 32, 16, 26 42, 32, 11, 21 42, 41, 31, 32, 11, 21 42, 42, 31, 32, 16, 26 41, 31, 11, 21, 16, 26 42, 32, 11, 21, 16, 26 42, 41, 31, 32, 11, 21, 16, 26 Sum of Upper Cnine nd Premolrs Femle (r) Mle (r) Totl (r) 0.51 0.52 0.58 0.66 0.46 0.50 0.55 0.59 0.57 0.66 Sttisticl significnce (P.001) for ll the Person correltion coefficients (r). b FDI tooth numbering system is used. 0.53 0.50 0.61 0.55 0.59 0.58 Sum of Lower Cnine nd Premolrs Femle (r) Mle (r) Totl (r) 0.61 0.44 0.61 0.55 0.74 0.51 0.47 0.57 0.59 0.58 the mxill, nd X 2 is 0 for femle nd 1 for mle) ws clculted including sex nd rch s dditionl independent vribles. The SPCP estimted by the MLRE ws more precise thn the one obtined by just using the men SPCP (ANOVA, P.001). Also, ll the coefficients were sttisticlly different from zero (t-test, P.001). An evlution of the suppositions of independence (colinerity), normlity, nd homoscedsticity of the MLRE ws completed through nlysis of the residuls, which ws clculted s the difference between the rel nd estimted SPCP. Furthermore, residuls were trnsformed to the Z score (Studentized) for identified typicl cses nd then represented grphiclly ginst the distribution of the vlues estimted by the MLRE (Figure 1). This nlysis demonstrted tht homogeneous vrince (homoscedsticity) nd normlity existed mong the residuls, s well s bsence of nonliner pttern. Therefore, the eqution ws considered liner. Two cses were identified s potentil problemtic, but no substntil improvement ws noted neither in explntory cpbility (r 2 4) nor in ccurcy (SEE 0.791 mm) of the MLRE fter both cses were deleted from the dtbse. Therefore, both cses were mintined in the nlysis. Vlidtion of the proposed MLRE ws done through the evlution of its prediction cpbility for the SPCP in the vlidtion smple (25 mle nd 25 femle). For this, SPCP were estimted by using the proposed MLRE nd then compred with the ctul SPCP. Tble 2 exhibits frequencies distribution for the overll difference between ctul nd predicted SPCP seprted by sex nd rch. In 34% of the vlidtion smple (68 from 200 SPCP becuse in ech subject the four hemirches were mesured) the sum predicted by the MLRE under- or overestimte the rel SPCP. The MLRE under- nd overestimte by more thn 1 mm the rel SPCP in 7% (14) nd 27% (54) from the cses evluted, respectively. DISCUSSION Of ll the different mixed dentition nlysis methods reported in the literture (regression equtions, rdiogrphic methods, or combintion of both), the regression equtions bsed on mesurements from the lredy erupted permnent teeth in erly mixed dentition re the most brodly used. Therefore, the present study ws conducted to corroborte their principles in Peruvin smple. Significnt differences for the SPCP ccording to rch nd sex were found, which ws consistent with previous findings. 6,7,9,11,13,15 As expected, on the bsis of other studies, 6,7,11,22 no differences for the SPCP between rch sides were found. To determine the best tooth-type combintion for predicting SPCP, 15 different groups were configured only on the bsis of permnent teeth lredy erupted in the erly mixed dentition. Lower first permnent molrs were not included in the clcultions becuse they my be still covered by gingivl tissue in the distl groove, mking mesurements difficult. 15 Upper lterl incisors lso were not included becuse of their size nd form vribility. 1,15,23 Becuse the low Person correltion coefficient of ny selected pir, more pirs were dded to get higher correltion vlues. Even then, the correltion coefficients were, t most, only moderte but still higher thn the ones reported in the literture for only lower incisors. 3,6,10,11,15,24 Although comprisons between pirs of correltion coefficients did not find ny significnt differences, the group 13 (upper nd lower centrl incisors nd upper first molrs) ws selected s the best predictor group becuse its higher correltion with the SPCP thn groups 3 nd 8 nd becuse
