Development of a prediction equation for the mixed dentition in a Pakistani sample


Regression equations are widely used for mixed dentition analysis. However, estimations from these equations can vary in different population groups. The aim of this study was to produce simple linear equations and tables for Pakistani children.


Two hundred subjects of Pakistani descent who met our criteria (ages, 13-15 years; 100 boys, 100 girls) were selected from local schools. The mesiodistal widths of all mandibular permanent incisors, canines, and premolars were measured and analyzed by using paired t tests. The results were also compared with predicted values from the Moyers and the Tanaka and Johnston methods. Correlation and linear regression analyses were performed between the predicted and actual tooth sizes for Pakistani children, and standard regression equations were developed.


No significant differences were observed for measured canine and premolar antimeres and sex. Significant and high positive correlations were found between the mandibular incisors and the combined mesiodistal widths of the canines and premolars for the maxillary (r = 0.65; P <0.001) and mandibular (r = 0.59; P <0.001) segments.


The equations and charts commonly used for North American children (75th percentile) did not accurately predict for our sample. The regression equations and tables developed in this study can be used for orthodontic treatment planning for children in Pakistan.

As the number of patients demanding early orthodontic treatment continues to rise, it is important for the orthodontist to estimate any deficiency of arch space in advance and initiate appropriate treatment in a timely manner. An accurate mixed dentition space analysis is an important criterion in determining whether the treatment plan will involve serial extractions, guidance of eruption, space maintenance, space regaining, or just periodic observation of the patient. Early attempts by Black at estimating tooth sizes were based on tables of average mesiodistal widths. Clinically, these approximations were found to be unreliable because of the great variability in tooth sizes between persons. Subsequently, 3 main approaches have been used to estimate the mesiodistal crown widths of unerupted maxillary and mandibular canines and premolars in mixed dentition patients: direct measurement of the teeth from radiographs ; estimations from prediction equations and tables based on measurements of deciduous teeth or other erupted permanent teeth ; and a combination of radiographic measurements and prediction tables, such as prediction tables associated with measurements of erupted and unerupted teeth.

Orthodontics is an evolving discipline in Pakistan. Therefore, general dentists have the first opportunity to examine patients in the early mixed dentition and thus predict the development of the occlusion, so that a proper assessment can be made. If the prediction is accurate, and if patients faced with developing malocclusions are properly referred to orthodontists, dental irregularities in their adult dentition would probably be reduced. On the other hand, it is useless to refer patients who are only suspected of having such orthodontic problems, when in reality there is no problem.

Furthermore, the accuracy of radiographic prediction methods is largely influenced by the quality of the radiograph and the technique with which the films are taken; this can be poor in countries where dental services are gradually developing. Even if these variables are controlled, the teeth can be rotated in their crypts, giving false measurements. These disadvantages can be overcome with prediction tables or equations alone. Since these prediction tables and equations were developed for white North American children, their applicability in other populations is questionable because tooth sizes differ in various racial groups.

Evidence of racial tooth size variability suggests that prediction techniques based on 1 racial sample might not be universal. A recent study by Sakrani showed marked variability in the mesiodistal dimensions of Pakistani subjects when compared with other population groups, and advised caution regarding the use of the mixed dentition prediction methods of Moyers and Tanaka and Johnston for Pakistani children. To date, no data have been published regarding the study and development of mixed dentition analyses with nonradiographic means in Pakistani subjects. Therefore, in this study, we aimed to (1) measure the mesiodistal crown diameters of the mandibular incisors, canines, and premolars and study their relationships; (2) see any sex dimorphism of the above; (3) construct prediction tables and equations for Pakistani children; and (4) check the reliability of both the Moyers and the Tanaka and Johnston methods in the local setting. This will help in orthodontic diagnosis and treatment planning for our children.

