Eur Arch Paediatr Dent DOI 10.1007/s40368-014-0157-5
ORIGINAL SCIENTIFIC ARTICLE
Effect of intermaxillary tooth-size discrepancy on accuracy of prediction equations for mixed dentition space analysis R. Khanna • R. K. Pandey • S. Tripathi
Received: 10 July 2014 / Accepted: 8 October 2014 European Academy of Paediatric Dentistry 2014
Abstract Aim Correlation-statistical methods are widely used for prediction of size of unerupted permanent canines and premolars in mixed dentition space analysis. The present study was planned to evaluate the effect of selecting dental study casts with no intermaxillary tooth-size discrepancy on the accuracy of predicting mesiodistal widths (MDWS) of permanent canines and premolars. Study design Bolton ratios were calculated for all the screened study dental casts fulfilling the inclusion criteria. Subjects were divided into two groups. Group A: all subjects with no intermaxillary tooth-size discrepancy within ±2 SD (Standard deviation) of the mean values. Group B: increased percentage of subjects with intermaxillary toothsize discrepancy beyond ±2 SD (Standard deviation) of the mean values. Statistics Linear regression equations were established for both maxilla and mandible in both the groups, with different tooth combinations as independent variables. Validation of best possible regression equations was done on an independent set of 40 subjects. The actual and predicted values of MDWS of permanent canines and premolars were compared by paired samples t test in both groups, for both arches.
R. Khanna (&) R. K. Pandey Department of Paediatric and Preventive Dentistry, King George’s Medical University, Lucknow 226003, Uttar Pradesh, India e-mail: [email protected] R. K. Pandey e-mail: [email protected] S. Tripathi Department of Prosthodontics and Crown &Bridge, King George’s Medical University, Lucknow, Uttar Pradesh, India e-mail: [email protected]
Results The accuracy of equations derived from group A was higher than those derived from group B. The difference between actual and predicted values was statistically insignificant in group A and statistically significant in group B. Conclusion The results confirm the accuracy of simple linear regression equations derived from a sample of children with no intermaxillary tooth-size discrepancy. Keywords Bolton ratio Mixed dentition analysis Intermaxillary tooth-size discrepancy
Introduction Diagnosis and treatment planning for ‘tooth size-arch length discrepancy’ (TSALD) during the mixed dentition period of a child are dependent on accurate predictions of mesiodistal widths (MDWS) of unerupted permanent teeth (canines and premolars). Precise predictions help in guiding the developing occlusion of a growing child. Different methods have been reported in the literature for these predictions. The choice of method adopted is based on its accuracy, simplicity, speed and applicability in different situations. The methods used are categorised as: application of middle value (Pancherz and Schaffer 1999); correlation-statistical method (Tanaka and Johnston 1974); radiographic method (Hixon and Oldfather 1958) and combination of correlation-statistical and radiographic methods (de Paula et al. 1995). Amongst these, the correlation-statistical approach are the most widely used owing to their simplicity and ease of use. The correlation-statistical methods are based on the possibility of establishing significant correlation relationships between the sum of MDWS of erupted and unerupted permanent teeth. Both simple linear (Tanaka and Johnston
123
Eur Arch Paediatr Dent
1974) and multiple linear (Bernabe and Flores-Mir 2005) regression models have been reported. Different combinations of permanent teeth with many modifications have been established as best known predictors in these models (Carey 1949; Nourallah et al. 2002; Legovic et al. 2003; Bernabe and Flores-Mir 2005; Boboca and Dibbets 2010). These prediction methods, are not without limitations. First, their applicability in populations of different ethnic origin is questionable. Second, there is emerging evidence of a different school of thought, which states that the prediction equations for size of unerupted permanent canines and premolars (PCPMs) should be derived from a sample of subjects with no intermaxillary tooth-size (Bolton) discrepancy. Bolton (1958) developed two ratios for estimating intermaxillary tooth-size discrepancy by measuring the summed MDWS of the mandibular to the maxillary anterior teeth. Only one reported study by Uysal et al. (2009) has found very high correlation coefficients between the four mandibular permanent incisors and the actual widths of the mandibular PCPMs in Turkish subjects when Bolton tooth-size discrepancy was taken into consideration. They also found extremely low standard errors of estimate and recommended the revision of currently popular prediction methods for various populations on the basis of their observations. In the light of above the present study was completed answer: ‘Whether there should be consideration of Bolton discrepancy in selection of sample subjects, for prediction of sum of MDWS of PCPMs, with the help of linear regression equations?’
Materials and method The patients in the age group of 10–15 years, attending an outpatient Department of Paediatric and Preventive Dentistry, King George’s Medical University, Lucknow, Uttar Pradesh (India), were considered for inclusion in the study. Most of the patients had their ethnic backgrounds traced back to regions within Northern India. Impressions of the maxillary and mandibular dental arches were taken in alginate and poured in dental stone (type III) to obtain good-quality dental study casts. The criteria for inclusion in the study were: no previous orthodontic treatment; fully erupted, complete permanent dentition (excluding second and third permanent molars) devoid of fractures or developmental anomalies of tooth number, size or shape; no clinically visible dental caries, restorations, or attrition in proximal or occlusal surfaces in any of the erupted teeth; consent to participate in the study. Most of the patients were attending the outpatient department in need of routine oral prophylaxis or consultation for correction of minor irregularities in teeth alignment.