BEST PREDICTORS FOR CUSPID AND BICUSPIDS SUMS 205 FIGURE 1. Residul dispersion vs the sum estimted of cuspid nd bicuspids. Studentized residuls were obtined by trnsforming to Z score the differences between ctul nd estimted sum of cuspid nd bicuspids. TABLE 2. Difference (mm) Between the Predicted SPCP Through the MLRE nd the Actul SPCP in the Vlidtion Smple Difference Between Predicted nd Actul SPCP Vlues Sex Dentl Arch 1.01 mm 1.00 to 0.51 mm 0.50 to 0.50 mm 0.51 to 1.00 mm 1.01 mm Totl Femle Mle Lower Upper Lower Upper 7 (14%) 15 (30%) 14 (28%) 18 (36%) 15 (30%) 4 (8%) 12 (24%) 11 (22%) 17 (34%) 25 (50%) 15 (30%) 16 (32%) 3 (6%) 3 (6%) 7 (14%) 4 (8%) 8 (16%) 3 (6%) 2 (4%) 1 (2%) Numbers between prentheses represent the percentge of cses in ech group. the evlution of four pirs of tooth types (including lower lterl incisors), nd not three, did not hve ny potentil significnt increment in the vlues of the correltion coefficients. Only Nourllh et l 15 nd Legovic et l 16 hd previously reported tht lower incisors re not the best predictor for the SPCP, nd the present results re in greement with them. On the other hnd, vn de Merwe et l 7 reported tht in their popultion, the sum of the four lower incisors ws the best predictor fter compring liner ssocitions with other tooth-type combintions. Serching for the best predictor for the SPCP on the bsis of correltion coefficients must lwys be done before strting the regression nlysis independently from the results. Vritions tht exist between nd within popultions support the implementtion of this strtegy. 25,26 Legovic et l 16 reported MLRE tht lso considered the buccolingul tooth size. The buccolingul tooth widths were not considered in this study becuse their mesurement would ugment significntly the mesurement time needed for the clinicl use of the mixed dentition nlysis nd becuse mximum buccolingul tooth width cn not be mesured ccurtely on dentl csts. 27 29 Becuse mximum buccolingul tooth width is often locted subgingivlly, it cn not lwys be mesured properly on plster csts, which could bis the results. 30 32 On the bsis of group 13, new MLRE ws clculted including sex nd rch s dditionl independent vribles. Only Hshim nd Al-Shln 17 erlier reported the use of sex s n extr predictor vrible though they did not explin their results thoroughly. The influence from ech of the three independent vribles entered to the MLRE on SPCP could be nlyzed by checking stndrdized regression coefficients (Tble 3). Upper nd lower centrl incisors nd upper first molr sum ws the vrible with the highest stndrdized coefficient, followed immeditely by rch nd sex of the students (vrible with the lowest stndrdized coefficient). Furthermore, the contribution of ech explntory vrible on vribility of the SPCP ws evluted through unstndrdized regression coefficients. If the upper nd lower centrl in-
206 BERNABÉ, FLORES-MIR TABLE 3. Vrible Constnt Group 13 (X 0 ) Arch (X 1 ) Sex (X 2 ) MLRE for Predicting the Sum of Cuspid nd Bicuspids,b Bet 3.763 0.370 1.057 0.366 Regression Coefficient Bet Stndrdized 1 0.415 0.144 Sig Lower Bound 2.288 0.329 0.928 0.236 95% CI Upper Bound 5.239 0.389 1.186 0.496 MLRE: Y 0.370 X 0 1.057 X 1 0.366 X 2 3.763. b MLRE indictes multiple liner regression eqution; CI, confidence intervls; nd Sig, sttisticl significnce. cisors nd upper first molr sum incresed 1 mm, then the SPCP lso incresed 0.37 mm. If predictions for both rches in the sme child re mde, the upper estimtions will be higher for bout 1 mm thn lower. If prediction is done for the sme dentl rches in two children with different sexes, the SPCP estimted will be 0.3 mm lrger in the mle child. The proposed MLRE hs multiple correltion of 0.78; it mens, tht the three predictor vribles explin pproximtely 60% of the vribility which exists in SPCP (determintion coefficient of 1). This vlue is mong the highest in the literture when only mesiodistl tooth width mesurements from dentl csts were used. 3,6,10,11,15,24 The prediction cpbility of one liner regression eqution cn be evluted by two interrelted methods. The first is entirely on the bsis of