SCIENTIFIC SECTION
Journal of Orthodontics, Vol. 41, 2014, 118–123
Tooth size discrepancies in Class II division 1 and Class III malocclusion requiring surgical–orthodontic or orthodontic treatment Timothy P. McSwiney1, Declan T. Millett1, Grant T. McIntyre2, Mark K. Barry3 and Michael S. Cronin4 1
Cork University Dental School and Hospital, University College Cork, Cork, Ireland; 2Dundee Dental Hospital, Dundee, UK; 3School of Manufacturing Engineering, Dublin Institute of Technology, Dublin, Ireland; 4Department of Statistics, University College Cork, Cork, Ireland
Objective: To compare mean anterior (AR) and mean overall (OR) tooth size ratios, prevalence of clinically significant tooth size discrepancies (TSDs) and correlation between AR and OR in subjects with Class II division 1 and Class III malocclusion treated by surgical–orthodontic or orthodontic means. Design: Retrospective, cross-sectional. Setting: State-funded and private clinics. Participants: From pre-treatment cohorts of 770 surgical and 610 non-surgical subjects, Class II division 1 and Class III malocclusion groups were identified with 60 surgical and 60 non-surgical subjects, comprising 30 males and 30 females, in each. Methods: AR and OR were calculated by landmarking digital models. Differences in AR and OR and their relationship were analysed using two-way analysis of variance (ANOVA) and a correlation coefficient, respectively. The proportions of the surgical and non-surgical groups with a TSD were assessed using logistic regression. Intra-examiner reproducibility involved re-landmarking 30 randomly selected image sets and differences in ARs and ORs were compared using a paired t-test. Random error was assessed using the intraclass correlation coefficient (ICC). Analyses were performed using SAS (SAS Institute Inc., Cary, NC, USA) at the 5% level of significance. Results: There were no statistically significant differences associated with the measurement of either the mean AR (P50.913) or the mean OR (P50.874). ICC values were very high (AR50.95; OR50.90). Differences existed between both Class II and Class III surgical (AR: P,0.001; OR: P,0.001) and non-surgical groups (AR: P50.012; OR: P50.003). The AR and OR relationship was strong (correlation coefficient50.72). The highest percentage of clinically significant TSDs was seen in the AR of both Class II and Class III surgical groups (23.3%). Conclusions: In the cohort examined: AR and OR differed significantly for malocclusion groups. The prevalence of clinically significant TSDs did not differ significantly between surgical and non-surgical groups although the highest percentage of clinically significant TSDs was recorded for AR in Class II and Class III surgical cases. AR and OR were closely related. Key words: Orthodontic, surgical, tooth size discrepancy, tooth size ratio Received 8 February 2013; accepted 17 November 2013
Introduction A tooth size discrepancy (TSD) occurs when there is disproportion among the sizes of individual permanent teeth (Bolton, 1958). TSDs may be described as anterior (involving the incisors and canines) or overall (involving all teeth, excluding the second and third molars). The anterior ratio (AR) is calculated by dividing the sum of the mesio-distal widths of the six mandibular anterior teeth by the mesio-distal widths of the six maxillary anterior teeth. The overall ratio (OR) is calculated by dividing the sum of the mesio-distal widths of the mandibular first molar to first molar by the mesio-distal widths of the maxillary first molar to first molar. To achieve an optimum occlusion, an AR of 77.2¡1.65% and an OR of 91.3¡1.91% should be obtained (Bolton, Address for correspondence: Professor D. T. Millett, Cork University Dental School and Hospital, University College Cork, Co. Cork, Ireland. Email: [email protected] # 2014 British Orthodontic Society
1958). The term TSD involves both anterior and overall tooth sizes and discrepancies in tooth size ratios, the latter being described by Bolton. These terms have been used by some authors interchangeably (Santoro et al., 2000; Bernabe et al., 2004). Clinically significant tooth size discrepancies occur when AR or OR is more than two standard deviations from Bolton’s mean (Bolton, 1958). As Bolton ratios were derived from a sample of excellent occlusions, others have suggested a discrepancy of 1.5– 2 mm (Proffit, 2000; Bernabe et al., 2004; Othman and Harradine, 2007) as a more accurate threshold for clinical significance. Bernabe et al. (2004) found that an adjustment in the lower arch had a greater effect on the Bolton ratio than the equivalent adjustment in the upper arch because of the larger total tooth width in the upper arch.
DOI 10.1179/1465313313Y.0000000089
JO June 2014
Scientific Section
Among orthodontic patients, 17–37.9% present with an anterior TSD (Crosby and Alexander, 1989; Freeman et al., 1996; Santoro et al., 2000; Araujo and Souki, 2003; Othman and Harradine, 2007; O’Mahony et al., 2011), but in non-orthodontic patients, this is estimated to be 20.5% (Bernabe et al., 2004). In contrast, the corresponding prevalence for overall TSDs ranges from 4 to 11% in orthodontic patients (Santoro et al., 2000; Bernabe et al., 2004; Endo et al., 2007; Strujic et al., 2009) and 5% in non-orthodontic patients (Bernabe et al., 2004). Prevalence is influenced by malocclusion type (Nie and Lin, 1999; Ta et al., 2001; Alkofide et al., 2002; Uysal et al., 2005), gender (Lavelle, 1972; Bishara, 1989; Smith et al., 2000) and ethnic group (Lavelle, 1972; Smith et al., 2000; Othman and Harradine, 2007). Although TSDs have been extensively explored in the orthodontic literature, the analysis of TSDs for patients requiring orthognathic surgery has received little attention. Identification and management of clinically significant TSDs for patients undergoing surgical– orthodontic and orthodontic treatment is a pre-requisite to attain the best occlusion (Bennett and McLaughlin, 2002). Where clinically significant TSDs are not identified, inadequate decompensation will occur before surgery resulting in under correction of skeletal movements and a poor occlusal fit is likely after surgery. Only three studies have investigated the prevalence of TSDs in surgical Class II (Crosby and Alexander, 1989) and surgical Class III (Sperry et al., 1977; Nie and Lin, 1999) groups. Crosby and Alexander (1989) evaluated TSDs in Class II subjects (20 surgical– orthodontic, 59 orthodontic) in the USA and found no statistically significant differences in the prevalence of TSDs among the groups. Gender differences were not accounted for. Sperry et al. (1977) investigated 78 subjects (40 surgical–orthodontic, 38 orthodontic) treated for mandibular prognathism in the USA and found that a greater proportion of this group had a mandibular tooth excess (for OR) compared to their Class II and Class I groups. Differences between surgical–orthodontic and orthodontic groups and between genders were not analysed (Sperry et al., 1977). In a Chinese population, Nie and Lin (1999) identified that Class III surgical– orthodontic (30 patients) and Class III orthodontic (30 patients) groups had a greater frequency of mandibular tooth size excess compared to other malocclusion groups. Understanding the correlation between anterior and overall tooth size ratios is helpful in the management of patients with a TSD. If AR and OR are highly correlated, then, a comparison of the size of the upper and lower lateral incisors can determine not only the likelihood of an AR discrepancy, but also the likelihood of an OR discrepancy. Othman and Harradine