123
Measurement of MDWS on all the casts was completed using a digital calliper (Aerospace, China) with an accuracy of 0.01 mm. Study casts with severe crowding/spacing ([2–4 mm), inaccessible proximal contacts for measurement, or impression flaws compromising accuracy of measurements, were excluded from the study. Following the strict inclusion and exclusion criteria, study casts of 305 subjects (mean age: 13.5 ± 1.8 years; 148 males and 157 females) were selected for measurement. The standardised technique proposed by Moorrees et al. (1957) was followed for all the measurements. The measurements were made by the primary investigator. The reliability of measurements was assessed by double-determination method on 20 randomly selected study casts, and the error was calculated with the help of Dahlberg’s formula (Dahlberg 1940). Only eight to ten pairs of study casts were measured in a day to avoid errors due to eye fatigue. The measurement consistency was determined by intraclass correlation coefficient (ICC). Descriptive statistics including means, standard deviations and maximum–minimum values were calculated for the measured tooth MDWS. Students unpaired t test was used to compare the tooth dimensions between males and females. Paired samples t test was used to compare between left and right side measurements. Bolton ratios for each subject (both anterior and posterior) were calculated thereafter. The descriptive statistics for both anterior and posterior Bolton ratio were also determined for the present sample size. A threshold of ±2 SD (Standard deviation) was considered as the criterion for selecting subjects under group A. A total of 272 study casts were finally included in group A. Power analysis (using G 9 Power 3.1.9) indicated that standard deviation of one would be detected with a power of 0.8 for the present sample size of group A. The remaining 33 study casts that exhibited extreme values beyond the ±2 SD were included in group B. The sample size of group B was also made up to a total of 272, by randomly replacing subjects from group A. Therefore, group A exclusively included subjects with no intermaxillary tooth-size discrepancy, while group B had *12 % of subjects exhibiting intermaxillary tooth-size discrepancy. In the mixed dentition period, six pairs of permanent teeth (considering left and right together) are normally present, fully erupted, during the chronologic age period of 7–9 years. All these permanent teeth available can be utilised for prediction of MDWS of PCPMs. The permanent maxillary lateral incisors are excluded due to high incidence of developmental variations in shape and size, leaving only five pairs of teeth available (Table 1). According to the theory of permutation–combination, five variables (considering left and right together) can result in twenty six different combinations (Table 1). The number
Eur Arch Paediatr Dent Table 1 Correlation coefficients for different teeth combinations Combination number
Teeth combinations according to available pairs of teeth : (11,21); (16,26); (31,41); (32,42); (36,46)
Maxillary
Mandibular
C1
46,16,42,41,11,21,31,32,26,36
0.74
0.67
0.71
0.68
C2
46,16,41,11,21,31,26,36
0.71
0.66
0.68
0.64
C3 C4
46,16,42,11,21,32,26,36 16,42,41,11,21,31,32,26
0.68 0.71
0.62 0.68(SEE = 0.92)
0.67 0.68
0.6 0.63
C5
46,16,42,41,31,32,26,36
0.74
0.65
0.73
0.69
C6
46,42,41,11,21,31,32,36
0.74
0.67
0.72
0.7
C7
46,16,42,32,26,36
0.72
0.63
0.71
0.67
C8
46,42,11,21,32,36
0.74
0.66
0.71
0.68
C9
46,16,41,31,26,36
0.7
0.62
0.69
0.64
C10
42,41,11,21,31,32
0.7
0.65
0.66
0.63
C11
16,41,11,21,31,26
0.67
0.65
0.64
0.58
C12
46,16,11,21,26,36
0.68
0.63
0.66
0.61
C13
16,42,11,21,32,26
0.69
0.67
0.67
0.61
C14
46,41,11,21,31,36
0.73
0.65
0.71
0.66
C15
16,42,41,31,32,26
0.71
0.65
0.69
0.64
C16
46,42,41,31,32,36
0.77(SEE = 0.83)
0.64
0.75(SEE = 0.79)
0.72(SEE = 0.83)
C17
46,42,32,36
0.75
0.61
0.73
0.71
C18 C19
46,41,31,36 16,11,21,26
0.74 0.62
0.59 0.61
0.71 0.59
0.68 0.52
C20
42,41,31,32
0.7
0.61
0.65
0.63
C21
16,41,31,26
0.65
0.6
0.63
0.56
C22
16,42,32,26
0.64
0.6
0.68
0.59
C23
46,16,26,36
0.64
0.56
0.64
0.58
C24
46,11,21,36
0.69
0.61
0.65
0.61
C25
41,11,21,31
0.67
0.63
0.61
0.57
C26
42,11,21,32
0.64
0.6
0.62
0.58
Group A
Group B
Group A
Group B
Five pairs of teeth available: (11,21); (16,26); (31,41); (32,42); (36,46) SEE = Standard error of estimate
of combinations for n variables taken k variables at a time is given by the following ratio (Makinson 2008): ½n!=½k! ðn kÞ! The combinations for the five variables available were calculated for values of ‘k’ from 2 to 5, resulting in 26 different combinations. The difference in calculating the number of combinations to that of permutations is the fact that the order of variables is not of concern for any combination. In a permutation, however, different orders of arrangement of the variables result in different sets of permutation. In the present study, the order in which the mdw of different teeth was added was not significant, therefore, calculation of possible combinations was completed. Simple linear regression was computed between MDWS of all 26 combinations of teeth and MDWS of maxillary and mandibular PCPMs for both group A and B. The regression
equations generated were in the standard form of y = a ? bx, where a, b are constants; y is the dependent variable (averaged MDWS of PCPMs of both left and right sides in maxilla/mandible) and x is the predictor or independent variable (sum of right and left side MDWS of different teeth combinations in maxilla/mandible). Correlation coefficients (R) and coefficients of determination (R2) were determined for all the possible teeth combinations in each group in each arch (Table 1). The best predictors were those with highest R and R2. Validity of the best prediction equations from both the groups in each arch was then tested by applying these equations on a random set of 40 subjects each. The level of closeness of prediction was determined by calculating the absolute difference between actual and predicted values and categorising it by the criteria shown in Table 2. The actual and predicted values of MDWS of PCPMs were compared by paired samples t test in both the groups, for both the arches.
123
Eur Arch Paediatr Dent Table 2 Criteria for determining proximity of prediction
Table 4 Comparison of mean MDWS between males and females
Category
Score
Error in prediction (mm)
Mean MDWS (mm)
Close
A
0–0.5
Male
B
0.5–1
Maxillary central incisor
8.76
8.64
0.14*
C
1–1.5
Maxillary lateral incisor
7.18
7.1
0.33*
D
1.5–2
Maxillary canine
8.08
7.84
0.001#
E
[2
Maxillary first premolar
7.35
7.24
0.11*
Maxillary second premolar
6.99
6.89
0.13*
11.05
10.88
Acceptable Poor
The prime objective was to assess whether exclusion/ inclusion of subjects with extreme deviations in Bolton values could affect the accuracy of prediction equations derived from that specific subject group.
Maxillary first molar
Female
0.06*
Mandibular central incisor Mandibular lateral incisor
5.57 6.17
5.527 6.101
0.1* 0.25*
Mandibular canine
7.1
6.88
0.007#
Mandibular first premolar
7.35
7.24
0.11*
Mandibular second premolar
7.4
7.32
0.29*
11.23
10.99
0.003#
Mandibular first molar
Results
P value
* Not significant difference
The mean measurement error for MDWS of all the teeth, as determined by the double-determination method, was found to be 0.182 mm which was well within the clinically acceptable limit. The intraclass correlation coefficient (ICC) was found to be 0.97, indicating good measurement consistency. Descriptive statistics for tooth mesiodistal widths (Table 3) showed no statistically significant differences between measurements from left and right side. The values of predictor variables were, however, combined for both the sides. Gender differences (Table 4) were seen in measurements of some teeth such as permanent maxillary and mandibular canines, and permanent mandibular molars (p \ 0.05). The difference in the means of these teeth ranged from 0.17 to 0.25 mm for each side. Considering the small difference of mean values of tooth MDWS between males and females, common equations were derived. Descriptive statistics for anterior and posterior Bolton ratios are presented in Table 5. The mean value for anterior and posterior Bolton ratio was found to be 78.19 and 90.29, respectively. The subjects were divided into group A and B accordingly. Table 3 Comparison of mesiodistal width tooth measurements from right and left sides of maxillary and mandibular dental arches Mesiodistal width (in mm corrected to two decimal places) Tooth
Right
p value
Left
Maxillary central incisor
8.74
8.72
0.16
Maxillary lateral incisor Maxillary molar
7.14 10.96
7.12 10.96
0.27 0.8
Mandibular central incisor
5.58
5.58
0.92
Mandibular lateral incisor
6.14
6.13
0.65
11.11
11.11
0.63
Mandibular molar
123
# Significant difference
Table 5 Descriptive statistics for Bolton ratios Descriptive statistics
Anterior bolton ratio
Overall bolton ratio
Mean Standard error
78.19 0.25
90.29 0.20
Median
78
91
Mode
78
91
Standard deviation
3.53
2.86
Confidence level (95.0 %)
0.49
0.40
Correlation coefficients (R) and coefficients of determination (R2) between all the teeth combinations and PCPMs for both the groups are presented in Table 1. The best predictor in group A was the sum of four mandibular incisors and mandibular first permanent molar (C16) for both maxilla and mandible. In group B, however, the sum of four mandibular incisors and mandibular first permanent molar (C16) was the combination with highest correlation coefficient for predicting maxillary PCPMs; but in the mandible, the sum of four mandibular incisors and maxillary central incisor with maxillary first permanent molar (C4) was the best predictor combination. The standard errors of estimate (SEE) of these best combinations were also found to be quite low (Table 1). The best derived regression equations for both the arches in both group A and B were: Group A: Maxillary: y = 3.03 ? 0.42 (C16); Mandibular: y = 3.79 ? 0.39 (C16). Group B: Maxillary: y* = 5.59 ? 0.26 (C4); Mandibular: y* = 4.27 ? 0.38 (C16).
