Patterns of vertical facial growth in Korean adolescents analyzed with mixed-effects regression analysis Sung-Chul Moon, a Hong-Kyun Kim, b Taek-Ka Kwon, c Seong Ho Han, d Chang-Hyeon An, e and Young-Seok Park f Seoul, Suwon, and Daegu, Korea Introduction: To understand the growth patterns of skeletal open bite and deepbite, we present observations from 9 years of pure longitudinal data based on lateral cephalometric radiographs using mixed-effects regression model analysis. Methods: In total, 51 children (14 years old) with extreme values for the ratio of lower anterior facial height to total anterior facial height were assigned to 1 of 2 groups: a skeletal open-bite group (11 boys, 14 girls) or a skeletal deepbite group (14 boys, 12 girls). Measurements of total anterior facial height, upper anterior facial height, lower anterior facial height, total posterior facial height, ramus height, and ratio of lower anterior facial height to total anterior facial height were obtained for all subjects. All data were analyzed and interpreted using a mixed-effects regression model analysis with random effects. Results: From these 4 groups at 14 years old, statistically significant differences were observed between the groups when subjects of the same sex were compared; however, statistical significance was not reached between sub- jects of opposite sexes in each group. Morphologic differences were clearly evident from the start and became more pronounced with age. There were statistical significances in the initial values and increases with age in all 6 variables except for increases with age in the ratio of lower anterior facial height to total anterior facial height. Statistical significance was also reached for morphologic differences between the annual increases in the ratio of lower anterior facial height to total anterior facial height and lower anterior facial height. In general, individual random variability was high in all variables when compared with the annual changes over time. Conclusions: Divergent patterns were established early and became more pronounced with age, with anterior facial height dimensions primarily contributing to these differences. Individual variations were so pronounced that caution is recommended for all clinical decisions. (Am J Orthod Dentofacial Orthop 2013;143:810-8) O rthodontic practice is founded on understanding the growth of the face, not only where growth occurs but also when it occurs or ceases to oc- cur. 1 The pattern of vertical growth as a component of facial growth has become a topic of great interest 2-4 to orthodontists, because failure of its control often causes compromised results, and extreme vertical deficiency or excess requires surgical intervention. 5-7 Vertical skeletal patterns have frequently been studied in the context of overbite in the orthodontic literature, 8,9 although controversy still exists regarding the relationship between these 2 phenomena. 10,11 Dentoalveolar compensations for abnormal vertical patterns have also been demonstrated. 8,12,13 Skeletal open bite and skeletal deepbite—alternatively termed long-face syndrome or hyperdivergent, and short-face syndrome or hypodivergent—are 2 distinct facial morphologies associated with the most common form of vertical dysplasia. 14,15 To better understand the growth patterns in patients with vertical dysplasia according to the morphologic classifications, an a Clinical associate professor, Department of Orthodontics, School of Dentistry, Seoul National University, Seoul, Korea; private practice, Suwon, Korea. b Postgraduate student, Department of Oral Anatomy, Dental Research Institute and School of Dentistry, Seoul National University, Seoul, Korea. c Assistant professor, Division of Prosthodontics, Department of Dentistry, St Vincent Hospital, Catholic University of Korea, Suwon, Korea. d Assistant professor, Division of Orthodontics, Department of Dentistry, St Vincent Hospital, Catholic University of Korea, Suwon, Korea. e Associate professor, Department of Oral and Maxillofacial Radiology, School of Dentistry, Kyungpook National University, Daegu, Korea. f Assistant professor, Department of Oral Anatomy, Dental Research Institute and School of Dentistry, Seoul National University, Seoul, Korea. Sung-Chul Moon and Hong-Kyun Kim are joint first authors and contributed equally to this work. The authors report no commercial, proprietary, or financial interest in the products or companies described in this article. Supported by Bumsuk Academic Research Fund in 2011. Reprint requests to: Young-Seok Park, Department of Oral Anatomy, Dental Research Institute and School of Dentistry, Seoul National University, 275-1 Yeongeon-Dong, Jongro-Gu, Seoul 110-768, Korea (ROK); e-mail, ayoayo7@ snu.ac.kr. Submitted, August 2012; revised and accepted, January 2013. 0889-5406/$36.00 Copyright Ó 2013 by the American Association of Orthodontists. http://dx.doi.org/10.1016/j.ajodo.2013.01.016 810 ORIGINAL ARTICLE