probbilities nd consists in determining the stndrd error of estimtion of the MLRE proposed (0.805 mm). In sttisticl terms, pproximtely 68% nd 95% of the scholr popultion evluted hd differences between the ctul SPCP nd the predicted ones below or bove 0.8 nd 1.6 mm, respectively. Becuse difference between both sums less or equl to 1 mm hs been estblished previously s clinicl cutoff point for previous reports, 9,10,14,22 nd ccording to this method of evlution, pproximtely 20% from the cses evluted hd differences between both sums less or higher thn 1 mm, under- nd overestimting 10% in both cses. The second method consisted in the prediction of SPCP through the MLRE in vlidtion smple. Using n extr smple results in more precise vlidtion of the MLRE becuse it is on the bsis of ctul mesurements nd not on probbilities. When the proposed MLRE ws pplied to the vlidtion smple selected rndomly from the sme popultion, underestimtion of the ctul SPCP of more thn 1 mm occurred only in 14 (7%) from the 200 SPCP obtined. Therefore, this MLRE could be considered good clinicl dignostic lterntive on the bsis of its prediction cpbility for this smple. It is lso importnt to note tht in 54 (27%) from the 200 SPCP, the MLRE overestimted tht the true SPCP is more thn 1 mm (with mximum of 2.5 mm), but this problem is considered of less clinicl importnce on the bsis of the fct tht orthodontists re more concerned bout the prediction for the lck of thn the excess of spce in specific dentl rch. A primordil issue with mixed dentition nlysis is the ccurcy tht cn be obtined using the prediction eqution. Therefore, further studies tht include more explntory vribles for the SPCP should be conducted with the gol of explining the overll vribility present in the SPCP. These studies should be lso on the bsis of the ctul knowledge of tooth size heritbility nd genetics. Finlly, even Peruvin clinicins should use this MLRE crefully. An ssumption tht the ptient fulfills the selection criteri of the present popultion should be mde. Further studies with lrger nd representtive smples re required to confirm these findings. CONCLUSIONS The combintion of upper nd lower centrl incisors nd upper first molrs ws the best predictor for the SPCP in this smple of Peruvin schoolchildren; the MRLE proposed presented explntory cpbility from the vribility in the SPCP of 60% nd stndrd error of estimtion of 0.8 mm; nd in 90% of the cses evluted the estimtion of the SPCP ws smller thn 1 mm compred with the ctul vlues in vlidtion smple. ACKNOWLEDGMENTS Specil thnks to Ruben Durnd nd Luz Crbjl from the Sttistics, Biometry nd Demogrphy Deprtment of the Fculty of Sciences nd Philosophy of the Universidd Perun Cyetno Heredi for their sttisticl dvice nd support in nlyzing the dt. REFERENCES 1. Moyers RE. Hndbook of Orthodontics. Chicgo: Yer Book Medicl Publishers; 1988. 2. Moyers RE. Hndbook of Orthodontics for the Student nd Generl Prctitioner. Chicgo: Yer Book Medicl Publishers; 1972. 3. Tnk MM, Johnston LE. The prediction of the size of unerupted cnines nd premolrs in contemporry orthodontic popultion. J Am Dent Assoc. 1974;88:798 801. 4. Crey CW. Liner rch dimension nd tooth size. Am J Orthod. 1946;35:762 775. 5. Ferguson FS, Mcko DJ, Sonnenberg EM, Shkun ML. The use of regression constnts in estimting tooth size in Negro popultion. Am J Orthod. 1978;73:68 72. 6. Frnkel HH, Benz EM. Mixed dentition nlysis for blck Americns. Peditr Dent. 1986;8:226 230. 7. vn der Merwe SW, Rossouw P, vn Wyk Kotze TJ, Trutero H. An dpttion of the Moyers mixed dentition spce nlysis for Western Cpe Cucsin popultion. J Dent Assoc S Afr. 1991; 46:475 479. 8. l-khdr BH. Prediction of the size of unerupted cnines nd premolrs in Sudi Arb popultion. Am J Orthod Dentofcil Orthop. 1993;104:369 372. 9. Yuen KK, Tng EL, So LL. Mixed dentition nlysis for Hong Kong Chinese. Angle Orthod. 1998;68:21 28. 10. Lee-Chn S, Jcobson BN, Chw KH, Jcobson RS. Mixed dentition nlysis for Asin-Americns. Am J Orthod Dentofcil Orthop. 1998;113:293 299.