Eur Arch Paediatr Dent Table 6 Comparison of actual and predicted values of sum of PCPMs (mm)
*
Not significant difference
# Significant difference
Group A
Group B
Actual sum of PCPMs
Predicted sum of PCPMs
Mean diff
P value
Actual sum of PCPMs
Predicted sum of PCPMs
Mean diff
P value
Maxillary
22.39
22.29
0.1*
0.28
22.39
21.93
0.46#
0.002
Mandibular
21.83
21.68
0.15*
0.48
21.83
21.32
0.51#
0.05
Table 7 Proximity of predictions (%) Maxillary
Mandibular
Group A
Group B
Group A
Group B
0–0.5 mm
23
22
35
32
0.5–1 mm
25
28
22
23
1–1.5 mm
14
10
10
7
1.5–2 mm
20
15
18
13
[2 mm
18
25
15
25
The validity of equations so derived was tested in an independent set of 40 subjects. In group A, there was no statistically significant difference between actual and predicted values of PCPMs for both maxillary and mandibular arches (Table 6). In group B, highly significant difference (p \ 0.01) between actual and predicted values was seen in the maxillary arch and moderately significant difference (p = 0.05) was observed in the mandibular arch (Table 6). The proximity of prediction values to the actual values is shown in Table 7 for both the groups. The total percentage of close and acceptable predictions was observed to be higher for equations derived from group A than group B in both maxillary and mandibular arches. Similarly, the percentage of poor predictions was considerably lower in group A than in group B.
Discussion The measurement error for tooth MDWS was well within the clinically acceptable limits (Abu Alhaija and Qudeimat 2006; Tahere nik et al. 2007) in the present study. The consistency of measurements in the present study was also very high (ICC = 0.95). Common equations for both males and females, derived as the difference in MDWS of their teeth, was minimal (\0.5 mm per arch). Similar considerations were reported by other workers (Nourallah et al. 2002; Martinelli et al. 2005; Shah et al. 2013). Descriptive statistics for Bolton ratio revealed differences from the standard Bolton values (Bolton 1958). Similar variations have been reported for the Indian population (Sharma et al. 2011). The standard of clinical significance used, mostly by previous authors, was a Bolton
discrepancy of ±2 SD (Crosby and Alexander 1989; Johe et al. 2010). Similar considerations were taken in the present study. The combination of radiographic and statistical methods (Hixon and Oldfather 1958; Staley and Hoag 1978; Staley and Kreber 1980) involves additional radiation exposure in the mixed dentition and sophisticated equipment. Therefore non-radiographical correlation-statistical methods for prediction of total MDWS of PCPMs have been preferred in the past (Moyers 1958; Tanaka and Johnston 1974; Bernabe and Flores-Mir 2005; Melgac¸o et al. 2007; Al-Bitar et al. 2008). It has also been suggested that multiple linear regression may result in correlation coefficients not high enough to ensure a good correlation, (Parades et al. 2006) although many investigators have contradicted this view (Legovic et al. 2003; Memon and Fida 2012). In the present study, however, a simple linear regression owing to ease of use and simplicity was preferred. The independent/predictor variable in the simple linear regression equations derived, for predicting total MDWS of PCPMs, has been found to vary in different models established so far. The sum of MDWS of four permanent mandibular incisors has been suggested as the best predictor in this regard by many authors (Moyers 1958; Carey 1949; Huckaba 1964; Tanaka and Johnston 1974). Others have contradicted this view and have found other combinations of teeth as better predictors (Nourallah et al. 2002; Legovic et al. 2003; Bernabe and Flores-Mir 2005; Parades et al. 2006; Melgac¸o et al. 2007). Therefore, in the present study simple linear regression models for all possible teeth combinations were used as predictor variables and to derive the best predictors in each group. The sum of four mandibular incisors and mandibular first permanent molars has been used as the independent predictor variable in various studies, as established for the mandibular arch in the present study (Melgac¸o et al. 2007; Shah et al. 2013). The combination of the sum of four mandibular incisors, maxillary central incisor with maxillary first permanent molar, derived as the best predictor for the maxillary arch in the present study, has however been never reported. The highest values of correlation coefficients in both the groups for both the arches were found to be comparable and also superior to many of the previous studies
123
Eur Arch Paediatr Dent
(Nourallah et al. 2002; Abu Alhaija and Qudeimat 2006; Tahere nik et al. 2007; Al-Bitar et al. 2008; Memon and Fida 2012; Shah et al. 2013) although with different predictor variables. The standard errors of estimate were also low and comparable to that in other studies (Nourallah et al. 2002; Abu Alhaija and Qudeimat 2006; Al-Bitar et al. 2008). These values were lower in group A than in group B, indicating better accuracy of equations derived from group A. The correlation coefficients determined while deriving equations from group A were also higher than in group B, further emphasising their accuracy. These findings suggest that the correlation between the predicted and predictor variable was stronger when established from a sample with no intermaxillary discrepancy. When the percentage of subjects with intermaxillary discrepancy was increased, the correlation became weaker. The comparison was further tested on an independent set of individuals with no information of Bolton discrepancy. It was seen that the percentage of poor predictions was considerably lower in group A than in group B. Therefore, the validity test also confirmed the accuracy of simple linear regression equations derived from group A. A special point of interest here is that the clinical significance of the difference between actual and predicted values is still not supported by some substantial evidence. In the present study, the criteria used by other investigators were chosen (Parades et al. 2006; Altherra et al. 2007; Durgekar and Naik 2009) where a total of 2 mm of discrepancy per arch is the maximal permissible limit, above which the prediction has been considered to be not acceptable or poor. This flexibility allows a compensation for the variations in growth taking place during the transitional period of the child’s dentition. The pattern of correlation coefficients obtained for different tooth combinations in both groups is also suggestive of the importance of sample selection. The subjects with Bolton values outside the set threshold will have significant deviations from the normal mesiodistal dimension of teeth for that population. This deviation can exist in the maxilla or mandible or both and would affect the accuracy of the equations derived, as ‘mesiodistal dimension of teeth’ here is the dependent variable. In the maxilla, the PCPMs were strongly correlated to mandibular teeth combinations (C16, C17) in group A. In group B (with increased percentage of subjects with intermaxillary discrepancy beyond ±2 SD of the mean values), the trend was different in respect that, the correlation of maxillary PCPMs with exclusive mandibular teeth (C16) was very weak. The mandibular PCPMs in both the groups were better correlated with mandibular teeth combinations (C16, C17). The combinations with exclusively maxillary teeth (C19) had weak correlations with mandibular PCPMs in both the groups. Addition of the
123
maxillary teeth to mandibular teeth (C5, C6) also weakened the correlation in both the groups for mandibular PCPMs. All these observations can be explained by hypothesising that most of the subjects with abnormal Bolton ratio values (group B) had discrepancies in dimensions of maxillary teeth. Therefore, it can be stated that not only the Bolton ratio values of selected samples are significant, but also diagnosing the culprit arch with major variations; an important factor while establishing correlation equations for PCPMs.