Patterns of vertical facial growth in Korean adolescents analyzed with mixed-effects regression analysis
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Patterns of vertical facial growth in Korean adolescents analyzed with mixed-effects regression analysisPatterns of vertical facial growth in Korean adolescents analyzed with mixed-effects regression analysis
Sung-Chul Moon,a Hong-Kyun Kim,b Taek-Ka Kwon,c Seong Ho Han,d Chang-Hyeon An,e and Young-Seok Parkf
Seoul, Suwon, and Daegu, Korea
aClini Seoul bPost and S cAssis St Vin dAssis St Vin eAsso Denti fAssis Schoo Sung- equal The a produ Suppo Reprin Resea Yeong snu.a Subm 0889- Copyr http:/
810
Introduction: To understand the growth patterns of skeletal open bite and deepbite, we present observations from 9 years of pure longitudinal data based on lateral cephalometric radiographs using mixed-effects regressionmodel analysis.Methods: In total, 51 children (14 years old) with extreme values for the ratio of lower anterior facial height to total anterior facial height were assigned to 1 of 2 groups: a skeletal open-bite group (11 boys, 14 girls) or a skeletal deepbite group (14 boys, 12 girls). Measurements of total anterior facial height, upper anterior facial height, lower anterior facial height, total posterior facial height, ramus height, and ratio of lower anterior facial height to total anterior facial height were obtained for all subjects. All data were analyzed and interpreted using a mixed-effects regression model analysis with random effects. Results: From these 4 groups at 14 years old, statistically significant differences were observed between the groups when subjects of the same sex were compared; however, statistical significance was not reached between sub- jects of opposite sexes in each group. Morphologic differences were clearly evident from the start and became more pronouncedwith age. There were statistical significances in the initial values and increases with age in all 6 variables except for increases with age in the ratio of lower anterior facial height to total anterior facial height. Statistical significance was also reached for morphologic differences between the annual increases in the ratio of lower anterior facial height to total anterior facial height and lower anterior facial height. In general, individual random variability was high in all variables when compared with the annual changes over time. Conclusions: Divergent patterns were established early and became more pronounced with age, with anterior facial height dimensions primarily contributing to these differences. Individual variations were so pronounced that caution is recommended for all clinical decisions. (Am J Orthod Dentofacial Orthop 2013;143:810-8)
cal associate professor, Department of Orthodontics, School of Dentistry, National University, Seoul, Korea; private practice, Suwon, Korea. graduate student, Department of Oral Anatomy, Dental Research Institute chool of Dentistry, Seoul National University, Seoul, Korea. tant professor, Division of Prosthodontics, Department of Dentistry, cent Hospital, Catholic University of Korea, Suwon, Korea. tant professor, Division of Orthodontics, Department of Dentistry, cent Hospital, Catholic University of Korea, Suwon, Korea. ciate professor, Department of Oral and Maxillofacial Radiology, School of stry, Kyungpook National University, Daegu, Korea. tant professor, Department of Oral Anatomy, Dental Research Institute and l of Dentistry, Seoul National University, Seoul, Korea. Chul Moon and Hong-Kyun Kim are joint first authors and contributed ly to this work. uthors report no commercial, proprietary, or financial interest in the cts or companies described in this article. rted by Bumsuk Academic Research Fund in 2011. t requests to: Young-Seok Park, Department of Oral Anatomy, Dental rch Institute and School of Dentistry, Seoul National University, 275-1 eon-Dong, Jongro-Gu, Seoul 110-768, Korea (ROK); e-mail, ayoayo7@ c.kr. itted, August 2012; revised and accepted, January 2013. 5406/$36.00 ight 2013 by the American Association of Orthodontists. /dx.doi.org/10.1016/j.ajodo.2013.01.016
