

ORIGINAL ARTICLE 



Year : 2013  Volume
: 31
 Issue : 3  Page : 135140 

Applicability of regression equation using widths of mandibular permanent first molars and incisors as a predictor of widths of mandibular canines and premolars in contemporary Indian population
Shalin Shah, Vijay Bhaskar, Karthik Venkataraghvan, Prashant Choudhary, Ganesh Mahadevan, Krishna Trivedi
Department of Pedodontics and Preventive Dentistry, College of Dental Sciences and Research Centre, Ahmedabad, India
Date of Web Publication  11Sep2013 
Correspondence Address: Shalin Shah A/ 7 Krutika Apts, Nr. CN Vidyalaya, Ambawadi, Ahmedabad India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09704388.117962
Abstract   
Background: Predicting the size of unerupted teeth during the mixed dentition period is a critical factor in managing the developing occlusion. Different studies found that the combined width of only the four mandibular permanent incisors is not a good predictor of the sum of unerupted mandibular permanent canines and premolars (SPCP). In 2007, Melgaço et al. developed a new method for SPCP by measuring the sum of the mandibular first permanent molars and four mandibular permanent incisors (SMI). Aim: It was aimed to evaluate the accuracy of this new method in comparison with Moyers' mixed dentition analysis table in contemporary Indian population. Settings and Design: Sixty boys and 60 girls from Gandhinagar district (age ranged from 12 to 14 years) were included. Materials and Methods: The mesiodistal crown widths of all fully erupted teeth were measured with digital vernier callipers and the odontometric values obtained were then subjected to statistical and linear regression analysis. Results: Student's unpaired ttest gave statistically significant difference between the original values of teeth and the values obtained by Melgaço's prediction equation as well as Moyers' mixed dentition analysis table (P < 0.001). High values of correlation (r = 0.77) and determination coefficients (r^{2} = 0.59) were found while considering Melgaço's method. Also, no statistically significant difference was found between the tooth sizes of males and females. Conclusion: From this study, it can be evaluated that Melgaço's method gives better prediction and a simplified equation Y = 0.925X can be suggested for the present population.
Keywords: Contemporary Indian population, mixed dentition analysis, simple linear regression
How to cite this article: Shah S, Bhaskar V, Venkataraghvan K, Choudhary P, Mahadevan G, Trivedi K. Applicability of regression equation using widths of mandibular permanent first molars and incisors as a predictor of widths of mandibular canines and premolars in contemporary Indian population. J Indian Soc Pedod Prev Dent 2013;31:13540 
How to cite this URL: Shah S, Bhaskar V, Venkataraghvan K, Choudhary P, Mahadevan G, Trivedi K. Applicability of regression equation using widths of mandibular permanent first molars and incisors as a predictor of widths of mandibular canines and premolars in contemporary Indian population. J Indian Soc Pedod Prev Dent [serial online] 2013 [cited 2019 Jun 18];31:13540. Available from: http://www.jisppd.com/text.asp?2013/31/3/135/117962 
Introduction   
The first attempts to estimate tooth mesiodistal widths were made by Black 1897, who proposed tables based on average widths. ^{[1]} Later, periapical radiographs were used to determine unerupted permanent canines and premolars sizes. Because this method tended to overestimate tooth widths, ^{[2]} a mathematical proportion was proposed to compensate for image enlargement. ^{[3]} Today, the methods of mixed dentition analysis based on 45° cephalometric radiographs seem to be the most precise, ^{[4],[5]} but are time consuming and require sophisticated equipment. ^{[6],[7]} To avoid these inconveniences, the correlation statistical methods such as prediction tables and regression equations were proposed by many authors and are frequently applied. ^{[8],[9],[10]}
Carey reported the existence of a significant linear association between the sum of the lower permanent incisors and the sum of the unerupted mandibular permanent canines and premolars (SPCP) in 1946. ^{[11]} Since then, several simple linear regression equations have been proposed for populations of different ethnic origins. ^{[8],[9],[12],[13],[14],[15]} The Moyers' mixed dentition analysis table is the globally used method to estimate the mesiodistal crown width of the unerupted teeth.