Conclusions • •
•
•
Sample selection is highly critical in correlation-statistical methods of mixed dentition analysis. Correlation was stronger when established from a sample with no intermaxillary (Bolton) discrepancy. Increasing the percentage of subjects with intermaxillary (Bolton) discrepancy made the correlation weaker. Extreme variations in Bolton discrepancy of sample subjects can lead to derivation of regression equations that are not accurate. Therefore, it is proposed that customised correlationstatistical methods of mixed dentition analysis for different populations should be derived from sample of subjects with no Bolton discrepancy. A careful collection of data is, hence, recommended.
References Abu Alhaija ESJ, Qudeimat MA. Mixed dentition space analysis in a Jordanian population: comparison of two methods. Int J Pediatr Dent. 2006;16:104–10. Al-Bitar ZB, Al-Omari IK, Sonbol HN, Al-Ahmed HT, Hamdan AM. Mixed dentition analysis in a Jordanian population. Angle Orthod. 2008;78:670–5. Altherra ER, Korolukb LD, Phillips C. Influence of sex and ethnic tooth-size differences on mixeddentition space analysis. Am J Orthod Dentofacial Orthop. 2007;132(3):332–9. Bernabe E, Flores-Mir C. Are lower incisors the best predictors for the unerupted canine and premolars sums? An analysis of a Peruvian sample. Angle Orthod. 2005;75:198–203. Boboca A, Dibbets J. Prediction of the mesiodistal width of unerupted permanent canines and premolars: a statistical approach. Am J Orthod Dentofacial Orthop. 2010;137(4):503–7. Bolton WA. Disharmony in tooth size and its relation to the analysis and treatment of malocclusion. Angle Orthod. 1958;28:113–30. Carey CW. Linear arch dimension and tooth size. Am J Orthod. 1949;35:762–75. Crosby DR, Alexander CG. The occurrence of tooth size discrepancies among different malocclusion groups. Am J Orthod Dentofacial Orthop. 1989;95(6):457–61. Dahlberg G. Statistical methods for medical and biological students. London: George Allen and Unwin; 1940. p. 122–32.
Eur Arch Paediatr Dent de Paula S, Almeida MA, Lee PC. Prediction of the mesiodistal diameter of unerupted lower canines and premolars using 45 degree cephalometric radiography. Am J Orthod Dentofacial Orthop. 1995;107:309–14. Durgekar SG, Naik V. Evaluation of Moyers mixed dentition analysis in school children. Indian J Dent Res. 2009;20(1):26–30. Hixon EH, Oldfather RE. Estimation of the sizes of unerupted cuspid and bicuspid teeth. Angle Orthod. 1958;28:236–40. Huckaba GW. Arch size analysis and tooth size prediction. Dent Clin North Am. 1964;9:685–97. Johe RS, Steinhart T, Sado N, Greenberg B, Jing S. Intermaxillary tooth-size discrepancies in different sexes, malocclusion groups, and ethnicities. Am J Orthod Dentofacial Orthop. 2010;138(5):599–607. Legovic M, Novosel A, Legovic A. Regression equations for determining mesiodistal crown diameters of canines and premolars. Angle Orthod. 2003;73:314–8. Makinson D. Counting things combinatorics. In: Mackie I, editor. Sets, logic and maths for computing. London: Springer; 2008. p. 113–36. Martinelli FL, Lima EM, Rocha R, Arau´ jo MST. Prediction of lower permanent canine and premolars width by correlation methods. Angle Orthod. 2005;75(3):236–40. Melgac¸o CA, de Sousa Arau´jo MT, de Oliveira Ruellas A. Mandibular permanent first molar and incisor width as predictor of mandibular canine and premolar width. Am J Orthod Dentofacial Orthop. 2007;132:369–72. Memon S, Fida M. Development of a prediction equation for the estimation of mandibular canine and premolar widths from mandibular first permanent molar and incisor widths. Eur J Orthod. 2012;34:340–4. Moorrees CF, Thomsen SN, Jensen E, Yen PK. Mesiodistal crown diameters of the deciduous and permanent teeth in individuals. J Dent Res. 1957;36:39–47. Moyers RE. Handbook of orthodontics. 4th ed. Chicago: Year Book Medical Publishers; 1958.
Nourallah AW, Gesch D, Khordaji MN, Splieth C. New regression equations for predicting the size of unerupted canines and premolars in a contemporary population. Angle Orthod. 2002;72:216–21. Pancherz H, Schaffer C. Individual-based prediction of size of the supporting zones in the permanent dentition. A comparison of the Moyers method with a unitary prediction value. J Orofac Orthop. 1999;60:227–35. Parades V, Gandia JL, Cibrian RA. New, accurate and fast digital method to predict unerupted tooth size. Angle Orthod. 2006;76:14–9. Shah S, Bhaskar V, Venkataraghvan K, et al. 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;31:135–40. Sharma R, Kumar S, Singla A. Prevalence of tooth size discrepancy among North Indian orthodontic patients. Contemp Clin Dent. 2011;2:170–5. Staley RN, Hoag JF. Prediction of the mesiodistal widths of maxillary permanent canines and premolars. Am J Orthod. 1978;73(2):169–77. Staley RN, Kreber PE. A revision of the Hixon and Oldfather mixed dentition prediction method. Am J Orthod. 1980;78:296–302. Tahere nik H, Majid S, Mohandes Fateme M, Fard K, Javad M. Predicting the size of unerupted canines and premolars of the maxillary and mandibular quadrants in an Iranian population. J Clin Pediatr Dent. 2007;32(1):43–7. Tanaka MM, Johnston LE. The prediction of the size of unerupted canine and premolars in a contemporary orthodontic population. J Am Dent Assoc. 1974;88:798–801. Uysal T, Ayhan Basciftci F, Goyenc Y. New regression equations for mixed-dentition arch analysis in a Turkish sample with no Bolton tooth-size discrepancy. Am J Orthod Dentofacial Orthop. 2009;135(3):343–8.
