Prediction of the mesiodistal width of unerupted permanent canines and premolars: A statistical approach

Introduction

Prediction of the mesiodistal width of unerupted permanent canines and premolars is of major interest for orthodontic diagnosis and treatment planning.

Methods

To improve the accuracy of the prediction, we looked for the best combination of independent variables with multiple linear regression.

Results

The most accurate prediction was obtained for the combination of the mandibular right first molar and lateral incisor, and the maxillary left central incisor. Adding to the regression equation 1 erupted canine or premolar improved the accuracy of the prediction considerably. Because of the variable character of the eruption sequence during the second transitional period, a separate regression model for every canine or premolar was necessary. The precision of our new method and other methods from the literature was tested in a separate study group.

Conclusions

The results of this study show that our prediction method of the mesiodistal crown diameters of unerupted canines and premolars during the dental transition is accurate. A computer program was developed for user-friendly clinical application.

The aim of any mixed dentition analysis is to predict as accurately as possible the space required for the alignment of the canines and the premolars. Because the space available between the lateral incisor and the first permanent molar is limited, it is important to have a precise estimate of the space that will be needed for the canines and premolars that will erupt in this segment. Thus, space analysis has 2 components: space available and space required. Although space available is easily measured on plaster casts, problems arise with the prediction of the mesiodistal crown diameters of unerupted canines and premolars.

The mesiodistal crown diameters of unerupted canines and premolars can be predicted by several methods. The statistical method is based on the correlations between the crown diameters of the teeth. The radiologic method is based on the measurement of the unerupted teeth on radiographs. There are also combined methods that use the advantages of both methods to improve the precision. It has been shown that statistical methods based on multiple linear regression yield the same precision as radiologic methods and notably without additional radiographic images for the patient.

The purposes of this study were to develop an accurate method for estimating the widths of unerupted canines and premolars and to evaluate the accuracy of the various prediction methods.

Material and methods

Plaster casts from orthodontically treated patients (158 male, 162 female) were selected from the files of the Department of Orthodontics of the University of Marburg in Germany.The selection criteria were all 28 teeth fully erupted; no extractions and no stripping; no caries, trauma, approximal restorations, or tooth defects; well-distinguishable contact points; no anomalies in tooth form, number, and structure; and mesial and distal contact points of all teeth accessible for sliding calipers.

The casts were randomly divided in 2 groups: 1 group of 223 patients (109 male, 114 female) and another group of 97 patients (49 male, 48 female). The larger group was used to develop a new prediction method (the method group). All methods were tested in the smaller group (the study group).

The mesiodistal crown diameters of the 28 permanent teeth—central incisor to second molar—were measured on all casts with a digital sliding caliper at the contact point level to obtain the greatest tooth width. The error of measurement was calculated with Dahlberg’s formula. For that, 25 casts were randomly selected, and all measurements were repeated 2 weeks later by the same person (A.B.).

The method for estimating the widths of unerupted canines and premolars was developed on the basis of multiple linear regression equations, by using the method group of 223 patients. The precision of this new prediction method and those from the literature was evaluated in the study group of 97 patients.

We developed an accurate method for estimating the widths of unerupted canines and premolars in the intertransitional period. The best combination of independent variables was determined with multiple linear regression equations, by using the casts from the method group. First, the minimum number of independent variables (eg, tooth width) required for an optimal estimate was explored. For that goal, regression equations were generated with all 12 independent variables (8 permanent incisors and 4 first permanent molars), and the multiple correlation coefficient (R 2 values, taken as the proportion of explained variance) was computed. One by one, the number of independent variables was reduced, and the R 2 values were compared with the R 2 values obtained with all 12 independent variables. The difference between the R 2 values with the 12 independent variables and the 3 independent variables was small: 0.05 in both jaws. Therefore, a good prognosis and an easy-to-handle method were obtained with 3 independent variables.

Because there were 560 possibilities to combine 3 of 12 variables, the next step was to find the 3 best predictors from the 12 teeth that erupt in the first transitional period (all incisors and first permanent molars). The best combination of 3 variables was selected by generating multiple linear regression equations for every possible combination of independent variables. The R 2 values of the regression analysis were then sorted in descending order so that the best combination rose to the top of the list.

We attempted to improve the accuracy of the prediction method in the second transitional period. During that period, the canines and premolars erupt. We evaluated, therefore, whether the inclusion in the regression equation of 1 more tooth, canine or premolar, would improve the prediction of the remaining unerupted teeth. Regression models for every eruption sequence of these teeth were generated; the R 2 values were evaluated and compared with the R 2 values from the equation without a canine or a premolar.

The expected mesiodistal values (EV) of canines and premolars were calculated by the procedures described in the literature. The accuracy of these 8 prediction methods and our new method was analyzed in the study group by calculating the difference (difference value [DV]) between the EV of the canine and premolars and their real values (RV), according to following formula: DV = EV – RV. RV was defined as the sum of the measured mesiodistal diameter of the canine and premolars, averaged between left and right sides in each jaw. In an ideal case, the 2 values—EV and RV—are identical and the difference between them is zero.

When the EV is larger than the RV, the DV will be positive, and the method will overestimate the sum of widths of the canine and premolars. But, when the EV is smaller than the RV, the DV will be negative, and the method underestimates the sum of the widths of the canine and premolars.

Because there is no ideal method where EV always equals RV, the method with the smallest over- or underprediction is second best. Since a DV over 1.5 mm per side was considered a clinical problem, we chose a DV of 0.75 mm per quadrant as clinically acceptable.