Orthodontic practice is founded on understanding the growth of the face, not only where growth occurs but also when it occurs or ceases to oc-
cur.1 The pattern of vertical growth as a component of facial growth has become a topic of great interest2-4 to orthodontists, because failure of its control often causes compromised results, and extreme vertical deficiency or excess requires surgical intervention.5-7
Vertical skeletal patterns have frequently been studied in the context of overbite in the orthodontic literature,8,9 although controversy still exists regarding the relationship between these 2 phenomena.10,11
Dentoalveolar compensations for abnormal vertical patterns have also been demonstrated.8,12,13
Skeletal open bite and skeletal deepbite—alternatively termed long-face syndrome or hyperdivergent, and short-face syndrome or hypodivergent—are 2 distinct facial morphologies associated with the most common form of vertical dysplasia.14,15 To better understand the growth patterns in patients with vertical dysplasia according to the morphologic classifications, an
Moon et al 811
analysis of adequate longitudinal samples would be particularly relevant. However, only a limited number of such longitudinal studies1,14,16-28 have evaluated vertical facial growth patterns to date, because these data are difficult to collect.1 Moreover, most study cohorts were composed of subjects of European descent.
Of the several studies mentioned above, the excellent quantification study by Nanda25 demonstrates several linear dimensions of facial vertical change in extreme facial types between childhood and early adulthood on a longitudinal basis. In this study, the subjects were recruited from the Denver Child Growth Study, which included 250 subjects. Of these, 32 were ultimately selected and divided equally into 4 groups—each with 8 subjects—of the most extreme values at both ends of the distribution: open-bite female, open-bite male, deepbite female, and deepbite male. We then statistically calculated the average values for the measured parame- ters, graphically concluding that whereas the anterior dimensions of the face have morphologically divergent patterns of development, no variation in the posterior dimension was observed between the 2 groups. Further- more, this study provided many valuable insights and meaningful clinical implications regarding vertical growth patterns.
Although longitudinal data provide significantly more information than cross-sectional counterparts, they are not easy to interpret properly. To develop a more general approach to analyzing longitudinal data with more realistic assumptions regarding the longitudinal change and the associated missing data, a wide variety of more rigorous approaches has been developed.29 Of these, the mixed-effects regression model is widely used30 because it can determine individual random variability that is not explained by conventional descriptive statistics.31,32
The aim of this study was to compare facial growth changes among patients with hypodivergent and hyperdivergent patterns. Specifically, we analyzed longitudinal cephalometric data from children with those patterns from the ages of 6 to 14 years. Moreover, unlike prior studies, we used the mixed-effects regres- sion model to analyze data from Korean adolescents.
MATERIAL AND METHODS
This study was conducted under the auspices of the Korean Dental Growth Study, which occurred from 1995 to 2003, with the exception of 1999, when the study was temporarily suspended because of financial problems. All subjects were of Korean origin and from the northern province of Gyeonggi-do. In total, 410 subjects were enrolled, of whom 223 had full sets of cephalometric radiographs during the study period.
American Journal of Orthodontics and Dentofacial Orthoped
All subjects were healthy and without systemic diseases or developmental anomalies. Lateral cephalometric radiographs from these children (107 boys, 116 girls) were made annually from the ages of 6 to 14 years, with the exception of the 10th year. No subject had received any treatment that interfered with growth or had a history of orthodontic treatment before or during the observation period. The parents or guardians of all subjects provided written informed consent. Before enrollment, the institutional review board for the protection of human subjects of the School of Dentistry, Seoul National University, reviewed and approved the re- search protocol (S-D2010013).