Some of the recent studies have reported that only the use of the sum of lower permanent incisors is not the best predictor. ^{[16],[17],[18]} Following these, in 2007, Melgaço found high values of correlation and determination coefficients when the mesiodistal widths of the mandibular first permanent molars were added to those of the four mandibular permanent incisors. ^{[19]}
Melgaço's ^{[19]} prediction equation and Moyers' mixed dentition analysis table were based on Brazilian population and American White population, respectively. So, the accuracy of these methods is questionable when applied to a population of different race, ethnic origin, or in different geographic locations.
Thus, a study was formulated to evaluate the applicability of the Melgaço's prediction equation ^{[19]} in comparison with Moyers' mixed dentition analysis table for prediction of SPCP in contemporary Indian Population.
Materials and Methods   
Around 578 children in the age group of 1214 years from a government funded school in a rural area of Gandhinagar, Gujarat were screened initially. From the pool of 578 children, 439 consented to participate in the study by means of informed consent letters obtained from the subjects' parents. Out of them, only 259 children fulfilled the selection criteria mentioned below. After obtaining ethical clearance from the ethical committee of the Ahmedabad Dental College college and consulting the statistician, out of 259 children, a sample size of 120 (60 boys and 60 girls) was selected with the children fulfilling the following criteria:
 All permanent teeth (with the exception of second and third molars) should be present and they should be fully erupted in both the maxillary and the mandibular arches.
 No congenital craniofacial anomalies or previous history of orthodontic treatment should be present.
 Presence of intact dentition with no proximal caries, restorations, or agerelated attrition.
 All subjects had a similar ethnic background (children are from three to four Gujarati cast).
Dental impressions of the selected children were taken with irreversible hydrocolloid alginate impression material (Tropicalgin; Zhermack, Badia polesine, Italy) and immediately poured with dental stone (Goldstone Type III; Asian Chemicals, Rajkot, India) to avoid any dimensional changes.
The mesiodistal dimensions of the mandibular permanent central and lateral incisors, permanent canines, the first and second premolars, and permanent first molars were measured using digital vernier calliper with a resolution of 0.01 mm (Mitutoyo, Kawasaki, Japan).
A standardized method proposed by Moorrees and Reed ^{[20]} was used to measure the mesiodistal crown widths. The greatest mesiodistal crown width of each tooth was measured between its contact points, with the sliding calliper placed parallel to the occlusal and vestibular surfaces. This method was reported to be highly repeatable and accurate for measuring mesiodistal crown widths by Doris et al. ^{[21]}
Values obtained from the right and left posterior segments were combined, so that there would be a combined value for the mandibular canines and premolars. ^{[9],[10],[19]} Measurement reliability was checked according to a method suggested by Lundstrom, where the same investigator measures all casts and then remeasures certain randomly selected casts. The coefficient of test reliability on 24 such randomly selected casts (each fifth cast was selected) was calculated. ^{[22]} R value was more than 0.97, hence the reliability was confirmed.
Results   
Descriptive statistics, including the mean and standard deviation were calculated. Student's unpaired ttest was used to compare the tooth dimensions between male and female subjects [Table 1]. No statistically significant difference was found between the tooth sizes of males and females.
The coefficient of correlation (r) and coefficient of determination (r^{2} ) were calculated to find the correlation between the SPCP and the sum of mandibular incisors (Moyers' method) and the sum of mandibular permanent incisors and permanent first molars (Melgaço's method) [Table 2]. On comparing these values, it was evident that the method given by Melgaço to use the sum of the mandibular first permanent molars and four mandibular permanent incisors (SMI) was a better predictor as compared to Moyers' method of using the sum of permanent mandibular incisors only.