TSD surgical or orthodontic
119
(2007) reported a moderate correlation (0.69) between anterior and overall tooth size ratios in an orthodontic population with 48% of the variation in the OR predicted from AR (Othman and Harradine, 2007). Investigations of TSDs in surgical–orthodontic patients were conducted almost two to four decades ago and none have compared Class II and Class III patients from the same population treated by surgical– orthodontic or orthodontic means (Sperry et al., 1977; Crosby and Alexander, 1989; Nie and Lin, 1999). With increasing numbers of patients undergoing surgical–orthodontic treatment (Keim et al., 2009), further assessment of TSDs in Class II and Class III surgical– orthodontic patients is required. Aims The aims of this study were to compare mean anterior (AR) and mean overall (OR) tooth size ratios, prevalence of clinically significant TSDs and correlation between AR and OR in subjects with Class II division 1 and Class III malocclusion treated by surgical– orthodontic or orthodontic means. Materials and methods Altman’s nomogram (Altman, 1980) determined that a sample size of 30 subjects in each groups would be required to detect a clinically significant difference of two standard deviations in TSD with a power of 0.8 at P,0.05. Two hundred and forty sets of study models were selected from pre-treatment cohorts of 770 surgical and 610 non-surgical consecutive subjects within state-funded and private orthodontic clinic archives in the Republic of Ireland. These fulfilled the following criteria:
N N N N
the same ethnic background and no history of orthodontic treatment, as verified from case records; high quality models with fully erupted permanent teeth from right first molar to left first molar in each arch; no factors which prevented accurate measurement of mesiodistal tooth widths including abnormal tooth morphology, restorations or fractured teeth; Class II division 1 and Class III malocclusions as determined using the British Standards Institute incisor classification (British Standard Incisor Classification, 1983).
The malocclusion groups (120 Class II division 1 and Class III subjects) comprised 60 surgical–orthodontic and 60 orthodontic cases with subgroups of 30 males and 30 females. Each subgroup consisted of a consecutive sample, obtained from the target cohort by stratified sampling, where the target population was
120
McSwiney et al.
Scientific Section
divided into eight pre-treatment strata (Class II division 1 surgical–orthodontic male and female, Class II division 1 orthodontic male and female, Class III surgical–orthodontic male and female and, Class III orthodontic male and female). The severity of malocclusion was not assessed. All study models were scanned using an R700 orthodontic study model scanner (3Shape A/S, Copenhagen, Denmark). The digital images were subsequently imported into the OrthoAnalyzerTM software program (3Shape A/S), for analysis. The mesial and distal contact points of each tooth from first molar to first molar (maxillary and mandibular) were landmarked from the occlusal aspect by zooming in on each individual tooth and rotating the digital models as necessary. This method has been found to be the best combination of accuracy, repeatability and speed of measurement (Horton et al., 2010). Following landmark identification, the tooth axes tool on the OrthoAnalyzer program was utilized. This ensured that the mesio-distal measurements were made through the long axis of the crown of each individual tooth. AR and OR were then automatically calculated. Any variation greater than two standard deviations from the normal ratios was considered to be clinically significant (Bolton, 1958). Statistical analysis Thirty study model image sets (12.5% of cases) were randomly selected and re-landmarked after a 2-week interval (Springate, 2012). Intra-examiner reproducibility of landmark identification was determined by comparing differences in ARs and ORs at the two time points using a paired t-test with the level of significance set at 5%. In addition, random error was assessed using the intra-class correlation coefficient (ICC). AR and OR data were analysed using analysis of variance (ANOVA) models, with malocclusion type, gender and their interaction included as fixed effects. Residual analyses were performed to confirm the suitability of the ANOVA models. All pair-wise comparisons were made between malocclusion types, correcting
JO June 2014
for multiple comparisons using Sidak’s adjustment to preserve the overall type I error rate at 5%. A correlation coefficient was calculated to assess the strength of the relationship between AR and OR. The proportion of cases with a clinically significant anterior or overall TSD for the surgical–orthodontic and orthodontic subgroups for malocclusion class was calculated. These were analysed using logistic regression models (Wald Chi-square), with malocclusion type, gender and their interaction included as fixed effects. These logistic regression models enable comparisons of the proportion of patients with a certain characteristic (clinically significant anterior or overall TSDs) between different levels of one or more categorical explanatory variables (malocclusion type and genders). The interaction term in these models assesses whether the differences in proportion between malocclusion type is dependent on gender or vice versa. All statistical analyses were performed using SAS (version 9.2; SAS Institute Inc., Cary, NC, USA) at 5% level of significance. Results There were no statistically significant differences associated with the measurement of either the mean AR (P50.913) or the mean OR (P50.874). The ICC values for both AR and OR were very high at 0.95 and 0.90, respectively, indicating excellent agreement and a high degree of examiner reliability. Tooth size ratios For the mean AR and mean OR data (Table 1), no statistically significant differences were found between the genders (anterior: P50.541; overall: P50.339) (Table 2). There were, however, statistically significant differences between malocclusion groups (Table 2). Statistically significant differences existed between both Class II division 1 and Class III surgical (anterior: P,0.001; overall: P, 0.001) and the equivalent non-surgical groups (anterior: P50.012; overall: P50.003).
Table 1 Descriptive statistics for AR and OR by gender and malocclusion groups Anterior ratio F (n530)
Class Class Class Class
II division 1 S II division 1 N-S III S III N-S
Overall ratio M (n530)
All (n560)
F (n530)
M (n530)
All (n560)
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Mean
SD
0.766 0.765 0.787 0.784
0.028 0.026 0.029 0.022
0.760 0.770 0.783 0.780
0.032 0.024 0.026 0.021
0.763 0.767 0.785 0.782
0.030 0.025 0.027 0.021
0.903 0.907 0.922 0.922
0.026 0.018 0.026 0.022
0.897 0.901 0.926 0.920
0.024 0.022 0.023 0.022
0.900 0.904 0.924 0.921
0.025 0.020 0.024 0.022
S5surgical; N-S5non-surgical; F5female; M5male.
