INTRODUCTION

In orthodontic treatment planning for patients with mixed dentition, accurate prediction of the sum of the mesiodistal diameters of the clinical crowns of unerupted permanent canines and premolars is indispensable, especially in choosing appropriate methods for space control, including space regaining and serial extraction. Numerous methods1–12 for anticipating the space that will be required to accommodate the unerupted permanent canines and premolars into the line of occlusion, with a premise of possible differences between the sexes, have been reported.

Utilizing a large sample size (n  =  506), Tanaka and Johnston2 employed the sum of the mesiodistal crown widths of the four mandibular incisors and calculated the least-squares regression equation for estimating the unerupted permanent tooth size in the same dental arch. To improve the accuracy of prediction, other variables, such as the mesiodistal crown widths of maxillary incisors and/or of both maxillary and mandibular molars, have also been used as predictors.8 Multiple regression equations, which enable us to compare the differences in the coefficient of determination among variables, were employed to estimate. Legović et al.7 used the buccolingual tooth widths as independent variables in their regression equations. Boboc and Dibbets12 added one erupted canine or premolar width to the regression equation as an independent variable.

Inclusion of sex factor as an independent variable or adding respective constants by gender for their estimation has been recognized as improving the accuracy of prediction. Bernabe and Flores-Mir13 added the constants for only male subjects as an additional independent variable. Ling and Wong14 used the respective constants for male and female subjects in their regression equations. However, whether there are differences between sexes remains controversial.

Previous studies1,3 using samples from Japanese populations have employed only tooth size as an independent variable, and details about the samples (ie, presence or absence of tooth crowding) were not provided.

The purposes of the present study were (1) to determine whether the accuracy of the prediction of the summed widths of unerupted permanent canines and premolars depends on the patient's sex and, if so, (2) to examine whether there are differences between sexes in the best combination of independent variables for predicting and (3) to evaluate the practical accuracy using our prediction models for males and females, respectively.

MATERIALS AND METHODS

Data Recording and Analysis

The mesiodistal crown diameters of the central incisors (U1 and L1), the lateral incisors (U2, L2), the canines (U3, L3), the first premolar (U4, L4), the second premolar (U5, L5), and the first molars (U6, L6) in the maxillary and mandibular dentitions were measured on dental casts obtained from the subjects. We used the mean of the right and left mesiodistal crown diameters for each tooth.

Molar basal arch lengths (UBAL for the upper dentition and LBAL for the lower dentition) and intermolar distances (UIMD for the upper dentition, LIMD for the lower dentition) were also recorded. (Definitions of variables are provided in Figure 1.) Measurements were made by one examiner using a digital caliper (Absolute Digimatic Caliper, Mitutoyo Co, Kanagawa, Japan) with an accuracy of ±0.02 mm. To assess for intraexaminer errors, 20 randomly selected dental casts were measured twice at an interval of 2 weeks. Intraexaminer errors were assessed using a paired t-test.

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Pearson's correlation coefficients (r) between each independent variable and dependent variable were calculated. In this study, P values of <.05 were assigned as significant.

Stepwise multiple regression analysis was performed, with U1, U2, U6, L1, L2, L6, UBAL, LBAL, UIMD, and LIMD as the independent variables and the sum of the mesiodistal crown diameters of the permanent canines and premolars in the same dental arch as dependent variables. For each dental arch, the best combination of independent variables with the greatest R² values was determined. Correlation and linear regression analyses between the estimated widths and the measured widths of the permanent canines and premolars were performed. In addition, for each dental cast, we calculated the absolute difference between the estimate and the measurement per quadrant as an absolute error. The absolute error greater than 1.5 mm was considered to be a clinical problem.12 We also tested the accuracy of our prediction method using control subjects (10 males and 13 females; the conditions of these subjects were the same as those described above).

Statistical analysis was performed using statistical analysis software (SPSS v17.0, SPSS Inc, Chicago, Ill). The significance of coefficients and mean differences were tested at the α  =  .05 level.

