The applicability of the Tanaka and Johnston analysis in a contemporary Western Australian population

The mixed dentition period is a critical phase for the prevention or interception of a developing malocclusion. Treating dental irregularities during this active growth phase has benefits related to guiding the occlusion, removing aetiological factors, or the management of eruption anomalies.¹ A mixed dentition space analysis (MDSA) is a valued supplementary procedure which may be conducted during the dental developmental period after the eruption of the permanent first molars and four mandibular incisors.^2,3 The analysis is a helpful diagnostic tool to determine tooth size and arch length discrepancies before eruption⁴ by predicting the sum of the mesiodistal dimensions (MD) of the permanent canine and first and second premolars in both arches. It helps us to determine the difference between the arch space available and the space required to accommodate succedaneous teeth, and also for the transitional changes that occur during occlusal development.⁵

Various MDSA protocols have been used to identify arch space discrepancies and include (a) radiographic methods, involving periapical and oblique cephalometric radiographs, from which teeth are measured,^6–10 (b) non-radiographic methods using correlation, prediction tables, and regression equations based on measurements of deciduous teeth⁷ or other erupted permanent teeth,^5,6 and (c) a combination of both methods.^7,11,12

Although 45° cephalometric radiographic methods are considered to be more accurate,^13,14 they are less practical since they are more time-consuming, require special equipment and involve increased radiation exposure.^6,15 The Tanaka and Johnston analysis is a simplified protocol which has advantages including ease and simplicity, is relatively non-invasive, and applies to both arches and genders with relatively acceptable accuracy.^16,17 Tanaka and Johnston have developed prediction formulae for the estimation of unerupted tooth sizes, which are based on a linear regression model. The analysis utilises the permanent four mandibular incisors to predict the mesiodistal dimensions of the permanent canines and premolars in both arches. The study sample consisted of 506 North European children, and the formulae were applied to both genders without consideration of sexual dimorphism.⁶

It has been established that tooth size variation exists within different racial populations and ethnic groups.^16,18 In addition, research has shown that sexual dimorphism related to tooth size has generally indicated larger teeth in males.^19,20 As a result, many researchers have raised questions about the applicability of the Tanaka and Johnston analysis in all populations.^8,16,19,21 Additionally, secular trends related to tooth dimensions have been reported to indicate the need for progressive modification of the MDSA for different populations.¹⁶

With the advancements in technology, digital models have been introduced, which facilitate dental measurements and eliminate difficulties that are associated with plaster models.²² Several researchers have assessed the accuracy of digital models compared to plaster models and determined that tooth-width measurements are more accurate and reliable when conducted on digital models.^23–28 In addition, Krieger et al. tested the measurement precision of Invisalign software and reported good accuracy.²⁹

To date, no data has been found to determine the applicability of the Tanaka and Johnston analysis in an Australian sample. Therefore, the present study was conducted to evaluate and validate the use of the Tanaka and Johnston analysis in a West Australian adolescent population using Invisalign software, and to develop a formula to predict the mesiodistal dimensions of permanent canines and premolars for both arches and genders.

Following the protocol of the analysis, the combined MD dimensions of the premolars and canines of the 500 Australian adolescents was calculated based on the MD dimensions of the mandibular incisors.

Table I represents the descriptive statistics for the sum of the maxillary canine-premolar segment (max-CPM), the sum of the mandibular canine-premolars segment (man-CPM), and the sum of the permanent mandibular incisors (I) measured separately for each gender. The difference in the averages between the measured sum of the mandibular incisors and maxillary and mandibular CPM widths was significant and the MD dimensions were found to be higher in males than in females by 0.344 mm, 0.334 mm, and 0.504 mm, respectively.

Using paired t tests, the values for the MD dimensions of the measured maxillary and mandibular canine-premolars segment were compared with those obtained by using the Tanaka and Johnston equation. The results revealed that in males, the average width of the max-CPM estimated (Y₁) from the Tanaka and Johnston analysis was 22.79 ± 0.66 mm, while the actual max-CPM averaged 22.17 ± 1.30 mm. The measured max-CPM dimensions were significantly lower than the estimated width (Y₁) by an average of 0.62 mm which was significant at a P-value of <0.001. Similarly, there was a disparity of 0.45 mm between the actual man-CPM and the estimated man-CPM dimensions (Y₂) and this difference was also found to be significant at a P-value of <0.001. Similarly, in females, both maxillary and mandibular canine and premolar values predicted from the Tanaka and Johnston analysis were higher than the actual values at a P-value of <0.001 (Table II).

The results of the present study showed that the Tanaka and Johnston analysis overestimated the MD dimensions of the maxillary and mandibular CPM in Western Australian adolescents, and so there was a need to develop regression equations specific to the study population.

Table III indicates the regression parameters for the estimation of the MD dimensions of the CPM (Y₁, Y₂) as dependent variables using the sum of the MD dimensions of the mandibular incisors (X) as an independent variable. The correlation coefficient (r) ranged from 0.58 to 0.74 for the maxillary and mandibular arches for both genders, while the coefficient of determination R ² ranged from 0.33 to 0.54. The standard error of the estimate ranged from 0.88 to 1.04 and was found to be lower in the maxillary arch in males.

A linear regression analysis was applied to develop a new regression equation in the form of Y = a+b (x) to be utilised by clinicians in the estimation of the MD dimensions of the maxillary and mandibular CPM in a Western Australian population. The linear regression equations were estimated for males and females separately (Table IV).