JO June 2014
Table 2
Scientific Section
TSD surgical or orthodontic
121
Results of two-way ANOVA for AR and OR for surgical–orthodontic and orthodontic groups Anterior
Overall
Effect
Num DF
Den DF
F value
P value
Num DF
Den DF
F value
P value
Gender Malocclusion Gender*Malocclusion
1 3 3
232 232 232
0.38 10.57 0.51
0.541 ,0.0001 0.677
1 3 3
232 232 232
0.92 16.47 0.62
0.339 ,0.0001 0.605
Num DF5numerator degrees of freedom; Den DF5denominator degrees of freedom.
Prevalence of clinically significant TSDs The prevalence of clinically significant TSDs (anterior or overall) was higher in the combined surgical groups than in the non-surgical groups with the highest percentage recorded for AR in the Class II and Class III surgical groups at 23.3% (Table 3). In contrast, the lowest prevalence (13.3%) was found for anterior TSDs in the Class III non-surgical group. No statistically significant differences existed between surgical and nonsurgical groups for clinically significant anterior or mean overall TSDs with P50.1125 and P50.2436, respectively. No statistically significant differences were found for clinically significant mean anterior or overall TSDs between genders (anterior: P50.752; overall: P50.813) or malocclusion groups (anterior: P50.361; overall: P50.370) (Table 4). Correlation between AR and OR The correlation between AR and OR was strong (r50.72). Fifty-two per cent of the variation in OR could be predicted from the AR as calculated by r2 (regression model). Discussion Clinically significant anterior TSDs were determined in 23.3% of surgical and 14.1% of non-surgical cases. In contrast, 20% of surgical and 13.3% of non-surgical cases presented with clinically significant overall TSDs. The differences between the surgical and non-surgical groups were not statistically significant for either anterior (P50.112) or overall (P50.243) TSDs. While Table 3
one previous study has investigated TSDs in Class II surgical subjects (Crosby and Alexander, 1989) and two have assessed TSDs in Class III surgical subjects (Sperry, 1977; Nie and Lin, 1999), this appears to be the first study to examine TSDs in a cohort of both Class II and Class III surgical patients. In our Class II surgical group, the values for both mean AR (0.763¡0.030) and mean OR (0.900¡0.025) were lower than those reported by Crosby and Alexander (1989) (0.775¡0.027 and 0.915¡0.031, respectively). Furthermore, we found an almost three times greater prevalence of overall TSDs (18.3%) in this surgical group in comparison to Crosby and Alexander (1989) (6.8%). Differences in the inclusion criteria between the studies may account for this variation. Our Class II surgical group consisted solely of Class II division 1 cases, but this was not specified by Crosby and Alexander (1989). In addition, they did not clarify the gender distribution and ethnicity of their sample. In Chinese subjects, Nie and Lin (1999) found significantly higher tooth size ratios for Class III surgical– orthodontic and orthodontic cases compared to Class II orthodontic cases. In the present study, statistically significant differences in mean AR and mean OR were noted between the Class II and Class III malocclusion groups and these were most pronounced between the surgical groups. Both mean AR (0.785¡0.027) and mean OR (0.924¡0.024) were lower than those reported by Nie and Lin (1999) (0.826¡0.026 and 0.956¡0.024, respectively). Unfortunately, Nie and Lin (1999) did not state the prevalence of clinically significant TSDs for Class III surgical cases. Variation in ethnicity between
Prevalence of clinically significant TSDs in surgical–orthodontic and orthodontic groups Anterior (%)
Class Class Class Class
II division 1 S II division 1 N-S III S III N-S
Overall (%)
F (n530)
M (n530)
All (n560)
F (n530)
M (n530)
All (n560)
16.7 13.3 23.3 16.7
30.0 16.7 23.3 10.0
23.3 15.0 23.3 13.3
20.0 6.7 23.3 16.7
16.7 13.3 20.0 16.7
18.3 10.0 21.7 16.7
S5surgical; N-S5non-surgical; F5female; M5male.
122
McSwiney et al.
Scientific Section
the groups reported on by Nie and Lin (1999) and those in our study are likely to have contributed to the differences in mean AR and mean OR (Lavelle, 1972; Smith et al., 2000; Paredes et al., 2006). No comparisons were possible with the investigation by Sperry et al. (1977) as they did not define tooth size ratios. They did, however, note that the frequency of mandibular tooth-size excess for mean OR was greater in their Class III group than in their Class II group (Sperry et al., 1977). Our findings corroborate the general trend towards higher tooth size ratios in Class III malocclusion (Nie and Lin, 1999; Alkofide and Hashim, 2002; Othman and Harradine, 2007). No statistically significant differences were found for mean AR and mean OR between the genders or for equivalent surgical and non-surgical groups. These findings concur with those of Crosby and Alexander (1989) and Nie and Lin (1999) with regard to surgical and non-surgical Class II and Class III malocclusions, respectively. Our study highlighted a strong but not perfect relationship between AR and OR (correlation coefficient: 0.72). This was similar to the value of 0.69 found by Othman and Harradine (2007). Fifty-two per cent of the variation in OR could be predicted from AR. Hence, the presence of a clinically significant anterior TSD was not always indicative of a clinically significant overall TSD and vice versa. In all the malocclusion groups, except the Class III non-surgical group, there were a greater proportion of clinically significant anterior TSDs in comparison to overall TSDs. There are limitations within this study. Firstly, only subjects from one population were included so the findings may not be generalizable to other ethnic groups; secondly, cases were selected from orthodontically referred samples rather than from a general population. The strengths of this study, however, may be considered as follows: instead of random sampling from the general population, only patients who required
JO June 2014
surgical–orthodontic or orthodontic treatment were included so the results are of greater relevance to clinicians treating patients in the former group; the Class II and Class III surgical and non-surgical groups were matched for both malocclusion type and gender; the method adopted had a high degree of reproducibility for both AR and OR and Class II division 2 surgical cases were excluded to reduce heterogeneity of the Class II sample. In addition, the sample sizes of the cohorts assessed were greater than those of previous studies, which have compared TSDs in subjects who have received treatment by surgical–orthodontic or orthodontic means (Sperry et al., 1977; Crosby and Alexander, 1989; Nie and Lin, 1999). The results of this study have implications for clinical practice. The relatively high prevalence of anterior and overall TSDs in this surgical population may complicate occlusal management. Clinicians should assess TSDs at the diagnosis and treatment planning stage for surgical cases, and where discrepancies are found, the treatment plan should be modified as necessary to resolve these. In particular, surgical cases with diminutive maxillary lateral incisors and hypodontia should receive restorative input. The identification of a TSD resulting from excessively narrow or wide teeth may also influence the extraction decision in relation to alignment (Tong et al., 2004) and decompensation. Conclusion In the cohort examined:
N N
Mean AR and mean OR differed significantly between equivalent surgical and non-surgical malocclusion groups. The prevalence of clinically significant TSDs did not differ significantly between surgical and non-surgical groups, although the highest percentage of clinically significant TSDs was recorded for AR in Class II and Class III surgical cases.