BEST PREDICTORS FOR CUSPID AND BICUSPIDS SUMS 11. Jroonthm J, Godfrey K. Mixed dentition spce nlysis in Thi popultion. Eur J Orthod. 2000;22:127 134. 12. Mrchionni VMT, Silv MCA, Arujo TM, Reis SRA. [Evlution of the effectiveness of the Tnk-Johnston method for prediction of the mesiodistl dimeter of unerupted cnines nd premolrs]. Pesqui Odontol Brs. 2001;15:35 40. 13. Digne F, Diop-B K, Ngom PI, Mbow K. Mixed dentition nlysis in Seneglese popultion: elbortion of prediction tbles. Am J Orthod Dentofcil Orthop. 2003;124:178 183. 14. Flores-Mir C, Bernbé E, Cmus C, Crhuyo MA, Mjor PW. Prediction of mesiodistl cnine nd premolr tooth width in smple of Peruvin dolescents. Orthod Crniofc Res. 2003;6: 173 176. 15. Nourllh AW, Gesch D, Khordji MN, Splieth C. New regression equtions for predicting the size of unerupted cnines nd premolrs in contemporry popultion. Angle Orthod. 2002;72: 216 221. 16. Legovic M, Novosel A, Legovic A. Regression equtions for determining mesiodistl crown dimeters of cnines nd premolrs. Angle Orthod. 2003;73:314 318. 17. Hshim HA, Al-Shln TA. Prediction of the size of un-erupted permnent cuspids nd bicuspids in Sudi smple: pilot study. J Contemp Dent Prct. 2003;4:40 53. 18. Moorrees CF, Thomsen SO, Jensen E, Yen PK. Mesiodistl crown dimeters of the deciduous nd permnent teeth in individuls. J Dent Res. 1957;36:39 47. 19. Bernbé E, Flores-Mir C, Mjor PW. Tooth width rtio discrepncies in smple of Peruvin dolescents. Am J Orthod Dentofcil Orthop. 2004;125:361 365. 20. Bernbé E, Villnuev KM, Flores-Mir C. Tooth width rtios in crowded nd non-crowded dentitions. Angle Orthod. Scheduled for 74: Dec 2004. 21. Sntoro M, Ayoub ME, Prdi VA, Cngilosi TJ. Mesiodistl 207 crown dimensions nd tooth size discrepncy of the permnent dentition of Dominicn Americns. Angle Orthod. 2000;70:303 307. 22. Bishr SE, Jkobsen JR, Abdllh EM, Fernndez Grci A. Comprisons of mesiodistl nd buccolingul crown dimensions of the permnent teeth in three popultions from Egypt, Mexico, nd the United Sttes. Am J Orthod Dentofcil Orthop. 1989; 96:416 422. 23. Arn VE. Frequency of Tooth Crown Altertions in Primry nd Permnent Incisors. BSc thesis, Lim: Universidd Perun Cyetno Heredi; 1983. 24. Peng H, Wng X, Chen K. [The prediction eqution of the permnent cnine nd premolr crown]. Hu Xi Kou Qing Yi Xue Z Zhi. 2000;18:55 57. 25. Dhlberg AA. The chnging dentition of mn. J Am Dent Assoc. 1945;32:676 690. 26. Bilit HL. Dentl vrition mong popultions. An nthropologic view. Dent Clin North Am. 1975;19:125 139. 27. Peck H, Peck S. An index for ssessing tooth shpe devitions s pplied to the mndibulr incisors. Am J Orthod. 1972;61:384 401. 28. Peck S, Peck H. Crown dimensions nd mndibulr incisor lignment. Angle Orthod. 1972;42:148 153. 29. Peck S, Peck H. Orthodontic spects of dentl nthropology. Angle Orthod. 1975;45:95 102. 30. Keene A, Engel G. The mndibulr dentl rch, prt IV: prediction nd prevention of lower nterior relpse. Angle Orthod. 1979; 49:173 180. 31. Smith RJ, Dvidson WM, Gipe DP. Incisor shpe nd incisor crowding: re-evlution of the Peck nd Peck rtio. Am J Orthod. 1982;82:231 235. 32. Puneky PJ, Sdowsky C, BeGole EA. Tooth morphology nd lower incisor lignment mny yers fter orthodontic therpy. Am J Orthod. 1984;86:299 305.