Material and methods

The subjects for this cross-sectional study were selected from 5 schools after approval from the hospital ethical review committee and the school board in Karachi, Pakistan. Additionally, consent was obtained from the subjects and their parents for dental examinations and for possible selection for subsequent dental impressions. Students were called in groups from their classrooms to a specially equipped room where the clinical examinations and screenings were conducted. After we examined children in the age range of 13 to 15 years, we selected a sample of 200 (100 boys, 100 girls) who met our study criteria. Inclusion criteria were Pakistani descent; all permanent teeth present in each arch (fully erupted with the exception of the second and third molars) ; Class I molar and canine relationships ; and minor malocclusions such as minimal incisor crowding or spacing. The exclusion criteria were subjects with congenital craniofacial anomalies or previous orthodontic treatment, and teeth with fractures, malformations, proximal caries, proximal restorations, or attrition. Alginate impressions of the subjects were obtained at Aga Khan University Hospital and local schools, and poured in orthodontic plaster. A number was assigned to each cast.

Two investigators (A.K., G.E.) measured the unsoaped plaster study models manually and independently. The mesiodistal widths of all mandibular permanent incisors, canines, and premolars were measured with pointed vernier calipers, read to the nearest 0.1 mm. The beaks of the calipers were machine sharpened to a fine taper to improve accessibility to the proximal surfaces of the teeth, especially for the mesiodistal dimensions. All measurements were made perpendicular to the long axis of the tooth, with the beaks entering the interproximal area from either the buccal or the occlusal side. The preferred method was from the buccal side, unless the tooth appeared to be severely rotated. Interexaminer and intraexaminer reliability was predetermined at 0.2 mm as suggested by Bishara et al. The 2 measurements obtained by the investigators were compared; if less than a 0.2-mm variation was found, then the values were averaged. If there was more than 0.2 mm, the teeth were remeasured, and the closest 3 measurements were averaged.

Statistical analysis

Descriptive statistics, including means, standard deviations, and ranges, were calculated for age, teeth (canines, premolars, and mandibular incisors), and groups of teeth (canines, premolars, and mandibular incisors) according to sex and between the maxillary and mandibular arches. Student t tests were used to determine whether there were significant differences between the right and left sides in each arch for the boys and girls, as well as between the sexes by using the independent samples t test. Correlation coefficients and regression equations were formulated to see any relationship between the summed widths of the 4 mandibular incisors and the canines and premolars of each dental arch. Statistical calculations and analyses, including standard errors of the estimate and coefficients of determination, were carried out by using the SPSS for Windows statistical computer package (version 10.0.1; SPSS, Chicago, Ill).


A total of 200 plaster study models were obtained from our male and female subjects with mean chronologic ages of 14.2 years (SD, 1.3) and 13.9 years (SD, 0.8), respectively. On comparing individual teeth in the buccal segment with their opposing units, the mandibular second premolars and the maxillary canines showed increased mesiodistal dimensions ( Table I ). Similarly, the sums of the maxillary canines and premolars showed higher mean differences when compared with the sums of the mandibular canines and premolars for the male and female subjects, and for all subjects.

Table I
Descriptive statistics for CPM and LI
Tooth Sex Mandibular arch (mm) Maxillary arch (mm)
Mean Range SD Mean Range SD
PM 1 Both 7.01 2.45 0.418 6.99 2.35 0.418
M 7.01 2.05 0.430 6.99 2.35 0.432
F 7.01 2.40 0.408 6.99 1.90 0.388
PM 2 Both 7.18 2.08 0.411 6.76 2.18 0.398
M 7.18 1.95 0.421 6.78 1.80 0.390
F 7.18 2.03 0.403 6.73 2.18 0.407
C Both 6.73 2.08 0.385 7.72 2.38 0.402
M 6.86 2.08 0.371 7.80 2.38 0.411
F 6.60 1.80 0.355 7.63 1.90 0.393
LLI Both 5.95 1.80 0.331
M 6.00 1.73 0.286
F 5.90 1.80 0.364
LCI Both 5.38 1.73 0.329
M 5.42 1.73 0.309
F 5.35 1.70 0.345
CPM Both 20.93 5.75 1.04 21.47 6.08 1.01
M 21.06 5.25 1.05 21.58 5.80 1.05
F 20.80 5.37 1.02 21.37 4.50 0.96
LI Both 22.69 6.70 1.25
M 22.86 6.10 1.12
F 22.51 6.70 1.35
PM1 , First premolar; PM2 , second premolar; C , canine; LLI , lower lateral incisor; LCI , lower central incisor; CPM , canine and premolars; LI , lower incisors; M , male; F , female.