123
ORIGINAL SCIENTIFIC ARTICLE
Effect of intermaxillary tooth-size discrepancy on accuracy of prediction equations for mixed dentition space analysis R. Khanna • R. K. Pandey • S. Tripathi
Received: 10 July 2014 / Accepted: 8 October 2014 European Academy of Paediatric Dentistry 2014
Abstract Aim Correlation-statistical methods are widely used for prediction of size of unerupted permanent canines and premolars in mixed dentition space analysis. The present study was planned to evaluate the effect of selecting dental study casts with no intermaxillary tooth-size discrepancy on the accuracy of predicting mesiodistal widths (MDWS) of permanent canines and premolars. Study design Bolton ratios were calculated for all the screened study dental casts fulfilling the inclusion criteria. Subjects were divided into two groups. Group A: all subjects with no intermaxillary tooth-size discrepancy within ±2 SD (Standard deviation) of the mean values. Group B: increased percentage of subjects with intermaxillary toothsize discrepancy beyond ±2 SD (Standard deviation) of the mean values. Statistics Linear regression equations were established for both maxilla and mandible in both the groups, with different tooth combinations as independent variables. Validation of best possible regression equations was done on an independent set of 40 subjects. The actual and predicted values of MDWS of permanent canines and premolars were compared by paired samples t test in both groups, for both arches.
R. Khanna (&) R. K. Pandey Department of Paediatric and Preventive Dentistry, King George’s Medical University, Lucknow 226003, Uttar Pradesh, India e-mail: [email protected] R. K. Pandey e-mail: [email protected] S. Tripathi Department of Prosthodontics and Crown &Bridge, King George’s Medical University, Lucknow, Uttar Pradesh, India e-mail: [email protected]
Results The accuracy of equations derived from group A was higher than those derived from group B. The difference between actual and predicted values was statistically insignificant in group A and statistically significant in group B. Conclusion The results confirm the accuracy of simple linear regression equations derived from a sample of children with no intermaxillary tooth-size discrepancy. Keywords Bolton ratio Mixed dentition analysis Intermaxillary tooth-size discrepancy
Introduction Diagnosis and treatment planning for ‘tooth size-arch length discrepancy’ (TSALD) during the mixed dentition period of a child are dependent on accurate predictions of mesiodistal widths (MDWS) of unerupted permanent teeth (canines and premolars). Precise predictions help in guiding the developing occlusion of a growing child. Different methods have been reported in the literature for these predictions. The choice of method adopted is based on its accuracy, simplicity, speed and applicability in different situations. The methods used are categorised as: application of middle value (Pancherz and Schaffer 1999); correlation-statistical method (Tanaka and Johnston 1974); radiographic method (Hixon and Oldfather 1958) and combination of correlation-statistical and radiographic methods (de Paula et al. 1995). Amongst these, the correlation-statistical approach are the most widely used owing to their simplicity and ease of use. The correlation-statistical methods are based on the possibility of establishing significant correlation relationships between the sum of MDWS of erupted and unerupted permanent teeth. Both simple linear (Tanaka and Johnston
123
Eur Arch Paediatr Dent
1974) and multiple linear (Bernabe and Flores-Mir 2005) regression models have been reported. Different combinations of permanent teeth with many modifications have been established as best known predictors in these models (Carey 1949; Nourallah et al. 2002; Legovic et al. 2003; Bernabe and Flores-Mir 2005; Boboca and Dibbets 2010). These prediction methods, are not without limitations. First, their applicability in populations of different ethnic origin is questionable. Second, there is emerging evidence of a different school of thought, which states that the prediction equations for size of unerupted permanent canines and premolars (PCPMs) should be derived from a sample of subjects with no intermaxillary tooth-size (Bolton) discrepancy. Bolton (1958) developed two ratios for estimating intermaxillary tooth-size discrepancy by measuring the summed MDWS of the mandibular to the maxillary anterior teeth. Only one reported study by Uysal et al. (2009) has found very high correlation coefficients between the four mandibular permanent incisors and the actual widths of the mandibular PCPMs in Turkish subjects when Bolton tooth-size discrepancy was taken into consideration. They also found extremely low standard errors of estimate and recommended the revision of currently popular prediction methods for various populations on the basis of their observations. In the light of above the present study was completed answer: ‘Whether there should be consideration of Bolton discrepancy in selection of sample subjects, for prediction of sum of MDWS of PCPMs, with the help of linear regression equations?’
Materials and method The patients in the age group of 10–15 years, attending an outpatient Department of Paediatric and Preventive Dentistry, King George’s Medical University, Lucknow, Uttar Pradesh (India), were considered for inclusion in the study. Most of the patients had their ethnic backgrounds traced back to regions within Northern India. Impressions of the maxillary and mandibular dental arches were taken in alginate and poured in dental stone (type III) to obtain good-quality dental study casts. The criteria for inclusion in the study were: no previous orthodontic treatment; fully erupted, complete permanent dentition (excluding second and third permanent molars) devoid of fractures or developmental anomalies of tooth number, size or shape; no clinically visible dental caries, restorations, or attrition in proximal or occlusal surfaces in any of the erupted teeth; consent to participate in the study. Most of the patients were attending the outpatient department in need of routine oral prophylaxis or consultation for correction of minor irregularities in teeth alignment.