All radiographs were traced by 1 observer (Y.S.P.) to eliminate interexaminer variability and were analyzed us- ing Vceph (version 6.0; Osstem, Seoul, Korea). As in the study of Nanda,25 a total of 5 linear distances were mea- sured for use as discriminators of vertical facial dysplasia. The measured distance parameters were defined as fol- lows (Fig 1): (1) total anterior face height, nasion to men- ton; (2) upper anterior face height, nasion, to anterior nasal spine; (3) lower anterior face height, anterior nasal spine to menton; (4) total posterior face height, sella to gonion; and (5) ramal height, articulare to gonion.
In selecting hypodivergent (deepbite) and hyperdi- vergent (open bite) subjects, the protocol from a previous study was followed with some modification.25 We selected the records at age 14 years and then looked back to see how early the growth pattern was established. One radiograph obtained at 14 years of age was used for the final measurements, since it represented each subject's most mature state. All
ics June 2013 Vol 143 Issue 6
812 Moon et al
subjects were selected from the aforementioned cohort of 223 subjects on the basis of the ratio of lower anterior face height to total anterior face height, with some exhibiting the most extreme values at both ends of the distribution (ie, .1 SD from the mean) were selected to create 4 groups, instead of 8 subjects in each group as in the previous study.25 In the end, 11 boys with open bite, 14 girls with open bite, 14 boys with deepbite, and 12 girls with deepbite were selected for this study. The terms “open” and “deep” were used for the sake of comparison with the study of Nanda,25 although these do not indicate dental open bite or deepbite but, rather, the skeletal tendency.
All data were analyzed by both graphic and statistical methods to present individual as well as group findings (Fig 2). Descriptive statistics for each group were calculated at each age to characterize yearly absolute values and relative percentages to the final measurements of the 5 dimensions and 1 ratio between the ages of 6 and 14 years. Since the serial measurements were correlated according to the individual subjects, a mixed-effects regression model was used for the following analysis model: yijk 5 m 1 b1 sexi 1 b2 groupij 1 b3 ageijk 1 b4 sexi * groupij 1 b5 sexi * ageijk 1 b6 groupij * ageijk 1 b7 sexi * groupij * ageijk 1 bij 1 bij2 * ageij 1 eijk, where m represents total mean; b1, sex effect; b2, group effect; b3, age effect; b4, interaction effect between sex and group; b5, interaction effect between sex and age; b6, interaction effect be- tween group and age; b7, interaction effect among sex, group, and age; and bi (i5 1, 2, . . ., 51), the random effect by each subject. Comparisons between sexes and groups at each age were performed. All statistical analy- ses were performed using the language R, and P values less than 0.05 were predetermined as statistically signif- icant, although they were also assessed at the 0.01 level of confidence.
RESULTS
Intraexaminer reliability coefficients ranged from 0.965 to 0.983. In terms of root mean square values, the random errors of estimation were less than 0.42 mm. No variables were significantly different between the test and retest measurements.
The means, standard deviations, and ranges of the ratio of lower anterior face height to total anterior face height at the age of 14 years are shown in Table I for the entire cohort of 223 subjects and the 4 selected groups. From the 4 groups, statistically significant differences were observed between the same-sex groups, although not between the opposite sexes within each group. Descriptive statistics at each age regarding the
June 2013 Vol 143 Issue 6 American
5 measured distance variables as well as the ratio of lower anterior face height to total anterior face height are reported in Tables II-IV.
A graphic representation of the mean absolute growth curves for the 6 variables is given in Figure 2, with the ratio of lower anterior face height to total anterior face height growth curve exhibiting some fluctuations. Morphologic differences clearly evident at the first measurement became more pronounced with age. Except at the age of 8 years, there were no statisti- cally significant differences between the sexes. However, there were significant differences between groups at all ages (Table IV). The male and female open-bite curves were nearly congruent during the entire study period, whereas the male and female deepbite curves came together at the end.