Table 4 Results of the two-way ANOVA for clinically significant anterior and overall TSDs for gender and malocclusion groups Anterior
Overall
Effect
DF
Chi-square
P value
DF
Chi-square
P value
Gender Malocclusion Gender*Malocclusion
1 3 3
0.100 3.206 1.914
0.752 0.361 0.591
1 3 3
0.056 3.144 0.922
0.813 0.370 0.820
DF5degrees of freedom. These logistic regression models enable comparisons of the proportions of patients with a certain characteristic (clinically significant anterior or overall TSDs) between different levels of one or more categorical explanatory variables (malocclusion type and genders). The interaction term in these models assesses whether the differences in proportions between malocclusion type is dependent on gender or vice versa.
JO June 2014
N
Scientific Section
AR and OR were closely related with 52% of the variation in OR predicted from AR.
Acknowledgements The authors would like to thank the Consultant Orthodontists and Specialist Orthodontists who allowed access to study model records as well as the staff at ESM Digital Solutions Ltd, Swords, Co. Dublin, Ireland, for their assistance with scanning the study models. We would also like to thank Ms Niamh Kelly for her IT support. References Alkofide E, Hashim H. Intermaxillary tooth size discrepancies among different malocclusion classes: a comparative study. J Clin Pediatr Dent 2002; 26: 383–387. Altman DG. Statistics and ethics in medical research: III How large a sample? Br Med J 1980; 281: 1336–1338. Araujo E, Souki M. Bolton anterior tooth size discrepancies among different malocclusion groups. Angle Orthod 2003; 73: 307–313. Bennett JC, McLaughlin RP. Orthodontic Management of the Dentition with the Pre-adjusted Appliance. St Louis, MO: Mosby. 2002. Bernabe E, Major PW, Flores-Mir C. Tooth-width ratio discrepancies in a sample of Peruvian adolescents. Am J Orthod Dentofacial Orthop 2004; 125: 361–365. Bishara SE, Jakobsen JR, Abdallah EM, Fernandez Garcia A. Comparisons of mesiodistal and buccolingual crown dimensions of the permanent teeth in three populations from Egypt, Mexico, and the United States. Am J Orthod Dentofacial Orthop 1989; 96: 416–422. Bolton WA. Disharmony in tooth size and its relation to the analysis and treatment of malocclusion. Angle Orthod 1958; 28: 113–130. British Standard Incisor Classification. Glossary of Dental Terms BS 4492. London: British Standard Institute. 1983. Crosby DR, Alexander CG. The occurrence of tooth size discrepancies among different malocclusion groups. Am J Orthod Dentofacial Orthop 1989; 95: 457–461. Endo T, Abe R, Kuroki H, Oka K, Shimooka S. Tooth size discrepancies among different malocclusions in a Japanese orthodontic population. Angle Orthod 2007; 78: 994–999.
TSD surgical or orthodontic
123
Freeman JE, Maskeroni AJ, Lorton L. Frequency of Bolton tooth-size discrepancies among different malocclusion groups. Am J Orthod Dentofacial Orthop 1996; 110: 24–27. Horton MH, Miller JR, Gaillard PR, Larson BE. Technique comparison for efficient orthodontic tooth measurements using digital models. Angle Orthod 2010; 80: 254–261. Keim RG, Gottlieb EL, Nelson AH, Vogels DS 3rd. JCO Orthodontic Practice Study. Part 1 Trends. J Clin Orthod 2009; 43: 625–634 Lavelle CL. Maxillary and mandibular tooth size in different racial groups and in different occlusal categories. Am J Orthod 1972; 61: 29–37. Nie Q, Lin J. Comparison of intermaxillary tooth size discrepancies among different malocclusion groups. Am J Orthod Dentofacial Orthop 1999; 116: 539–544. O’Mahony G, Millett DT, Barry MK, McIntyre GT, Cronin MS. Tooth size discrepancies in Irish orthodontic patients among different malocclusion groups. Angle Orthod 2011; 81: 130–133. Othman SA, Harradine NW. Tooth size discrepancies in an orthodontic population. Angle Orthod 2007; 77: 668–674. Paredes V, Gandia JL, Cibrian R. Do Bolton’s ratios apply to a Spanish population? Am J Orthod Dentofacial Orthop 2006; 129: 428–430. Proffit WR. Contemporary Orthodontics. 3rd edn. St Louis, MO: Mosby, 2000. p. 170. Santoro M, Ayoub ME, Pardi VA, Cangialosi TL. Mesiodistal crown dimensions and tooth size discrepancy of the permanent dentition of Dominican Americans. Angle Orthod 2000; 70: 303–307. Smith SS, Buschang PH, Watanabe E. Interarch tooth size relationships of 3 populations: ‘does Bolton’s analysis apply?’. Am J Orthod Dentofacial Orthop 2000; 117: 169–174. Sperry TP, Worms FW, Isaacson RJ. Tooth size discrepancy in mandibular prognathism. Am J Orthod 1977; 72: 183–190. Springate SD. The effect of sample size and bias on the reliability of estimates of error: a comparative study of Dahlberg’s formula. Eur J Orthod 2012; 34: 158–163. Strujic M, Anic-Milosevic S, Mestrovic S, Slaj M. Tooth size discrepancy in orthodontic patients among different malocclusion groups. Eur J Orthod 2009; 31: 584–589. Ta TA, Ling JY, Hagg U. Tooth-size discrepancies among different occlusion groups of southern Chinese children. Am J Orthod Dentofacial Orthop 2001; 120: 556–558. Tong H, Chen D, Xu L, Liu P. The effect of premolar extractions on tooth size discrepancies. Angle Orthod 2004; 74: 508–511. Uysal T, Sari Z. Intermaxillary tooth size discrepancy and mesiodistal crown dimensions for a Turkish population. Am J Orthod Dentofacial Orthop 2005; 128: 226–230.