The actual measurements were compared with the values obtained by the Moyers' mixed dentition analysis tables at 75 ^{th} percentile confidence levels and from Melgaço's prediction equation. Student's ttest was used to compare the actual and predicted values [Figure 1]. Clear statistically significant differences (P < 0.001) were found between the original values and the values obtained by the abovementioned methods.  Table 1: Mean range and standard deviation for various tooth groups in different groups of subjects
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 Table 2: Coefficient of correlation (r), regression constants (a, b), and coefficient of determination (r^{2}) for various tooth groups in different groups of subjects
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 Figure 1: Comparison of original tooth widths with those obtained by 75^{th} percentile of Moyers' prediction table and formula given by Melgaço
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Since none of the abovementioned methods was completely applicable for the present population, a new Simple Linear Regression Equation [SLRE] that can be applicable for the present population to predict their SPCP was obtained, which was as follows:
Male: Y = 10.417 + 0.705X Female: Y = 9.802 + 0.725X Both: Y = 10.692 + 0.702X
In the above equations, Y (dependent variable) equals the predicted sum of the mesiodistal widths (in millimetres) of the mandibular permanent canines and premolars on both sides and X (independent variable) equals the sum of the mesiodistal width (in millimetres) of the four mandibular permanent incisors plus the mesiodistal widths of the two mandibular first permanent molars on both sides. The values of the constants a and b were obtained for the present population.
Validation of the proposed equation was done through evaluation of its prediction capability for the SPCP in the validation sample (50 males and 50 females). For this, SPCP were estimated by using the proposed equation and then compared with the actual SPCP. No statistically significant difference was found between the original values of SPCP and the values obtained from the new equation [Figure 2].  Figure 2: Comparison of original tooth widths with those obtained by new SLRE formulated in this study
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Discussion   
Of all the different mixed dentition analysis methods reported in the literature (regression equations, radiographic methods, or combination of both), the regression equations based on measurements from the already erupted permanent teeth in the early mixed dentition are the most widely used. ^{[18]} Moyers' mixed dentition analysis tables and Melgaço's prediction equation were given for American White population and Brazilian population, respectively. Since it is necessary to check their applicability on different populations, the present study was planned to evaluate their applicability in the contemporary Indian population.
The sample representation of this study based on the odontometric data of the chosen sample is acceptable due to the good sample size and uniform ethnicity of the selected sample. In addition to racial differences of the tooth size, sexual dimorphism has been reported by various authors, ^{[19]} but in this study, no statistically significant difference between male and female tooth widths was found, as reported by some other authors. ^{[16],[22],[23],[24]}
The size of the teeth is related to genetics (e.g. gender and ethnicity) and environment. Racial and genderspecific mixed dentition space analyses require revision or validation once for every generation (approximately 30 years) because of the changing trends in malocclusion and tooth size. ^{[21],[25],[26]}
The accurate width of an unerupted tooth is important for the correct diagnosis of a case. Neither overestimation nor underestimation of the tooth widths is acceptable, and they could lead to erroneous treatment planning. For the present sample, the Moyer's mixed dentition analysis and Melgaço's prediction equation overestimated the tooth dimension. It could be clearly evaluated from [Figure 1] that there is a statistically significant difference between the original widths and the predicted values, which will lead to faulty treatment plans like extraction of tooth. Similar results were found by Durgekar and Naik ^{[27]} at Belgaum where Moyers' mixed dentition analysis tables overestimated the tooth size, while in a study by Philip et al., it underestimated the tooth size in Punjabi children. ^{[28]}
This overestimation or underestimation by Moyer's mixed dentition analysis when applied to different populations prompted to make new probability tables for different populations by different authors like Priya and Munshi ^{[29]} for South Indian, Schirmer and Wiltshire ^{[30]} for Black South African, and AlKhadra ^{[14]} for Saudi Arabian populations. But no published studies have been reported so far checking the applicability of Melgaço's prediction equation in the contemporary Indian population. Values obtained from the present study show the need of a new prediction equation for the present population. To predict SPCP based on the values of SMI, the following linear regression equation was used:
Y = a + bX,
where Y (dependent variable) equals the predicted sum of the mesiodistal widths (in millimetres) of the mandibular permanent canines and premolars on both sides and X (independent variable) equals the sum of the mesiodistal width (in millimetres) of the four mandibular permanent incisors plus the mesiodistal widths of the two mandibular first permanent molars on both sides. The values of constants a and b are indicated below:
Male: Y = 10.417 + 0.705X Female: Y = 9.802 + 0.725X Both: Y = 10.692 + 0.702X
As mentioned earlier, no statistically significant difference was found between the tooth sizes of males and females, hence a combined equation was proposed that can be applicable for the present population.