In contrast to the ratio of lower anterior face height to total anterior face height curve, the total anterior face height curves exhibited classic sexual dimorphism. There were significant differences between the sexes and between the groups at all ages (Table II). The differ- ences between the sexes were greater in the open-bite groups than in deepbite groups. Between the ages of 8 and 12 years, the female open-bite curve was positioned higher than the male deepbite curve, suggesting that morphologic factors are more pronounced than a normal sexual difference.
In the upper anterior face height curve, the value of the deepbite in male subjects exceeded that of the open bite in males, resulting in a cross between their open-bite and deepbite curves. However, the female groups exhibited a distinct difference from the first measurement that became more pronounced with age.
The lower anterior face height curves also exhibited both morphologic and sexual differences clearly in the graph, although the former were greater than the latter and became more so with advancing age.
In contrast to the anterior facial dimensions aforementioned, the total posterior face height curves were not segregated by type for either sex; only sexual differences were evident. The ramus height curves were well clustered and lacked prominent morphologic or sexual differences. There were no significant differences between the sexes or between the groups (Table III). Descriptive statistics of the relative percentages to the final measurements for each group at each age were basically similar to the absolute values.
The results of the mixed-effects regression model analysis are summarized in Tables V and VI. As components of the fixed effects, statistically significant differences in the initial values and increases with age in all 6 variables were observed, with the exception of an increase with age in the ratio of lower anterior face
Journal of Orthodontics and Dentofacial Orthopedics
Fig 2. Graphic representation of mean absolute curves of growth for the 6 measured variables for subjects with open bite and deepbite segregated by sex.
Moon et al 813
American Journal of Orthodontics and Dentofacial Orthopedics June 2013 Vol 143 Issue 6
Table I. Comparison of the ratio of lower anterior facial height to total anterior facial height for the open-bite and deepbite groups of 14-year-old subjects
Boys Girls
n Mean SD Range n Mean SD Range Deepbite 14 0.537 0.017 0.523-0.542 12 0.539 0.010 0.526-0.553 Open bite 11 0.588 0.007 0.581-0.601 14 0.588 0.006 0.580-0.603 Total subjects 107 0.561 0.018 0.523-0.601 116 0.561 0.018 0.526-0.603
There were statistically significant differences between the morphologic groups in the sexes (P\0.01) and no statistically significant differences between the sexes in the same morphologic group.
Table II. Descriptive statistics regarding anterior facial height dimensions (mm) according to age and group
Group Male open bite Female open bite Male deepbite Female deepbite
Age Mean SD Mean SD Mean SD Mean SD Total anterior facial height 6*,y 113.60 5.48 108.34 3.82 108.39 3.38 105.51 2.57 7*,y 116.09 5.51 110.06 4.27 110.22 4.42 108.46 3.57 8z,§ 118.36 6.39 112.97 4.28 112.91 4.66 110.76 3.40 9*,y 121.08 6.35 115.30 4.45 114.76 4.45 113.20 3.55 11*,§ 126.79 6.87 122.39 5.09 120.06 5.36 118.94 4.64 12*,y 130.26 7.68 124.50 4.86 123.52 5.53 120.11 3.78 13y,z 133.28 8.64 126.89 5.82 127.54 5.58 122.65 3.71 14*,y 137.54 8.96 128.08 5.11 131.64 5.50 123.54 3.54
Upper anterior facial height 6 48.86 3.75 46.59 1.57 48.84 1.69 49.19 1.99 7 50.48 2.48 47.84 2.34 50.12 2.68 50.51 2.37 8 52.36 2.74 49.19 2.60 51.42 2.08 52.34 1.85 9 53.67 2.39 50.67 2.26 52.56 1.67 53.50 1.99 11 55.94 3.15 52.86 2.95 55.11 1.81 56.16 1.88 12 57.33 2.48 53.69 3.13 57.41 3.08 57.03 1.81 13*,y 58.37 2.90 54.45 3.37 60.03 2.75 58.71 1.35 14*,y 59.41 3.27 54.84 2.72 62.15 3.34 59.45 1.17
Lower anterior facial height 6*,y 66.85 2.76 63.47 2.91 61.16 2.83 58.02 1.93 7*,y 67.82 3.78 63.92 2.80 61.88 3.41 59.18 2.13 8*,y 68.93 4.28 65.39 2.73 63.05 3.56 59.51 2.30 9*,y 70.29 4.24 66.53 3.23 64.03 4.00 61.30 2.36 11*,§ 73.13 4.63 71.06 3.32 65.70 4.23 63.43 2.89 12*,y 75.94 5.06 72.52 3.12 67.78 4.20 64.47 2.68 13*,y 77.48 6.20 74.16 3.56 69.12 4.23 65.28 3.34 14*,y 80.94 5.77 75.26 3.27 70.71 3.77 66.55 2.66
*Statistically significant differences between groups (P\0.01); ystatistically significant differences between sexes (P\0.01); zstatistically signif- icant differences between groups (P\0.05); §statistically significant differences between sexes (P\0.05).