123
Measurement of MDWS on all the casts was completed using a digital calliper (Aerospace, China) with an accuracy of 0.01 mm. Study casts with severe crowding/spacing ([2–4 mm), inaccessible proximal contacts for measurement, or impression flaws compromising accuracy of measurements, were excluded from the study. Following the strict inclusion and exclusion criteria, study casts of 305 subjects (mean age: 13.5 ± 1.8 years; 148 males and 157 females) were selected for measurement. The standardised technique proposed by Moorrees et al. (1957) was followed for all the measurements. The measurements were made by the primary investigator. The reliability of measurements was assessed by double-determination method on 20 randomly selected study casts, and the error was calculated with the help of Dahlberg’s formula (Dahlberg 1940). Only eight to ten pairs of study casts were measured in a day to avoid errors due to eye fatigue. The measurement consistency was determined by intraclass correlation coefficient (ICC). Descriptive statistics including means, standard deviations and maximum–minimum values were calculated for the measured tooth MDWS. Students unpaired t test was used to compare the tooth dimensions between males and females. Paired samples t test was used to compare between left and right side measurements. Bolton ratios for each subject (both anterior and posterior) were calculated thereafter. The descriptive statistics for both anterior and posterior Bolton ratio were also determined for the present sample size. A threshold of ±2 SD (Standard deviation) was considered as the criterion for selecting subjects under group A. A total of 272 study casts were finally included in group A. Power analysis (using G 9 Power 3.1.9) indicated that standard deviation of one would be detected with a power of 0.8 for the present sample size of group A. The remaining 33 study casts that exhibited extreme values beyond the ±2 SD were included in group B. The sample size of group B was also made up to a total of 272, by randomly replacing subjects from group A. Therefore, group A exclusively included subjects with no intermaxillary tooth-size discrepancy, while group B had *12 % of subjects exhibiting intermaxillary tooth-size discrepancy. In the mixed dentition period, six pairs of permanent teeth (considering left and right together) are normally present, fully erupted, during the chronologic age period of 7–9 years. All these permanent teeth available can be utilised for prediction of MDWS of PCPMs. The permanent maxillary lateral incisors are excluded due to high incidence of developmental variations in shape and size, leaving only five pairs of teeth available (Table 1). According to the theory of permutation–combination, five variables (considering left and right together) can result in twenty six different combinations (Table 1). The number
Eur Arch Paediatr Dent Table 1 Correlation coefficients for different teeth combinations Combination number
Teeth combinations according to available pairs of teeth : (11,21); (16,26); (31,41); (32,42); (36,46)
Maxillary
Mandibular
C1
46,16,42,41,11,21,31,32,26,36
0.74
0.67
0.71
0.68
C2
46,16,41,11,21,31,26,36
0.71
0.66
0.68
0.64
C3 C4
46,16,42,11,21,32,26,36 16,42,41,11,21,31,32,26
0.68 0.71
0.62 0.68(SEE = 0.92)
0.67 0.68
0.6 0.63
C5
46,16,42,41,31,32,26,36
0.74
0.65
0.73
0.69
C6
46,42,41,11,21,31,32,36
0.74
0.67
0.72
0.7
C7
46,16,42,32,26,36
0.72
0.63
0.71
0.67
C8
46,42,11,21,32,36
0.74
0.66
0.71
0.68
C9
46,16,41,31,26,36
0.7
0.62
0.69
0.64
C10
42,41,11,21,31,32
0.7
0.65
0.66
0.63
C11
16,41,11,21,31,26
0.67
0.65
0.64
0.58
C12
46,16,11,21,26,36
0.68
0.63
0.66
0.61
C13
16,42,11,21,32,26
0.69
0.67
0.67
0.61
C14
46,41,11,21,31,36
0.73
0.65
0.71
0.66
C15
16,42,41,31,32,26
0.71
0.65
0.69
0.64
C16
46,42,41,31,32,36
0.77(SEE = 0.83)
0.64
0.75(SEE = 0.79)
0.72(SEE = 0.83)
C17
46,42,32,36
0.75
0.61
0.73
0.71
C18 C19
46,41,31,36 16,11,21,26
0.74 0.62
0.59 0.61
0.71 0.59
0.68 0.52
C20
42,41,31,32
0.7
0.61
0.65
0.63
C21
16,41,31,26
0.65
0.6
0.63
0.56
C22
16,42,32,26
0.64
0.6
0.68
0.59
C23
46,16,26,36
0.64
0.56
0.64
0.58
C24
46,11,21,36
0.69
0.61
0.65
0.61
C25
41,11,21,31
0.67
0.63
0.61
0.57
C26
42,11,21,32
0.64
0.6
0.62
0.58
Group A
Group B
Group A
Group B
Five pairs of teeth available: (11,21); (16,26); (31,41); (32,42); (36,46) SEE = Standard error of estimate
of combinations for n variables taken k variables at a time is given by the following ratio (Makinson 2008): ½n!=½k! ðn kÞ! The combinations for the five variables available were calculated for values of ‘k’ from 2 to 5, resulting in 26 different combinations. The difference in calculating the number of combinations to that of permutations is the fact that the order of variables is not of concern for any combination. In a permutation, however, different orders of arrangement of the variables result in different sets of permutation. In the present study, the order in which the mdw of different teeth was added was not significant, therefore, calculation of possible combinations was completed. Simple linear regression was computed between MDWS of all 26 combinations of teeth and MDWS of maxillary and mandibular PCPMs for both group A and B. The regression
equations generated were in the standard form of y = a ? bx, where a, b are constants; y is the dependent variable (averaged MDWS of PCPMs of both left and right sides in maxilla/mandible) and x is the predictor or independent variable (sum of right and left side MDWS of different teeth combinations in maxilla/mandible). Correlation coefficients (R) and coefficients of determination (R2) were determined for all the possible teeth combinations in each group in each arch (Table 1). The best predictors were those with highest R and R2. Validity of the best prediction equations from both the groups in each arch was then tested by applying these equations on a random set of 40 subjects each. The level of closeness of prediction was determined by calculating the absolute difference between actual and predicted values and categorising it by the criteria shown in Table 2. The actual and predicted values of MDWS of PCPMs were compared by paired samples t test in both the groups, for both the arches.
123
Eur Arch Paediatr Dent Table 2 Criteria for determining proximity of prediction
Table 4 Comparison of mean MDWS between males and females
Category
Score
Error in prediction (mm)
Mean MDWS (mm)
Close
A
0–0.5
Male
B
0.5–1
Maxillary central incisor
8.76
8.64
0.14*
C
1–1.5
Maxillary lateral incisor
7.18
7.1
0.33*
D
1.5–2
Maxillary canine
8.08
7.84
0.001#
E
[2
Maxillary first premolar
7.35
7.24
0.11*
Maxillary second premolar
6.99
6.89
0.13*
11.05
10.88
Acceptable Poor
The prime objective was to assess whether exclusion/ inclusion of subjects with extreme deviations in Bolton values could affect the accuracy of prediction equations derived from that specific subject group.
Maxillary first molar
Female
0.06*
Mandibular central incisor Mandibular lateral incisor
5.57 6.17
5.527 6.101
0.1* 0.25*
Mandibular canine
7.1
6.88
0.007#
Mandibular first premolar
7.35
7.24
0.11*
Mandibular second premolar
7.4
7.32
0.29*
11.23
10.99
0.003#
Mandibular first molar
Results
P value
* Not significant difference
The mean measurement error for MDWS of all the teeth, as determined by the double-determination method, was found to be 0.182 mm which was well within the clinically acceptable limit. The intraclass correlation coefficient (ICC) was found to be 0.97, indicating good measurement consistency. Descriptive statistics for tooth mesiodistal widths (Table 3) showed no statistically significant differences between measurements from left and right side. The values of predictor variables were, however, combined for both the sides. Gender differences (Table 4) were seen in measurements of some teeth such as permanent maxillary and mandibular canines, and permanent mandibular molars (p \ 0.05). The difference in the means of these teeth ranged from 0.17 to 0.25 mm for each side. Considering the small difference of mean values of tooth MDWS between males and females, common equations were derived. Descriptive statistics for anterior and posterior Bolton ratios are presented in Table 5. The mean value for anterior and posterior Bolton ratio was found to be 78.19 and 90.29, respectively. The subjects were divided into group A and B accordingly. Table 3 Comparison of mesiodistal width tooth measurements from right and left sides of maxillary and mandibular dental arches Mesiodistal width (in mm corrected to two decimal places) Tooth
Right
p value
Left
Maxillary central incisor
8.74
8.72
0.16
Maxillary lateral incisor Maxillary molar
7.14 10.96
7.12 10.96
0.27 0.8
Mandibular central incisor
5.58
5.58
0.92
Mandibular lateral incisor
6.14
6.13
0.65
11.11
11.11
0.63
Mandibular molar
123
# Significant difference
Table 5 Descriptive statistics for Bolton ratios Descriptive statistics
Anterior bolton ratio
Overall bolton ratio
Mean Standard error
78.19 0.25
90.29 0.20
Median
78
91
Mode
78
91
Standard deviation
3.53
2.86
Confidence level (95.0 %)
0.49
0.40
Correlation coefficients (R) and coefficients of determination (R2) between all the teeth combinations and PCPMs for both the groups are presented in Table 1. The best predictor in group A was the sum of four mandibular incisors and mandibular first permanent molar (C16) for both maxilla and mandible. In group B, however, the sum of four mandibular incisors and mandibular first permanent molar (C16) was the combination with highest correlation coefficient for predicting maxillary PCPMs; but in the mandible, the sum of four mandibular incisors and maxillary central incisor with maxillary first permanent molar (C4) was the best predictor combination. The standard errors of estimate (SEE) of these best combinations were also found to be quite low (Table 1). The best derived regression equations for both the arches in both group A and B were: Group A: Maxillary: y = 3.03 ? 0.42 (C16); Mandibular: y = 3.79 ? 0.39 (C16). Group B: Maxillary: y* = 5.59 ? 0.26 (C4); Mandibular: y* = 4.27 ? 0.38 (C16).
