Investigation of the distribution of samples
Left–right difference in age distribution
The t-test of the difference in age distribution between the bilateral homonymous teeth of boys and girls showed no significant difference (that the lowest p > 0.05) p-value was for stage O (crypt, no calcification) maxillary third molars in girls, and that the p-values for all developmental stages ranged from 0.12 to 1.00. We concluded that there was no significant left–right difference for any developmental stages, so we combined the results for the left and right sides. These combined values were used for all subsequent analyses.
Age distribution in each developmental stage
A cumulative frequency distribution diagram of Crc (crown complete) and Rc (complete root formation) in anterior teeth is shown in Supplementary Fig. 1. The Crc of the lower central incisor of girls showed positive skewness, but the other curves were very close to normal. The distribution also showed that girls tended to be younger than boys. A cumulative frequency distribution diagram of Crc and Rc in premolars is shown in Supplementary Fig. 2. The Rc of the male upper first premolar showed negative skewness, but the other curves were very close to normal. There was no significant difference in the maximum frequency between boys and girls. A cumulative frequency distribution diagram of Crc and Rc in molars is shown in Supplementary Fig. 3. The Crc of the lower first molar showed positive skewness in both sexes, but the curves of the upper first molar and the upper and lower second molars were very close to normal. The Rc of the third molar showed negative skewness in both sexes, indicating that the Crc scatter was large for both sexes. The molar distributions showed that the dental age of girls with only the first molar was lower than that of boys.
Average age of permanent teeth by developmental stage
Central incisor
The dental age by developmental stage of the anterior teeth was calculated (Table 1). The data range for the upper central incisor was Cr3/4 (3/4 crown formation) to Rc. There was no difference in dental age between boys and girls until R1/4 (1/4 root formation), at approximately 6 years of age. After R1/2 (1/2 root formation) at approximately 7 years of age, the dental age of girls was significantly lower than that of boys in this developmental stage. The data range for the lower central incisor was Cr3/4 to Rc (as for the upper); for Crc, R1/2, and R3/4 (3/4 root formation), the dental age of girls was significantly lower than that of boys.
Lateral incisor
The data range for the upper lateral incisor was from Cr1/2 (1/2 crown formation) to Rc. The dental age of girls was significantly lower than that of boys in all developmental stages except Cr1/2 and R1/4. The data range for the lower lateral incisor was from Cr3/4 to Rc. The dental ages of Cr3/4, R1/2, and Rc were significantly lower in girls than in boys.
Canine
The data range for the upper canine was Cr1/2 to Rc. In all developmental stages, the dental age of girls was significantly lower than that of boys. The data range for the lower canine was Cr1/2 to Rc (as for the upper canine). There was no significant difference between boys and girls in Cr1/2, but girls showed significantly earlier growth than boys in all other developmental stages.
First premolar
The dental age by developmental stage of the premolars was calculated (Table 2). The data range for the upper first premolar was from Cco (coalescence of cusps) to Rc. The dental age of girls was significantly lower than that of boys for Cr3/4, R1/4, and R1/2, but there were no sex differences for the other developmental stages. The data range for the lower first premolar was from Cco to Rc (as for the upper first premolar). After Cr1/2 and Crc, at approximately 7 years of age, the dental age of girls was significantly lower than that of boys.
Second premolar
For the upper second premolar, data were available for all developmental stages from O to Rc. The dental age of Cr1/2, Crc, and R3/4 was significantly lower in girls; however, there were no sex differences in the other developmental stages. The data range for the lower second premolar was all developmental stages from O to Rc for girls (as for the upper second premolar), but was Ci (initial calcification) to Rc for boys. The dental ages of Cr3/4, Crc, and R1/4, from approximately 6.5 to 8.5 years of age, were significantly earlier in girls, but no sex differences were observed in the other developmental stages.
First molar
The dental age by developmental stage of the molars was calculated (Table 3). The data range for the upper first molar was from Cr3/4 to Rc. No difference was observed between the sexes until Crc at approximately 4.5 years of age, but girls were significantly younger at after R1/4 at approximately 5 years of age. The data range for the lower first molar was Cr3/4 to Rc for boys (as for the upper first molar), but Crc to Rc for girls. No sex difference was observed in the dental age of R1/2, but the average age of girls was significantly lower in all other developmental stages.