814 Moon et al
height to total anterior face height. Statistical significance was also reached in the morphologic differences of annual increases in the ratio of lower anterior face height to total anterior face height and lower anterior face height (P \0.01), both annual increases with regard to sexual difference and the interaction of sexual and morphologic difference for upper anterior face height (P \0.05). In terms of the effect of individual random variability, this was relatively large when compared with the annual
June 2013 Vol 143 Issue 6 American
change over time for all variables (minimum, 7.62; maximum, 16.24 times greater).
DISCUSSION
In our study, the sexual and morphologic differences of 6 distance-related variables were evaluated from 9 years of longitudinal cephalometric data from subjects with skeletal open bites and deepbites. Since it is difficult to collect eligible samples for longitudinal studies related to human growth, there is a shortage of pure
Journal of Orthodontics and Dentofacial Orthopedics
Table III. Descriptive statistics regarding posterior facial height dimensions (mm) according to age and group
Group Male open bite Female open bite Male deepbite Female deepbite
Age Mean SD Mean SD Mean SD Mean SD Total anterior facial height 6* 70.75 4.12 67.45 3.09 70.29 3.01 67.26 2.70 7* 72.21 4.12 68.28 3.17 71.44 2.60 69.35 2.87 8y 73.41 4.93 70.15 3.43 72.73 2.48 71.17 2.92 9y 75.56 5.30 71.91 3.77 74.84 2.91 73.51 3.71 11y 79.46 6.02 77.49 5.01 79.11 3.97 78.75 4.51 12y 82.96 5.54 80.10 4.97 82.56 4.58 80.85 3.69 13* 86.82 7.47 81.49 4.76 86.26 4.70 82.17 4.51 14* 89.36 6.47 82.47 4.41 89.69 4.59 83.03 4.42
Ramus height 6 41.49 2.87 39.51 3.15 40.75 2.52 40.11 2.56 7 41.96 2.53 40.26 2.57 41.94 2.55 41.29 2.87 8 42.90 2.77 41.11 2.87 42.72 2.48 41.76 3.24 9 44.47 3.44 41.87 2.72 44.43 3.08 42.91 3.01 11 46.24 3.39 45.66 3.77 46.44 3.07 47.11 4.36 12 48.09 3.34 47.28 3.39 48.90 3.80 48.65 4.27 13 51.35 4.15 49.20 3.89 51.41 4.26 50.06 6.05 14y 52.09 4.28 49.77 3.59 53.86 4.75 50.99 5.79
*Statistically significant differences between sexes (P\0.01); ystatistically significant differences between sexes (P\0.05).