Journal of Orthodontics, Vol. 41, 2014, 118–123
Tooth size discrepancies in Class II division 1 and Class III malocclusion requiring surgical–orthodontic or orthodontic treatment Timothy P. McSwiney1, Declan T. Millett1, Grant T. McIntyre2, Mark K. Barry3 and Michael S. Cronin4 1
Cork University Dental School and Hospital, University College Cork, Cork, Ireland; 2Dundee Dental Hospital, Dundee, UK; 3School of Manufacturing Engineering, Dublin Institute of Technology, Dublin, Ireland; 4Department of Statistics, University College Cork, Cork, Ireland
Objective: To compare mean anterior (AR) and mean overall (OR) tooth size ratios, prevalence of clinically significant tooth size discrepancies (TSDs) and correlation between AR and OR in subjects with Class II division 1 and Class III malocclusion treated by surgical–orthodontic or orthodontic means. Design: Retrospective, cross-sectional. Setting: State-funded and private clinics. Participants: From pre-treatment cohorts of 770 surgical and 610 non-surgical subjects, Class II division 1 and Class III malocclusion groups were identified with 60 surgical and 60 non-surgical subjects, comprising 30 males and 30 females, in each. Methods: AR and OR were calculated by landmarking digital models. Differences in AR and OR and their relationship were analysed using two-way analysis of variance (ANOVA) and a correlation coefficient, respectively. The proportions of the surgical and non-surgical groups with a TSD were assessed using logistic regression. Intra-examiner reproducibility involved re-landmarking 30 randomly selected image sets and differences in ARs and ORs were compared using a paired t-test. Random error was assessed using the intraclass correlation coefficient (ICC). Analyses were performed using SAS (SAS Institute Inc., Cary, NC, USA) at the 5% level of significance. Results: There were no statistically significant differences associated with the measurement of either the mean AR (P50.913) or the mean OR (P50.874). ICC values were very high (AR50.95; OR50.90). Differences existed between both Class II and Class III surgical (AR: P,0.001; OR: P,0.001) and non-surgical groups (AR: P50.012; OR: P50.003). The AR and OR relationship was strong (correlation coefficient50.72). The highest percentage of clinically significant TSDs was seen in the AR of both Class II and Class III surgical groups (23.3%). Conclusions: In the cohort examined: AR and OR differed significantly for malocclusion groups. The prevalence of clinically significant TSDs did not differ significantly between surgical and non-surgical groups although the highest percentage of clinically significant TSDs was recorded for AR in Class II and Class III surgical cases. AR and OR were closely related. Key words: Orthodontic, surgical, tooth size discrepancy, tooth size ratio Received 8 February 2013; accepted 17 November 2013
Introduction A tooth size discrepancy (TSD) occurs when there is disproportion among the sizes of individual permanent teeth (Bolton, 1958). TSDs may be described as anterior (involving the incisors and canines) or overall (involving all teeth, excluding the second and third molars). The anterior ratio (AR) is calculated by dividing the sum of the mesio-distal widths of the six mandibular anterior teeth by the mesio-distal widths of the six maxillary anterior teeth. The overall ratio (OR) is calculated by dividing the sum of the mesio-distal widths of the mandibular first molar to first molar by the mesio-distal widths of the maxillary first molar to first molar. To achieve an optimum occlusion, an AR of 77.2¡1.65% and an OR of 91.3¡1.91% should be obtained (Bolton, Address for correspondence: Professor D. T. Millett, Cork University Dental School and Hospital, University College Cork, Co. Cork, Ireland. Email: [email protected] # 2014 British Orthodontic Society
1958). The term TSD involves both anterior and overall tooth sizes and discrepancies in tooth size ratios, the latter being described by Bolton. These terms have been used by some authors interchangeably (Santoro et al., 2000; Bernabe et al., 2004). Clinically significant tooth size discrepancies occur when AR or OR is more than two standard deviations from Bolton’s mean (Bolton, 1958). As Bolton ratios were derived from a sample of excellent occlusions, others have suggested a discrepancy of 1.5– 2 mm (Proffit, 2000; Bernabe et al., 2004; Othman and Harradine, 2007) as a more accurate threshold for clinical significance. Bernabe et al. (2004) found that an adjustment in the lower arch had a greater effect on the Bolton ratio than the equivalent adjustment in the upper arch because of the larger total tooth width in the upper arch.
DOI 10.1179/1465313313Y.0000000089
JO June 2014
Scientific Section
Among orthodontic patients, 17–37.9% present with an anterior TSD (Crosby and Alexander, 1989; Freeman et al., 1996; Santoro et al., 2000; Araujo and Souki, 2003; Othman and Harradine, 2007; O’Mahony et al., 2011), but in non-orthodontic patients, this is estimated to be 20.5% (Bernabe et al., 2004). In contrast, the corresponding prevalence for overall TSDs ranges from 4 to 11% in orthodontic patients (Santoro et al., 2000; Bernabe et al., 2004; Endo et al., 2007; Strujic et al., 2009) and 5% in non-orthodontic patients (Bernabe et al., 2004). Prevalence is influenced by malocclusion type (Nie and Lin, 1999; Ta et al., 2001; Alkofide et al., 2002; Uysal et al., 2005), gender (Lavelle, 1972; Bishara, 1989; Smith et al., 2000) and ethnic group (Lavelle, 1972; Smith et al., 2000; Othman and Harradine, 2007). Although TSDs have been extensively explored in the orthodontic literature, the analysis of TSDs for patients requiring orthognathic surgery has received little attention. Identification and management of clinically significant TSDs for patients undergoing surgical– orthodontic and orthodontic treatment is a pre-requisite to attain the best occlusion (Bennett and McLaughlin, 2002). Where clinically significant TSDs are not identified, inadequate decompensation will occur before surgery resulting in under correction of skeletal movements and a poor occlusal fit is likely after surgery. Only three studies have investigated the prevalence of TSDs in surgical Class II (Crosby and Alexander, 1989) and surgical Class III (Sperry et al., 1977; Nie and Lin, 1999) groups. Crosby and Alexander (1989) evaluated TSDs in Class II subjects (20 surgical– orthodontic, 59 orthodontic) in the USA and found no statistically significant differences in the prevalence of TSDs among the groups. Gender differences were not accounted for. Sperry et al. (1977) investigated 78 subjects (40 surgical–orthodontic, 38 orthodontic) treated for mandibular prognathism in the USA and found that a greater proportion of this group had a mandibular tooth excess (for OR) compared to their Class II and Class I groups. Differences between surgical–orthodontic and orthodontic groups and between genders were not analysed (Sperry et al., 1977). In a Chinese population, Nie and Lin (1999) identified that Class III surgical– orthodontic (30 patients) and Class III orthodontic (30 patients) groups had a greater frequency of mandibular tooth size excess compared to other malocclusion groups. Understanding the correlation between anterior and overall tooth size ratios is helpful in the management of patients with a TSD. If AR and OR are highly correlated, then, a comparison of the size of the upper and lower lateral incisors can determine not only the likelihood of an AR discrepancy, but also the likelihood of an OR discrepancy. Othman and Harradine