RESULTS

There were no significant intraexaminer errors (P > .05). The mean absolute value of the difference between the two measurements was 0.21 mm.

The mean mesiodistal crown diameters of the teeth—other than those of the upper central incisors and the lower central and lateral incisors—differed between the female and male subject groups (Table 1). Standard deviations (SDs) and coefficients of variation (CVs, defined as the ratio of the SD to the mean) for the male subject group were significantly smaller (except for in the case of the upper and lower second premolars) than those for the female subject group (P < .05).

Table 1 Comparisons of Mean Differences in Mesiodistal Crown Diameters (mm) Between the Male and Female Subjects Groups and Between Those Two Groups and Corresponding Japanese Normative Data¹⁸

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Pearson's correlation coefficients between each independent variable and dependent variable are shown in Table 2. In the male subject group, there were statistically significant correlations between central incisor and lateral incisor widths in the maxilla (r  =  0.673) and in the mandible (r  =  0.755), and in the female subject group, there were statistically significant correlations between the central incisor and the lateral incisor widths for the mandible (r  =  0.656). Stronger correlations between each independent variable and dependent variable were found in the male subject group than in the female subject group.

Table 2 Pearson's Correlation Coefficients (r) Between Each Independent Variable and Dependent Variable

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The regression equations for estimating the sum of the mesiodistal crown widths of the unerupted canines and premolars, and their corresponding adjusted R² values, as determined by stepwise multiple regression analysis,3 were calculated. The regression equations derived in this study for predicting the mesiodistal crown widths of unerupted permanent canines and premolars were as follows: For the male patients,

For the female patients,

where Ŷ equals the estimated sum of mesiodistal crown widths of the unerupted permanent canines and premolars in millimeters.

The best combinations of independent variables for predicting the sum of the unerupted permanent canines and premolars were obtained by U1, U2, and U6 for the maxilla and by L1, L2, and L6 for the mandible in the male subject group and by U1, U6, and UIMD for the maxilla and by L1, L2, L6, and LBAL for the mandible in the female subject group. The adjusted R² values were 0.62 for the maxilla and 0.69 for the mandible in the male subject group, and R² values were 0.43 for the maxilla and 0.43 for the mandible in the female subject group. The female subject group exhibited significantly lower R² values than the male subject group.

Pearson's correlation coefficients between the measured values and the estimated values determined for the sum of the mesiodistal crown diameters of the canines and premolars and the statistical comparisons between the male and female subject groups and between the upper and lower dental arches in each subject group are shown in Table 3. Significant differences between the correlation coefficients calculated for the upper and the lower dentitions were not found in either the male or female subject groups. For the male subjects, stronger correlations were found between the measured values and the estimated values in the lower dental arch than were found for the female subjects (P < .001).

Table 3 Pearson's Correlation Coefficients Between Measured Values and Estimated Values That Were Determined for the Mesiodistal Crown Diameters of Canines and Premolars and Their Statistical Comparisons Between the Male and Female Subject Groups and Between the Upper and Lower Dental Arches in Each Subject Group

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Table 4 shows the proportions of difference between the measured and estimated sums of mesiodistal crown widths of canines and premolars. The multiple regression models established in the present study were found to estimate the sum of widths of the permanent canines and premolars within ±1.5 mm 92.1% of the time in the maxilla and 96.0% of the time in the mandible in the male subject; and in the female subjects, the models estimated the sum of widths 92.9% of the time in the maxilla and 97.1% of the time in the mandible. Furthermore, the differences between the measured and estimated sums of mesiodistal crown widths of canines and premolars calculated for the control group were found to be within ±1.5 mm in all subjects.