Thus, a DV lower than –0.75 mm was considered underprediction, a DV between –0.75 and 0.75 mm was considered close prediction, and a DV greater than 0.75 mm was considered overprediction.

Results

The averaged measurement error for tooth width in this study was 0.06 mm (maximum, 0.10 mm; minimum, 0.03 mm).

To develop an accurate method for estimating the widths of unerupted canines and premolars in the intertransitional period, we sorted the 10 best combinations of independent variables for the regression equations in descending order for the R 2 values ( Table I ). The mandibular right lateral incisor (tooth 42) and first permanent molar (tooth 46) were the best 2 predictors. The third predictor was chosen between the maxillary right first permanent molar (tooth 16) and left central incisor (tooth 21). We opted for tooth 21. Thus, the best combination of independent variables to predict the sum of the mesiodistal widths of the canines and premolars was obtained by teeth 42, 46, and 21.

Table I
The best predictors of the mesiodistal diameter of canines and premolars
UJ Tooth 1 Tooth 2 Tooth 3 R 2 LJ Tooth 1 Tooth 2 Tooth 3 R 2
1 16 42 46 0.50 1 21 42 46 0.58
2 12 42 46 0.50 2 22 42 46 0.57
3 21 42 46 0.50 3 16 32 46 0.57
4 11 42 46 0.49 4 16 42 46 0.57
5 12 36 42 0.49 5 12 42 46 0.56
6 26 42 46 0.49 6 22 36 42 0.56
7 16 36 42 0.49 7 31 42 46 0.56
8 21 36 42 0.49 8 12 31 36 0.56
9 22 42 46 0.48 9 21 32 46 0.55
10 11 12 46 0.48 10 21 36 42 0.55
UJ, Upper jaw; LJ, lower jaw; teeth 1 , 2 , and 3 , independent variables (predictors 1, 2, and 3).

The regression coefficients and the R 2 values for both jaws are shown in Table II . The close estimated values with this method based on the study group were 67% for the maxilla and 69% for the mandible ( Table III ).

Table II
Constant and regression coefficients
Independent
variable
Jaw Constant A A1
(tooth 21/C/PM)
A2
(tooth 42)
A3
(tooth 46)
R 2
21, 42, 46 UJ 6.56 0.41 0.82 0.60 0.50
LJ 3.35 0.54 0.87 0.71 0.58
Cinf, 42, 46 UJ 5.59 1.34 0.48 0.36 0.63
LJ 2.14 1.71 0.45 0.41 0.76
PM1inf, 42, 46 UJ 4.87 1.59 0.49 0.24 0.71
LJ 1.28 1.99 0.47 0.26 0.86
PM2inf, 42, 46 UJ 5.79 1.24 0.64 0.29 0.63
LJ 1.99 1.85 0.54 0.24 0.85
Csup, 42, 46 UJ 2.63 1.70 0.38 0.31 0.80
LJ 1.22 1.20 0.74 0.55 0.70
PM1sup, 42, 46 UJ 2.99 2.07 0.31 0.20 0.80
LJ 0.79 1.77 0.57 0.41 0.74
PM2sup, 42, 46 UJ 2.94 1.91 0.56 0.22 0.81
LJ 1.03 1.52 0.82 0.45 0.71
R 2 is the proportion of the variance in the values of the dependent variable explained by all independent variables in the equation together.
UJ, Upper jaw; LJ, lower jaw; C, canine; PM, premolar; Cinf, lower canine; PM1inf, first lower premolar; PM2inf, second lower premolar; Csup, upper canine; PM1sup, first upper premolar; PM2sup, second upper premolar.

Table III
Accuracy of the evaluated methods (values of Tränkmann and Raufmann were averaged) on the basis of the study group, sorted by the number of close predicted values
Method Dental arch n Mean
(mm)
SD
(mm)
Range Overpredicted
(%)
Close
predicted (%)
Underpredicted
(%)
Minimum Maximum
Our method Upper 97 +0.34 0.70 −1.27 +1.91 28 67 5
Lower 97 +0.33 0.66 −1.12 +1.87 26 69 5
Bachmann Upper 97 −0.07 0.78 −1.81 +1.69 13 66 23
Lower 97 −0.02 0.76 −1.82 +1.80 16 69 19
Tränkmann and Raufmann Upper 97 −0.07 0.77 −2.04 +1.49 16 64 18
Lower 97 −0.04 0.71 −1.66 +1.70 16 65 15
Miethke Upper 97 +0.79 0.81 −2.52 +1.10 3 52 45
Lower 97 +0.54 0.77 −1.34 +2.16 42 54 4
Moorrees et al Upper 97 +0.59 0.89 −1.64 +2.48 43 51 6
Lower 97 +0.56 0.94 −1.59 +2.76 39 52 9
Moyers (75%) Upper 97 +0.35 0.90 −1.37 +2.63 32 53 15
Lower 97 +0.63 0.83 −1.34 +2.66 45 48 7
Tanaka and
Johnston
Upper 97 +1.08 0.80 −0.82 +3.16 65 34 1
Lower 97 +1.04 0.78 −0.84 +2.81 67 32 1
Berendonk Upper 97 +0.99 0.87 −1.29 +2.83 64 33 3
Lower 97 +1.00 0.83 −1.25 +2.65 65 33 2
Pancherz and Schäffer Upper 97 +1.09 0.94 −0.87 +3.28 61 36 3
Lower 97 +1.57 1.03 −0.54 +4.27 81 19 0
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Apr 14, 2017 | Posted by in Orthodontics | Comments Off on Prediction of the mesiodistal width of unerupted permanent canines and premolars: A statistical approach
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