A model was proposed for the prediction of the maxillary and mandibular canine-premolar MD dimensions (Y₁, Y₂) for males and females considering the variable measurements (19–29 mm) from the sum of mandibular incisors (X) for the study population (Table V).

During the mixed dentition period, an estimation of the MD dimensions of unerupted permanent canines and premolars has clinical significance in orthodontic diagnosis and treatment planning. An accurate prediction helps the clinician to better treat tooth size and arch length discrepancies.¹⁵ The present investigation was conducted to determine the applicability of the Tanaka and Johnston analysis in Western Australian adolescents. A cross-sectional study was conducted to evaluate the correlation between the mandibular incisors and the posterior tooth arch segments. A younger age sample (13–18 years) was selected to minimise dental wear and loss. An adequate sample size ensured the validity and clinical implications of the prediction equation. The study utilised digital dental imaging technology (Invisalign) to determine the MD dimensions of the teeth. Several researchers have reported more reliable and accurate dental measurements on digital models rather than on plaster models.^24,30 The accuracy of Invisalign measurement software has been previously examined and reported to be good²⁹ but a comparison has not been made with plaster models.

A review of the literature has revealed that the Tanaka and Johnston analysis is a commonly used MDSA noted for its simplicity.³¹ It has been established that facial and dental characteristics show variations between people of different racial and ethnic groups.^16,18 Previous studies have reported accurate predictions using the analysis equation when applied to their populations.^32,33 In the present study, a statistically significant difference was found between the actual MD dimensions and those estimated using the Tanaka and Johnston analysis (P-value <0.001). The Tanaka and Johnston analysis overestimated the MD dimensions of the canine and premolars in both arches in a young Western Australian population. The findings are in agreement with past studies that have reported that an accurate prediction of the MD dimensions of unerupted canine and premolars is not possible with this analysis and have developed prediction equations suitable for their populations.^34–37 However, Lee-Chan et al. and Nourallah et al. reported an underestimation in Asian, American and Syrian populations, respectively.^4,17 Both overestimation and underestimation can influence clinical diagnosis and treatment planning.³⁴

As determined by the present study, sexual dimorphism was evident in the MD dimensions of all permanent teeth with males shown to have larger teeth than females. The results revealed a statistically significant difference in the combined sum of the MD dimensions of the man-CPM and the mandibular incisors between both genders with males having larger teeth (<0.001, 0.003). However, a borderline significance was observed in the MD dimensions of the max-CPM estimation between both males and females (0.006). This sexual dimorphism had been previously reported.^19,20,36 The Tanaka and Johnston prediction equation was developed for both genders combined. Therefore, following other studies, a separate prediction equation for males and females was essential when carrying out a MDSA.^16,35–37

Carey (1949) stated that a significant linear association existed between the sum of the MD dimensions of the mandibular incisors and the sum of the permanent canine and premolars.³⁸ A multiple linear regression analysis has shown that the MD dimensions of the permanent mandibular incisors are the best predictors of the sum of permanent unerupted canine and premolars in both arches.^39,40 The mandibular incisors are teeth which erupt early in the oral cavity during the mixed dentition period.³⁷

The regression parameters of the present study were compared with other studies and are shown in Table VI. In the current study, the correlation coefficient between the sum of the MD dimensions of the mandibular incisors and the maxillary and mandibular canine and premolars ranged from 0.58 to 0.74. Therefore, (r) was found above 0.50 for both arches and genders which indicates that the modified regression equations may be confidently utilised in clinical practice. The correlation coefficient (r) of the present study was found to be lower than that of African Americans²¹, Hong Kong Chinese,⁴¹ and Turkish³⁷ populations, but higher than in Indonesian³⁵ and Thai¹⁹ populations. The coefficient of determination (R ²) value indicates the predictive accuracy of the regression equation. R ² was found to be higher in Hong Kong Chinese⁴¹ and Turkish⁴⁰ populations compared to the present study (0.34–0.54), whereas a lower R ² was reported in the Indonesian¹² and Thai²⁴ populations. A Standard Error of Estimate (SEE) represents the error used in the prediction equation. In the present study, SEE ranged from 0.88 to 1.04 and was found to be relatively higher than previous studies.^{6,16,19,31,35} while comparable to other studies.^21,29 However, these differences were very small and likely did not have a clinical implication.

In contemporary orthodontics, an increasing number of patients are seeking early treatment which shows a rising awareness of a developing malocclusion.⁴² An accurate arch space prediction is therefore critically important to determine dental and occlusal guidance and determine the possible need for orthodontic intervention.¹ The present study affirms that the Tanaka and Johnston analysis as a MDSA is not suitable for application to Western Australian adolescents. Although the majority of the sample size was predominately female, separate regression equations were developed for each gender and should be used advisedly. The newly proposed equation and table should be considered more accurate and specific to the population and may be applied to predict the MD dimensions of unerupted canines and premolars when all permanent mandibular incisors have erupted. The limitations of the study include the retrospective data that was used as participants could not be randomly selected to obtain digital images for research purposes. In addition, the sample of Western Australian adolescents came from a variety of racial and ethnic backgrounds. This was a large sample, however, and more representative of the racial and ethnic composition of the larger Australian population. It is a limitation of the study that the results will not apply to all individuals, but at a population level, the generated equations would be more applicable than those developed by Tanaka and Johnson.