Table 4 Distribution of Proportions of Estimation Errors as Calculated by the Differences Between the Measured Values and the Estimated Values of the Sums of the Canine and Premolar Widths

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DISCUSSION

Because prediction models are generally applied to patients in the mixed dentition stage to estimate whether sufficient space can be attained in the permanent dentition for spontaneous tooth alignment, in our judgment, evaluating those subjects with obvious tooth crowding, rather than those subjects with normal occlusion, would be more useful for developing prediction models that can be generally applied to patients in the mixed dentition stage. Previous reports16,17 have documented that the mesiodistal diameters of clinical tooth crowns in subjects with crowding are greater than those of subjects who exhibit normal occlusion. Accordingly, we chose subjects who had been diagnosed as exhibiting crowding of teeth with a severity greater than 3 mm in terms of the irregularity index.15 The mesiodistal diameters of clinical tooth crowns, except for the upper and lower first molars, were found to be greater than those reported18 previously for individuals with normal occlusion (Table 1).

We applied the combination of variables employed for white subjects by Tanaka and Johnston2 to our sample of Japanese subjects and obtained an R² of 0.55 for the maxilla and of 0.60 for the mandible in the male subject group and an R² of 0.15 for the maxilla and of 0.29 for the mandible in the female subject group. We acknowledge the ease of practical use of the prediction model of Tanaka and Johnston, but the inclusion of some changes in tooth sizes and skeletal jaw-base size in our current models was found to have improved prediction efficiency, especially for the Japanese female subject group. In this study, we found the greater determination coefficients in female subjects when we added the skeletal jaw-base size (UIMD for maxilla; LBAL for mandible) as an independent variable to the regression equations, whereas we found high prediction accuracy in the male subjects without the skeletal jaw-base size factors.

By using our new predicting model, the greater determination coefficients (R²) for the male subject group, when compared with those for the female subject group, were observed. This result agrees with the data reported by Fränkel and Benz,19 Yuen et al.20 and Melgaço et al.,8 but it differs from the results of Altherr et al.9 (Table 5). The disagreement with our results may be due to the difference in the sample sizes employed.

The weaker correlations between each independent variable and dependent variable in the female subject group, as shown in Table 2, seem to have caused smaller determination coefficients in the regression equation. The sexual dimorphism in predicting tooth size may be explained by a previous study,21 which reported that the Y chromosome affects both dentin and enamel growth and, finally, may affect tooth crown size, while the X chromosome affects only enamel growth. In other words, it is likely that in the female subjects, the formation of the canines and premolars was little affected by heredity but strongly affected by environmental factors, such as a periradicular infection of a primary tooth and an infection associated with chemicals.22

Strong correlations, however, were found between the measured values and the estimated values for the canines and premolars that were calculated for the upper and lower dentitions in the male and female subject groups (Table 3). Additionally, the results of the present study exhibited higher accuracy of prediction compared with the previous studies (Tables 4 and 5). In the present study, more than 92% of the individuals in both the male and female subject groups showed estimation errors within ±1.5 mm per quadrant, regardless of the difference in R² values between the two sexes. In addition, the accuracy of prediction using our method was found to be high in control subjects. We considered that estimation errors of less than ±1.5 mm might not affect the decision for extraction or nonextraction of teeth in the permanent dentition. Thus, we concluded that the current prediction models are clinically useful for supporting proper diagnosis of orthodontic patients in the mixed dentition stage, who are anticipated to exhibit potential space problems in the permanent dentition.

Table 5 Comparison of Determination Coefficients (R²) Between the Sexes Documented in the Present and Previous Studies

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CONCLUSIONS

• We found higher accuracy in predicting the sum of mesiodistal tooth crown widths of unerupted permanent canines and premolars in the male subject group than in the female subject group.

• The best combination of independent variables for prediction was found to differ between sexes. Not only the dental tooth size factors but also the skeletal jaw-base size factors were employed in the female subjects, whereas only the dental tooth size factors were employed in the male subjects.

• Despite the sex differences in prediction accuracy, our prediction models achieved practical accuracy with errors of less than ±1.5 mm in both male and female subjects.