The correlation coefficient (r) obtained in this study is higher than that obtained in other studies where only four mandibular incisors were used as predictor teeth ^{[9],[12],[27],[28]} and is almost similar to the one obtained by Melgaço ^{[19]} (with the use of SMI) [Table 3]. This relatively consistent correlation of 0.70.8 suggests that the SMI is a better predictor of SPCP for the present population. It might mean that 7080% of the polygenes that determine tooth size are shared between the mandibular incisors and molars and the canines and the premolars. ^{[9]} This common genetic code gives theoretical justification for the estimation of unerupted canine and premolar widths based on the widths of already erupted mandibular permanent incisors and first permanent molars, even though these teeth belong to different morphologic classes. As some recent studies reported that using only four mandibular permanent incisors does not give the best prediction, ^{[16],[17],[18],[19]} involving the mandibular permanent molars will give better prediction.
The SLRE obtained through the present population also indicates the same. Similar to the use of mandibular incisors, the use of the first permanent molars has several advantages. They erupt early in the mixed dentition, are easily measured, and show little variability in size. ^{[8]} Moreover, they are the first permanent teeth to erupt in the oral cavity and the relationship of maxillary and mandibular first permanent molars provides an early indication of the developing permanent occlusion. ^{[31]}
Coefficients of determination (r^{2} ), which indicate the predictive accuracy of the regression equations, were between 0.50 and 0.68 for the canine  premolar segments [Table 3]. This means that 5068% of the total variances in canine  premolar widths are accounted for by knowing the SMI. ^{[9]} This value obtained is higher than those obtained by other studies ^{[9],[12],[27],[28]} and close to that obtained in Melgaço's study. ^{[19]} Comparison of coefficient of determinations in different studies is shown in [Table 3]. These higher values indicate the applicability of this proposed SLRE to the present representative sample of contemporary Indian children.
The proposed SLRE in this study is difficult to memorize and requires a tedious job of complicated calculations. According to Melgaço, a good nonradiographic prediction method must be precise, simple, practical, and specific for the population from which it was developed. ^{[19]} So, simple regression equation can be used in which value of the linear regression equation coefficient a would be zero and the value of b would be around 0.92. The new equation is as follows:
Both: Y = 0.925X,
where Y is the sum of the mesiodistal widths of the mandibular permanent canines and premolars in millimetres (both sides) and X is the sum of the mesiodistal widths of the mandibular first permanent molars and permanent incisors in millimetres (both sides).
The ideal prediction method should determine no difference between the predicted and actual widths of permanent canines and premolars. The standard deviation of the difference should be as small as possible. The present equation when applied on a fresh validation sample gave high degree of accuracy between the predicted and actual widths. The values of the differences between the predicted and actual tooth widths and standard deviations found in this study are among the smallest found among radiographic and nonradiographic methods. ^{[17],[18],[23],[32],[33],[34]}
From the abovementioned discussion, it is clear that the Melgaço's method (use of SMI) is a better predictor during mixed dentition stage. The new mixed dentition prediction equation developed in this study makes the analysis more accurate in the present population and Y = 0.925X can aid in the estimation of SPCP. Based on the encouraging results obtained, a further study with a larger sample size is being undertaken and, if possible, the values for maxillary as well as mandibular teeth would be obtained.
The present equation should be applied on other populations to check its applicability; if any difference is found, then different formulations should be made for different populations.
Conclusion   
 Neither Moyers' mixed dentition analysis tables nor Melgaço's prediction equation was completely accurate when applied to the present contemporary Indian population.
 Use of sum of the mandibular first permanent molars and four mandibular permanent incisors is a good predictor for the sum of the unerupted mandibular permanent canines and premolars.
 A simplified equation, Y = 0.925X, can be applied to the present Gujarati population without sexual dimorphism. Still further studies are required.
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[Figure 1], [Figure 2]
[Table 1], [Table 2], [Table 3]
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