Eur Arch Paediatr Dent Table 6 Comparison of actual and predicted values of sum of PCPMs (mm)
*
Not significant difference
# Significant difference
Group A
Group B
Actual sum of PCPMs
Predicted sum of PCPMs
Mean diff
P value
Actual sum of PCPMs
Predicted sum of PCPMs
Mean diff
P value
Maxillary
22.39
22.29
0.1*
0.28
22.39
21.93
0.46#
0.002
Mandibular
21.83
21.68
0.15*
0.48
21.83
21.32
0.51#
0.05
Table 7 Proximity of predictions (%) Maxillary
Mandibular
Group A
Group B
Group A
Group B
0–0.5 mm
23
22
35
32
0.5–1 mm
25
28
22
23
1–1.5 mm
14
10
10
7
1.5–2 mm
20
15
18
13
[2 mm
18
25
15
25
The validity of equations so derived was tested in an independent set of 40 subjects. In group A, there was no statistically significant difference between actual and predicted values of PCPMs for both maxillary and mandibular arches (Table 6). In group B, highly significant difference (p \ 0.01) between actual and predicted values was seen in the maxillary arch and moderately significant difference (p = 0.05) was observed in the mandibular arch (Table 6). The proximity of prediction values to the actual values is shown in Table 7 for both the groups. The total percentage of close and acceptable predictions was observed to be higher for equations derived from group A than group B in both maxillary and mandibular arches. Similarly, the percentage of poor predictions was considerably lower in group A than in group B.
Discussion The measurement error for tooth MDWS was well within the clinically acceptable limits (Abu Alhaija and Qudeimat 2006; Tahere nik et al. 2007) in the present study. The consistency of measurements in the present study was also very high (ICC = 0.95). Common equations for both males and females, derived as the difference in MDWS of their teeth, was minimal (\0.5 mm per arch). Similar considerations were reported by other workers (Nourallah et al. 2002; Martinelli et al. 2005; Shah et al. 2013). Descriptive statistics for Bolton ratio revealed differences from the standard Bolton values (Bolton 1958). Similar variations have been reported for the Indian population (Sharma et al. 2011). The standard of clinical significance used, mostly by previous authors, was a Bolton
discrepancy of ±2 SD (Crosby and Alexander 1989; Johe et al. 2010). Similar considerations were taken in the present study. The combination of radiographic and statistical methods (Hixon and Oldfather 1958; Staley and Hoag 1978; Staley and Kreber 1980) involves additional radiation exposure in the mixed dentition and sophisticated equipment. Therefore non-radiographical correlation-statistical methods for prediction of total MDWS of PCPMs have been preferred in the past (Moyers 1958; Tanaka and Johnston 1974; Bernabe and Flores-Mir 2005; Melgac¸o et al. 2007; Al-Bitar et al. 2008). It has also been suggested that multiple linear regression may result in correlation coefficients not high enough to ensure a good correlation, (Parades et al. 2006) although many investigators have contradicted this view (Legovic et al. 2003; Memon and Fida 2012). In the present study, however, a simple linear regression owing to ease of use and simplicity was preferred. The independent/predictor variable in the simple linear regression equations derived, for predicting total MDWS of PCPMs, has been found to vary in different models established so far. The sum of MDWS of four permanent mandibular incisors has been suggested as the best predictor in this regard by many authors (Moyers 1958; Carey 1949; Huckaba 1964; Tanaka and Johnston 1974). Others have contradicted this view and have found other combinations of teeth as better predictors (Nourallah et al. 2002; Legovic et al. 2003; Bernabe and Flores-Mir 2005; Parades et al. 2006; Melgac¸o et al. 2007). Therefore, in the present study simple linear regression models for all possible teeth combinations were used as predictor variables and to derive the best predictors in each group. The sum of four mandibular incisors and mandibular first permanent molars has been used as the independent predictor variable in various studies, as established for the mandibular arch in the present study (Melgac¸o et al. 2007; Shah et al. 2013). The combination of the sum of four mandibular incisors, maxillary central incisor with maxillary first permanent molar, derived as the best predictor for the maxillary arch in the present study, has however been never reported. The highest values of correlation coefficients in both the groups for both the arches were found to be comparable and also superior to many of the previous studies
123
Eur Arch Paediatr Dent
(Nourallah et al. 2002; Abu Alhaija and Qudeimat 2006; Tahere nik et al. 2007; Al-Bitar et al. 2008; Memon and Fida 2012; Shah et al. 2013) although with different predictor variables. The standard errors of estimate were also low and comparable to that in other studies (Nourallah et al. 2002; Abu Alhaija and Qudeimat 2006; Al-Bitar et al. 2008). These values were lower in group A than in group B, indicating better accuracy of equations derived from group A. The correlation coefficients determined while deriving equations from group A were also higher than in group B, further emphasising their accuracy. These findings suggest that the correlation between the predicted and predictor variable was stronger when established from a sample with no intermaxillary discrepancy. When the percentage of subjects with intermaxillary discrepancy was increased, the correlation became weaker. The comparison was further tested on an independent set of individuals with no information of Bolton discrepancy. It was seen that the percentage of poor predictions was considerably lower in group A than in group B. Therefore, the validity test also confirmed the accuracy of simple linear regression equations derived from group A. A special point of interest here is that the clinical significance of the difference between actual and predicted values is still not supported by some substantial evidence. In the present study, the criteria used by other investigators were chosen (Parades et al. 2006; Altherra et al. 2007; Durgekar and Naik 2009) where a total of 2 mm of discrepancy per arch is the maximal permissible limit, above which the prediction has been considered to be not acceptable or poor. This flexibility allows a compensation for the variations in growth taking place during the transitional period of the child’s dentition. The pattern of correlation coefficients obtained for different tooth combinations in both groups is also suggestive of the importance of sample selection. The subjects with Bolton values outside the set threshold will have significant deviations from the normal mesiodistal dimension of teeth for that population. This deviation can exist in the maxilla or mandible or both and would affect the accuracy of the equations derived, as ‘mesiodistal dimension of teeth’ here is the dependent variable. In the maxilla, the PCPMs were strongly correlated to mandibular teeth combinations (C16, C17) in group A. In group B (with increased percentage of subjects with intermaxillary discrepancy beyond ±2 SD of the mean values), the trend was different in respect that, the correlation of maxillary PCPMs with exclusive mandibular teeth (C16) was very weak. The mandibular PCPMs in both the groups were better correlated with mandibular teeth combinations (C16, C17). The combinations with exclusively maxillary teeth (C19) had weak correlations with mandibular PCPMs in both the groups. Addition of the
123
maxillary teeth to mandibular teeth (C5, C6) also weakened the correlation in both the groups for mandibular PCPMs. All these observations can be explained by hypothesising that most of the subjects with abnormal Bolton ratio values (group B) had discrepancies in dimensions of maxillary teeth. Therefore, it can be stated that not only the Bolton ratio values of selected samples are significant, but also diagnosing the culprit arch with major variations; an important factor while establishing correlation equations for PCPMs.