Second molar
For the upper second molar, data were available for all developmental stages from O to Rc. The dental age of Cr3/4 and Crc, from approximately 7 to 8.5 years, was significantly lower in girls, but there were no sex differences in other developmental stages. For the lower second molar, data were also available for all developmental stages from O to Rc. The dental age of girls was significantly lower for Cr3/4 and Crc, at approximately 7 to 8.5 years of age, but there were no sex differences in other developmental stages.
Third molar
The data range for the upper third molar was all developmental stages from O to Rc for boys, but O to R3/4 for girls. Crc, at approximately 14.5 years of age, was significantly earlier in girls, but R1/4, at approximately 16 years of age, was significantly earlier in boys. The data range for the lower third molar was all developmental stages from O to Rc for boys (as for the upper third molar), but O to R1/2 for girls. Crc was significantly earlier in boys. The standard deviation ranged from 0.8 to 2.0 years in boys and from 1.2 to 2.0 years in girls, indicating that the greatest variability in the sample data was for permanent teeth.
Comparison of time required for root formation
The time required for root formation was compared using the interval between Crc and Rc (Table 4). The root formation time was slowest for the canine, with approximately 6 years from Crc to Rc. In boys, the permanent tooth with the fastest root formation rate was the third molar, with approximately 2.5 to 3 years from Crc to Rc. In girls, there were no Rc data for the third molar, so the rate of root formation could not be determined.
Calculation of 50th percentile developmental stage of permanent teeth at each age
Central incisor
The 50th percentile developmental stage of the anterior teeth at each age was calculated (Table 5). The upper central incisor reached Crc at 4 years in both sexes. The upper central incisor reached Ac (apex closed) at 10 years in boys and 9 years in girls. The lower central incisor reached Ac at 8 years in both sexes.
Lateral incisor
The upper lateral incisor passed Crc at 5 to 6 years, and the lower lateral incisor reached Crc at 5 years in boys. The Ac age was 10 years for the upper lateral incisor and 9 years for the lower lateral incisor. In girls, the upper lateral incisor reached Crc at 5 years and the lower lateral incisor reached Crc at 4 years. In contrast, the Ac age was 9 years for both upper and lower lateral incisors.
Canine
The upper canine reached Crc at 6 years in boys. The lower canine in boys and the upper and lower canines in girls reached Crc at 5 years. Ac was reached in the upper and lower canines of both sexes at 13 and 12 years, respectively. In addition, the central incisor, lateral incisor, and canine reached Crc at similar ages, but Ac was delayed in the canine by more than 2 years.
First premolar
The 50th percentile developmental stage of the premolars at each age was calculated (Table 6). The upper and lower first premolars of both sexes reached Crc at 6 years. Ac was reached in the upper and lower first premolars of both sexes at 13 and 12 years, respectively.
Second premolar
In boys, the upper second premolar and lower second premolar reached Crc at 8 and 7 years, respectively. In girls, the upper and lower second premolars reached Crc at 7 years. In girls, Ac was reached in the upper second premolar at 12 years and the lower second premolar at 13 years. In boys, Ac was reached in the upper and lower second premolars at 13 years.
First molar
The 50th percentile developmental stage of the molars at each age was calculated (Table 7). For both sexes, the upper first molar reached Crc at 4 years and the lower first molar at 3 years. In both sexes, the upper and lower first molars reached Ac at 9 years.
Second molar
The upper and lower second molars of both sexes reached Crc at 8 years. Ac was reached in the upper and lower second molars of girls, and the lower second molar of boys, at 14 years. Ac was reached in the upper second molar of boys at 15 years.
Third molar
In boys, the upper third molar reached Crc at 14 years, and the lower third molar passed Crc at 14–15 years. In girls, the upper third molar reached Crc at 16 years and the lower third molar reached Crc at 15 years. In both sexes, less than half of the third molars reached Ac at age 18 years, the upper limit of the target age range.
Reliability of the study model
Correlation between total and variance of developmental scores
Cronbach’s alpha coefficients20 of 0.987 for boys and 0.986 for girls were both above 0.8, which shows high internal consistency in the sample data (Supplementary Table 1). This indicates that the evaluation criteria for the developmental stages of permanent teeth used by the raters in this study were not affected by the passage of time.
Confirmation by different evaluators
The Kendall’s rank correlation coefficient21 for the association between total dental age and chronological age in the test data was τ = 0.805, which is above 0.8, indicating a very strong correlation. This suggested that the method of evaluating the developmental stages of permanent teeth and the data obtained in this study were highly versatile, even when different evaluators were used.