TSD surgical or orthodontic
119
(2007) reported a moderate correlation (0.69) between anterior and overall tooth size ratios in an orthodontic population with 48% of the variation in the OR predicted from AR (Othman and Harradine, 2007). Investigations of TSDs in surgical–orthodontic patients were conducted almost two to four decades ago and none have compared Class II and Class III patients from the same population treated by surgical– orthodontic or orthodontic means (Sperry et al., 1977; Crosby and Alexander, 1989; Nie and Lin, 1999). With increasing numbers of patients undergoing surgical–orthodontic treatment (Keim et al., 2009), further assessment of TSDs in Class II and Class III surgical– orthodontic patients is required. Aims The aims of this study were to compare mean anterior (AR) and mean overall (OR) tooth size ratios, prevalence of clinically significant TSDs and correlation between AR and OR in subjects with Class II division 1 and Class III malocclusion treated by surgical– orthodontic or orthodontic means. Materials and methods Altman’s nomogram (Altman, 1980) determined that a sample size of 30 subjects in each groups would be required to detect a clinically significant difference of two standard deviations in TSD with a power of 0.8 at P,0.05. Two hundred and forty sets of study models were selected from pre-treatment cohorts of 770 surgical and 610 non-surgical consecutive subjects within state-funded and private orthodontic clinic archives in the Republic of Ireland. These fulfilled the following criteria:
N N N N
the same ethnic background and no history of orthodontic treatment, as verified from case records; high quality models with fully erupted permanent teeth from right first molar to left first molar in each arch; no factors which prevented accurate measurement of mesiodistal tooth widths including abnormal tooth morphology, restorations or fractured teeth; Class II division 1 and Class III malocclusions as determined using the British Standards Institute incisor classification (British Standard Incisor Classification, 1983).
The malocclusion groups (120 Class II division 1 and Class III subjects) comprised 60 surgical–orthodontic and 60 orthodontic cases with subgroups of 30 males and 30 females. Each subgroup consisted of a consecutive sample, obtained from the target cohort by stratified sampling, where the target population was
120
McSwiney et al.
Scientific Section
divided into eight pre-treatment strata (Class II division 1 surgical–orthodontic male and female, Class II division 1 orthodontic male and female, Class III surgical–orthodontic male and female and, Class III orthodontic male and female). The severity of malocclusion was not assessed. All study models were scanned using an R700 orthodontic study model scanner (3Shape A/S, Copenhagen, Denmark). The digital images were subsequently imported into the OrthoAnalyzerTM software program (3Shape A/S), for analysis. The mesial and distal contact points of each tooth from first molar to first molar (maxillary and mandibular) were landmarked from the occlusal aspect by zooming in on each individual tooth and rotating the digital models as necessary. This method has been found to be the best combination of accuracy, repeatability and speed of measurement (Horton et al., 2010). Following landmark identification, the tooth axes tool on the OrthoAnalyzer program was utilized. This ensured that the mesio-distal measurements were made through the long axis of the crown of each individual tooth. AR and OR were then automatically calculated. Any variation greater than two standard deviations from the normal ratios was considered to be clinically significant (Bolton, 1958). Statistical analysis Thirty study model image sets (12.5% of cases) were randomly selected and re-landmarked after a 2-week interval (Springate, 2012). Intra-examiner reproducibility of landmark identification was determined by comparing differences in ARs and ORs at the two time points using a paired t-test with the level of significance set at 5%. In addition, random error was assessed using the intra-class correlation coefficient (ICC). AR and OR data were analysed using analysis of variance (ANOVA) models, with malocclusion type, gender and their interaction included as fixed effects. Residual analyses were performed to confirm the suitability of the ANOVA models. All pair-wise comparisons were made between malocclusion types, correcting
JO June 2014
for multiple comparisons using Sidak’s adjustment to preserve the overall type I error rate at 5%. A correlation coefficient was calculated to assess the strength of the relationship between AR and OR. The proportion of cases with a clinically significant anterior or overall TSD for the surgical–orthodontic and orthodontic subgroups for malocclusion class was calculated. These were analysed using logistic regression models (Wald Chi-square), with malocclusion type, gender and their interaction included as fixed effects. These logistic regression models enable comparisons of the proportion of patients with a certain characteristic (clinically significant anterior or overall TSDs) between different levels of one or more categorical explanatory variables (malocclusion type and genders). The interaction term in these models assesses whether the differences in proportion between malocclusion type is dependent on gender or vice versa. All statistical analyses were performed using SAS (version 9.2; SAS Institute Inc., Cary, NC, USA) at 5% level of significance. Results There were no statistically significant differences associated with the measurement of either the mean AR (P50.913) or the mean OR (P50.874). The ICC values for both AR and OR were very high at 0.95 and 0.90, respectively, indicating excellent agreement and a high degree of examiner reliability. Tooth size ratios For the mean AR and mean OR data (Table 1), no statistically significant differences were found between the genders (anterior: P50.541; overall: P50.339) (Table 2). There were, however, statistically significant differences between malocclusion groups (Table 2). Statistically significant differences existed between both Class II division 1 and Class III surgical (anterior: P,0.001; overall: P, 0.001) and the equivalent non-surgical groups (anterior: P50.012; overall: P50.003).
Table 1 Descriptive statistics for AR and OR by gender and malocclusion groups Anterior ratio F (n530)
Class Class Class Class
II division 1 S II division 1 N-S III S III N-S
Overall ratio M (n530)
All (n560)
F (n530)
M (n530)
All (n560)
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Mean
SD
0.766 0.765 0.787 0.784
0.028 0.026 0.029 0.022
0.760 0.770 0.783 0.780
0.032 0.024 0.026 0.021
0.763 0.767 0.785 0.782
0.030 0.025 0.027 0.021
0.903 0.907 0.922 0.922
0.026 0.018 0.026 0.022
0.897 0.901 0.926 0.920
0.024 0.022 0.023 0.022
0.900 0.904 0.924 0.921
0.025 0.020 0.024 0.022
S5surgical; N-S5non-surgical; F5female; M5male.