No significant mesiodistal width difference was observed between the left and right sides for teeth measured individually as well as in combined segments of canine and first and second premolars ( P >0.05) for boys, girls, or the sexes combined ( Table II ). Based on these findings, either the right or the left measurements can be used to represent the mesiodistal width of the canine and premolar segment. However, in this study, the values were averaged for statistical analysis.

Table II
Left to right differences for CPM and LI
Sex Tooth segment Mean SD t df P value
M + F (n = 200) LC 0.090 0.006 −0.141 199 0.888
LPM1 0.139 0.009 0.061 199 0.952
LPM2 0.129 0.009 0.343 199 0.732
UC 0.090 0.006 −0.583 199 0.560
UPM1 0.096 0.006 0.404 199 0.687
UPM2 0.112 0.007 −1.876 199 0.062
LLI 0.079 0.005 −1.459 199 0.146
LCI 0.091 0.006 0.448 199 0.655
Lower CPM 0.002 0.208 0.194 199 0.847
Upper CPM −0.015 0.155 −1.45 199 0.148
F (n = 100) Lower CPM 0.010 0.230 0.442 99 0.659
Upper CPM −0.006 0.145 −0.440 99 0.661
M (n = 100) Lower CPM −0.004 0.183 −0.245 99 0.807
Upper CPM −0.02 0.164 −1.54 99 0.125
LC , Lower canine; LPM1 , lower first premolar; LPM2, lower second premolar; UC, upper canine; UPM1, upper first premolar; UPM2, upper second premolar; LLI , lower lateral incisor; LCI , lower central incisor; CPM , canine and premolars; M , male; F , female.

The values for boys and girls were computed separately to permit evaluation of sexual dimorphism, as shown in Table III . Individually, the mandibular and maxillary canines and the mandibular lateral incisors showed significantly greater mesiodistal widths in the boys than in the girls (data not shown). In spite of these individual differences, the combined dimensions of the canine, and first and second premolars between the sexes showed insignificant differences ( P <0.05).

Table III
Gender differences for CPM and LI
Tooth segment Sex Mean (mm) SD Mean difference P value
LC M (n = 100) 6.86 0.371 −0.261 0.000
F (n = 100) 6.60 0.355
LPM1 M (n = 100) 7.01 0.430 0.003 0.958
F (n = 100) 7.01 0.408
LPM2 M (n = 100) 7.18 0.421 0.001 0.975
F (n = 100) 7.18 0.403
UC M (n = 100) 7.80 0.432 −0.170 0.004
F (n = 100) 7.63 0.388
UPM1 M (n = 100) 6.99 0.411 0.001 0.976
F (n = 100) 6.99 0.393
UPM2 M (n = 100) 6.78 0.390 −0.047 0.401
F (n = 100) 6.73 0.407
LLI M (n = 100) 6.00 0.286 −0.104 0.025
F (n = 100) 5.90 0.364
LCI M (n = 100) 5.42 0.309 −0.074 0.112
F (n = 100) 5.35 0.345
Lower CPM M (n = 100) 21.06 1.05 −0.256 0.083
F (n = 100) 20.80 1.02
Upper CPM M (n = 100) 21.58 1.05 −0.216 0.133
F (n = 100) 21.37 0.96
LC , Lower canine; LPM1 , lower first premolar; LPM2, lower second premolar; UC, upper canine; UPM1, upper first premolar; UPM2, upper second premolar; LLI , lower lateral incisor; LCI , lower central incisor; CPM , canine and premolars; M , male; F , female.
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Apr 11, 2017 | Posted by in Orthodontics | Comments Off on Development of a prediction equation for the mixed dentition in a Pakistani sample
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