Conclusions • •
•
•
Sample selection is highly critical in correlation-statistical methods of mixed dentition analysis. Correlation was stronger when established from a sample with no intermaxillary (Bolton) discrepancy. Increasing the percentage of subjects with intermaxillary (Bolton) discrepancy made the correlation weaker. Extreme variations in Bolton discrepancy of sample subjects can lead to derivation of regression equations that are not accurate. Therefore, it is proposed that customised correlationstatistical methods of mixed dentition analysis for different populations should be derived from sample of subjects with no Bolton discrepancy. A careful collection of data is, hence, recommended.
References Abu Alhaija ESJ, Qudeimat MA. Mixed dentition space analysis in a Jordanian population: comparison of two methods. Int J Pediatr Dent. 2006;16:104–10. Al-Bitar ZB, Al-Omari IK, Sonbol HN, Al-Ahmed HT, Hamdan AM. Mixed dentition analysis in a Jordanian population. Angle Orthod. 2008;78:670–5. Altherra ER, Korolukb LD, Phillips C. Influence of sex and ethnic tooth-size differences on mixeddentition space analysis. Am J Orthod Dentofacial Orthop. 2007;132(3):332–9. Bernabe E, Flores-Mir C. Are lower incisors the best predictors for the unerupted canine and premolars sums? An analysis of a Peruvian sample. Angle Orthod. 2005;75:198–203. Boboca A, Dibbets J. Prediction of the mesiodistal width of unerupted permanent canines and premolars: a statistical approach. Am J Orthod Dentofacial Orthop. 2010;137(4):503–7. Bolton WA. Disharmony in tooth size and its relation to the analysis and treatment of malocclusion. Angle Orthod. 1958;28:113–30. Carey CW. Linear arch dimension and tooth size. Am J Orthod. 1949;35:762–75. Crosby DR, Alexander CG. The occurrence of tooth size discrepancies among different malocclusion groups. Am J Orthod Dentofacial Orthop. 1989;95(6):457–61. Dahlberg G. Statistical methods for medical and biological students. London: George Allen and Unwin; 1940. p. 122–32.
Eur Arch Paediatr Dent de Paula S, Almeida MA, Lee PC. Prediction of the mesiodistal diameter of unerupted lower canines and premolars using 45 degree cephalometric radiography. Am J Orthod Dentofacial Orthop. 1995;107:309–14. Durgekar SG, Naik V. Evaluation of Moyers mixed dentition analysis in school children. Indian J Dent Res. 2009;20(1):26–30. Hixon EH, Oldfather RE. Estimation of the sizes of unerupted cuspid and bicuspid teeth. Angle Orthod. 1958;28:236–40. Huckaba GW. Arch size analysis and tooth size prediction. Dent Clin North Am. 1964;9:685–97. Johe RS, Steinhart T, Sado N, Greenberg B, Jing S. Intermaxillary tooth-size discrepancies in different sexes, malocclusion groups, and ethnicities. Am J Orthod Dentofacial Orthop. 2010;138(5):599–607. Legovic M, Novosel A, Legovic A. Regression equations for determining mesiodistal crown diameters of canines and premolars. Angle Orthod. 2003;73:314–8. Makinson D. Counting things combinatorics. In: Mackie I, editor. Sets, logic and maths for computing. London: Springer; 2008. p. 113–36. Martinelli FL, Lima EM, Rocha R, Arau´ jo MST. Prediction of lower permanent canine and premolars width by correlation methods. Angle Orthod. 2005;75(3):236–40. Melgac¸o CA, de Sousa Arau´jo MT, de Oliveira Ruellas A. Mandibular permanent first molar and incisor width as predictor of mandibular canine and premolar width. Am J Orthod Dentofacial Orthop. 2007;132:369–72. Memon S, Fida M. Development of a prediction equation for the estimation of mandibular canine and premolar widths from mandibular first permanent molar and incisor widths. Eur J Orthod. 2012;34:340–4. Moorrees CF, Thomsen SN, Jensen E, Yen PK. Mesiodistal crown diameters of the deciduous and permanent teeth in individuals. J Dent Res. 1957;36:39–47. Moyers RE. Handbook of orthodontics. 4th ed. Chicago: Year Book Medical Publishers; 1958.
Nourallah AW, Gesch D, Khordaji MN, Splieth C. New regression equations for predicting the size of unerupted canines and premolars in a contemporary population. Angle Orthod. 2002;72:216–21. Pancherz H, Schaffer C. Individual-based prediction of size of the supporting zones in the permanent dentition. A comparison of the Moyers method with a unitary prediction value. J Orofac Orthop. 1999;60:227–35. Parades V, Gandia JL, Cibrian RA. New, accurate and fast digital method to predict unerupted tooth size. Angle Orthod. 2006;76:14–9. Shah S, Bhaskar V, Venkataraghvan K, et al. 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;31:135–40. Sharma R, Kumar S, Singla A. Prevalence of tooth size discrepancy among North Indian orthodontic patients. Contemp Clin Dent. 2011;2:170–5. Staley RN, Hoag JF. Prediction of the mesiodistal widths of maxillary permanent canines and premolars. Am J Orthod. 1978;73(2):169–77. Staley RN, Kreber PE. A revision of the Hixon and Oldfather mixed dentition prediction method. Am J Orthod. 1980;78:296–302. Tahere nik H, Majid S, Mohandes Fateme M, Fard K, Javad M. Predicting the size of unerupted canines and premolars of the maxillary and mandibular quadrants in an Iranian population. J Clin Pediatr Dent. 2007;32(1):43–7. Tanaka MM, Johnston LE. The prediction of the size of unerupted canine and premolars in a contemporary orthodontic population. J Am Dent Assoc. 1974;88:798–801. Uysal T, Ayhan Basciftci F, Goyenc Y. New regression equations for mixed-dentition arch analysis in a Turkish sample with no Bolton tooth-size discrepancy. Am J Orthod Dentofacial Orthop. 2009;135(3):343–8.
123