JO June 2014
Table 2
Scientific Section
TSD surgical or orthodontic
121
Results of two-way ANOVA for AR and OR for surgical–orthodontic and orthodontic groups Anterior
Overall
Effect
Num DF
Den DF
F value
P value
Num DF
Den DF
F value
P value
Gender Malocclusion Gender*Malocclusion
1 3 3
232 232 232
0.38 10.57 0.51
0.541 ,0.0001 0.677
1 3 3
232 232 232
0.92 16.47 0.62
0.339 ,0.0001 0.605
Num DF5numerator degrees of freedom; Den DF5denominator degrees of freedom.
Prevalence of clinically significant TSDs The prevalence of clinically significant TSDs (anterior or overall) was higher in the combined surgical groups than in the non-surgical groups with the highest percentage recorded for AR in the Class II and Class III surgical groups at 23.3% (Table 3). In contrast, the lowest prevalence (13.3%) was found for anterior TSDs in the Class III non-surgical group. No statistically significant differences existed between surgical and nonsurgical groups for clinically significant anterior or mean overall TSDs with P50.1125 and P50.2436, respectively. No statistically significant differences were found for clinically significant mean anterior or overall TSDs between genders (anterior: P50.752; overall: P50.813) or malocclusion groups (anterior: P50.361; overall: P50.370) (Table 4). Correlation between AR and OR The correlation between AR and OR was strong (r50.72). Fifty-two per cent of the variation in OR could be predicted from the AR as calculated by r2 (regression model). Discussion Clinically significant anterior TSDs were determined in 23.3% of surgical and 14.1% of non-surgical cases. In contrast, 20% of surgical and 13.3% of non-surgical cases presented with clinically significant overall TSDs. The differences between the surgical and non-surgical groups were not statistically significant for either anterior (P50.112) or overall (P50.243) TSDs. While Table 3
one previous study has investigated TSDs in Class II surgical subjects (Crosby and Alexander, 1989) and two have assessed TSDs in Class III surgical subjects (Sperry, 1977; Nie and Lin, 1999), this appears to be the first study to examine TSDs in a cohort of both Class II and Class III surgical patients. In our Class II surgical group, the values for both mean AR (0.763¡0.030) and mean OR (0.900¡0.025) were lower than those reported by Crosby and Alexander (1989) (0.775¡0.027 and 0.915¡0.031, respectively). Furthermore, we found an almost three times greater prevalence of overall TSDs (18.3%) in this surgical group in comparison to Crosby and Alexander (1989) (6.8%). Differences in the inclusion criteria between the studies may account for this variation. Our Class II surgical group consisted solely of Class II division 1 cases, but this was not specified by Crosby and Alexander (1989). In addition, they did not clarify the gender distribution and ethnicity of their sample. In Chinese subjects, Nie and Lin (1999) found significantly higher tooth size ratios for Class III surgical– orthodontic and orthodontic cases compared to Class II orthodontic cases. In the present study, statistically significant differences in mean AR and mean OR were noted between the Class II and Class III malocclusion groups and these were most pronounced between the surgical groups. Both mean AR (0.785¡0.027) and mean OR (0.924¡0.024) were lower than those reported by Nie and Lin (1999) (0.826¡0.026 and 0.956¡0.024, respectively). Unfortunately, Nie and Lin (1999) did not state the prevalence of clinically significant TSDs for Class III surgical cases. Variation in ethnicity between
Prevalence of clinically significant TSDs in surgical–orthodontic and orthodontic groups Anterior (%)
Class Class Class Class
II division 1 S II division 1 N-S III S III N-S
Overall (%)
F (n530)
M (n530)
All (n560)
F (n530)
M (n530)
All (n560)
16.7 13.3 23.3 16.7
30.0 16.7 23.3 10.0
23.3 15.0 23.3 13.3
20.0 6.7 23.3 16.7
16.7 13.3 20.0 16.7
18.3 10.0 21.7 16.7
S5surgical; N-S5non-surgical; F5female; M5male.
122
McSwiney et al.
Scientific Section
the groups reported on by Nie and Lin (1999) and those in our study are likely to have contributed to the differences in mean AR and mean OR (Lavelle, 1972; Smith et al., 2000; Paredes et al., 2006). No comparisons were possible with the investigation by Sperry et al. (1977) as they did not define tooth size ratios. They did, however, note that the frequency of mandibular tooth-size excess for mean OR was greater in their Class III group than in their Class II group (Sperry et al., 1977). Our findings corroborate the general trend towards higher tooth size ratios in Class III malocclusion (Nie and Lin, 1999; Alkofide and Hashim, 2002; Othman and Harradine, 2007). No statistically significant differences were found for mean AR and mean OR between the genders or for equivalent surgical and non-surgical groups. These findings concur with those of Crosby and Alexander (1989) and Nie and Lin (1999) with regard to surgical and non-surgical Class II and Class III malocclusions, respectively. Our study highlighted a strong but not perfect relationship between AR and OR (correlation coefficient: 0.72). This was similar to the value of 0.69 found by Othman and Harradine (2007). Fifty-two per cent of the variation in OR could be predicted from AR. Hence, the presence of a clinically significant anterior TSD was not always indicative of a clinically significant overall TSD and vice versa. In all the malocclusion groups, except the Class III non-surgical group, there were a greater proportion of clinically significant anterior TSDs in comparison to overall TSDs. There are limitations within this study. Firstly, only subjects from one population were included so the findings may not be generalizable to other ethnic groups; secondly, cases were selected from orthodontically referred samples rather than from a general population. The strengths of this study, however, may be considered as follows: instead of random sampling from the general population, only patients who required
JO June 2014
surgical–orthodontic or orthodontic treatment were included so the results are of greater relevance to clinicians treating patients in the former group; the Class II and Class III surgical and non-surgical groups were matched for both malocclusion type and gender; the method adopted had a high degree of reproducibility for both AR and OR and Class II division 2 surgical cases were excluded to reduce heterogeneity of the Class II sample. In addition, the sample sizes of the cohorts assessed were greater than those of previous studies, which have compared TSDs in subjects who have received treatment by surgical–orthodontic or orthodontic means (Sperry et al., 1977; Crosby and Alexander, 1989; Nie and Lin, 1999). The results of this study have implications for clinical practice. The relatively high prevalence of anterior and overall TSDs in this surgical population may complicate occlusal management. Clinicians should assess TSDs at the diagnosis and treatment planning stage for surgical cases, and where discrepancies are found, the treatment plan should be modified as necessary to resolve these. In particular, surgical cases with diminutive maxillary lateral incisors and hypodontia should receive restorative input. The identification of a TSD resulting from excessively narrow or wide teeth may also influence the extraction decision in relation to alignment (Tong et al., 2004) and decompensation. Conclusion In the cohort examined:
N N
Mean AR and mean OR differed significantly between equivalent surgical and non-surgical malocclusion groups. The prevalence of clinically significant TSDs did not differ significantly between surgical and non-surgical groups, although the highest percentage of clinically significant TSDs was recorded for AR in Class II and Class III surgical cases.
Table 4 Results of the two-way ANOVA for clinically significant anterior and overall TSDs for gender and malocclusion groups Anterior
Overall
Effect
DF
Chi-square
P value
DF
Chi-square
P value
Gender Malocclusion Gender*Malocclusion
1 3 3
0.100 3.206 1.914
0.752 0.361 0.591
1 3 3
0.056 3.144 0.922
0.813 0.370 0.820
DF5degrees of freedom. These logistic regression models enable comparisons of the proportions of patients with a certain characteristic (clinically significant anterior or overall TSDs) between different levels of one or more categorical explanatory variables (malocclusion type and genders). The interaction term in these models assesses whether the differences in proportions between malocclusion type is dependent on gender or vice versa.
JO June 2014
N
Scientific Section
AR and OR were closely related with 52% of the variation in OR predicted from AR.
Acknowledgements The authors would like to thank the Consultant Orthodontists and Specialist Orthodontists who allowed access to study model records as well as the staff at ESM Digital Solutions Ltd, Swords, Co. Dublin, Ireland, for their assistance with scanning the study models. We would also like to thank Ms Niamh Kelly for her IT support. References Alkofide E, Hashim H. Intermaxillary tooth size discrepancies among different malocclusion classes: a comparative study. J Clin Pediatr Dent 2002; 26: 383–387. Altman DG. Statistics and ethics in medical research: III How large a sample? Br Med J 1980; 281: 1336–1338. Araujo E, Souki M. Bolton anterior tooth size discrepancies among different malocclusion groups. Angle Orthod 2003; 73: 307–313. Bennett JC, McLaughlin RP. Orthodontic Management of the Dentition with the Pre-adjusted Appliance. St Louis, MO: Mosby. 2002. Bernabe E, Major PW, Flores-Mir C. Tooth-width ratio discrepancies in a sample of Peruvian adolescents. Am J Orthod Dentofacial Orthop 2004; 125: 361–365. Bishara SE, Jakobsen JR, Abdallah EM, Fernandez Garcia A. Comparisons of mesiodistal and buccolingual crown dimensions of the permanent teeth in three populations from Egypt, Mexico, and the United States. Am J Orthod Dentofacial Orthop 1989; 96: 416–422. Bolton WA. Disharmony in tooth size and its relation to the analysis and treatment of malocclusion. Angle Orthod 1958; 28: 113–130. British Standard Incisor Classification. Glossary of Dental Terms BS 4492. London: British Standard Institute. 1983. Crosby DR, Alexander CG. The occurrence of tooth size discrepancies among different malocclusion groups. Am J Orthod Dentofacial Orthop 1989; 95: 457–461. Endo T, Abe R, Kuroki H, Oka K, Shimooka S. Tooth size discrepancies among different malocclusions in a Japanese orthodontic population. Angle Orthod 2007; 78: 994–999.
TSD surgical or orthodontic
123
Freeman JE, Maskeroni AJ, Lorton L. Frequency of Bolton tooth-size discrepancies among different malocclusion groups. Am J Orthod Dentofacial Orthop 1996; 110: 24–27. Horton MH, Miller JR, Gaillard PR, Larson BE. Technique comparison for efficient orthodontic tooth measurements using digital models. Angle Orthod 2010; 80: 254–261. Keim RG, Gottlieb EL, Nelson AH, Vogels DS 3rd. JCO Orthodontic Practice Study. Part 1 Trends. J Clin Orthod 2009; 43: 625–634 Lavelle CL. Maxillary and mandibular tooth size in different racial groups and in different occlusal categories. Am J Orthod 1972; 61: 29–37. Nie Q, Lin J. Comparison of intermaxillary tooth size discrepancies among different malocclusion groups. Am J Orthod Dentofacial Orthop 1999; 116: 539–544. O’Mahony G, Millett DT, Barry MK, McIntyre GT, Cronin MS. Tooth size discrepancies in Irish orthodontic patients among different malocclusion groups. Angle Orthod 2011; 81: 130–133. Othman SA, Harradine NW. Tooth size discrepancies in an orthodontic population. Angle Orthod 2007; 77: 668–674. Paredes V, Gandia JL, Cibrian R. Do Bolton’s ratios apply to a Spanish population? Am J Orthod Dentofacial Orthop 2006; 129: 428–430. Proffit WR. Contemporary Orthodontics. 3rd edn. St Louis, MO: Mosby, 2000. p. 170. Santoro M, Ayoub ME, Pardi VA, Cangialosi TL. Mesiodistal crown dimensions and tooth size discrepancy of the permanent dentition of Dominican Americans. Angle Orthod 2000; 70: 303–307. Smith SS, Buschang PH, Watanabe E. Interarch tooth size relationships of 3 populations: ‘does Bolton’s analysis apply?’. Am J Orthod Dentofacial Orthop 2000; 117: 169–174. Sperry TP, Worms FW, Isaacson RJ. Tooth size discrepancy in mandibular prognathism. Am J Orthod 1977; 72: 183–190. Springate SD. The effect of sample size and bias on the reliability of estimates of error: a comparative study of Dahlberg’s formula. Eur J Orthod 2012; 34: 158–163. Strujic M, Anic-Milosevic S, Mestrovic S, Slaj M. Tooth size discrepancy in orthodontic patients among different malocclusion groups. Eur J Orthod 2009; 31: 584–589. Ta TA, Ling JY, Hagg U. Tooth-size discrepancies among different occlusion groups of southern Chinese children. Am J Orthod Dentofacial Orthop 2001; 120: 556–558. Tong H, Chen D, Xu L, Liu P. The effect of premolar extractions on tooth size discrepancies. Angle Orthod 2004; 74: 508–511. Uysal T, Sari Z. Intermaxillary tooth size discrepancy and mesiodistal crown dimensions for a Turkish population. Am J Orthod Dentofacial Orthop 2005; 128: 226–230.