Table IV. Descriptive statistics regarding the ratio of lower anterior facial height to total anterior facial height accord- ing to age and group
Group Male open bite Female open bite Male deepbite Female deepbite
Age Mean SD Mean SD Mean SD Mean SD 6* 0.589 0.014 0.586 0.014 0.564 0.016 0.550 0.013 7* 0.584 0.014 0.581 0.012 0.561 0.018 0.546 0.010 8*,y 0.583 0.027 0.579 0.015 0.558 0.014 0.537 0.014 9* 0.580 0.013 0.577 0.013 0.558 0.020 0.542 0.014 11* 0.576 0.015 0.581 0.012 0.547 0.017 0.533 0.012 12* 0.583 0.014 0.583 0.014 0.549 0.021 0.536 0.011 13* 0.581 0.016 0.58 0.015 0.542 0.017 0.532 0.016 14* 0.588 0.008 0.59 0.006 0.537 0.017 0.538 0.010
*Statistically significant differences between groups (P\0.01); ystatistically significant differences between sexes (P\0.05).
Moon et al 815
longitudinal reports.33 In the case of cephalometric radiographs, repeated radiologic exposures of healthy subjects could be considered unethical despite the abundant information they can provide. On the other hand, once they have been taken, it would be unethical not to use them for the good of the orthodontic community worldwide. The data used in this study were gathered from 1995 to 2003.
Although a mixed-effects regression model has the advantage of being able to analyze data with missing values, data with missing values were excluded from this…
Sung-Chul Moon,a Hong-Kyun Kim,b Taek-Ka Kwon,c Seong Ho Han,d Chang-Hyeon An,e and Young-Seok Parkf
Seoul, Suwon, and Daegu, Korea
aClini Seoul bPost and S cAssis St Vin dAssis St Vin eAsso Denti fAssis Schoo Sung- equal The a produ Suppo Reprin Resea Yeong snu.a Subm 0889- Copyr http:/
810
Introduction: To understand the growth patterns of skeletal open bite and deepbite, we present observations from 9 years of pure longitudinal data based on lateral cephalometric radiographs using mixed-effects regressionmodel analysis.Methods: In total, 51 children (14 years old) with extreme values for the ratio of lower anterior facial height to total anterior facial height were assigned to 1 of 2 groups: a skeletal open-bite group (11 boys, 14 girls) or a skeletal deepbite group (14 boys, 12 girls). Measurements of total anterior facial height, upper anterior facial height, lower anterior facial height, total posterior facial height, ramus height, and ratio of lower anterior facial height to total anterior facial height were obtained for all subjects. All data were analyzed and interpreted using a mixed-effects regression model analysis with random effects. Results: From these 4 groups at 14 years old, statistically significant differences were observed between the groups when subjects of the same sex were compared; however, statistical significance was not reached between sub- jects of opposite sexes in each group. Morphologic differences were clearly evident from the start and became more pronouncedwith age. There were statistical significances in the initial values and increases with age in all 6 variables except for increases with age in the ratio of lower anterior facial height to total anterior facial height. Statistical significance was also reached for morphologic differences between the annual increases in the ratio of lower anterior facial height to total anterior facial height and lower anterior facial height. In general, individual random variability was high in all variables when compared with the annual changes over time. Conclusions: Divergent patterns were established early and became more pronounced with age, with anterior facial height dimensions primarily contributing to these differences. Individual variations were so pronounced that caution is recommended for all clinical decisions. (Am J Orthod Dentofacial Orthop 2013;143:810-8)
cal associate professor, Department of Orthodontics, School of Dentistry, National University, Seoul, Korea; private practice, Suwon, Korea. graduate student, Department of Oral Anatomy, Dental Research Institute chool of Dentistry, Seoul National University, Seoul, Korea. tant professor, Division of Prosthodontics, Department of Dentistry, cent Hospital, Catholic University of Korea, Suwon, Korea. tant professor, Division of Orthodontics, Department of Dentistry, cent Hospital, Catholic University of Korea, Suwon, Korea. ciate professor, Department of Oral and Maxillofacial Radiology, School of stry, Kyungpook National University, Daegu, Korea. tant professor, Department of Oral Anatomy, Dental Research Institute and l of Dentistry, Seoul National University, Seoul, Korea. Chul Moon and Hong-Kyun Kim are joint first authors and contributed ly to this work. uthors report no commercial, proprietary, or financial interest in the cts or companies described in this article. rted by Bumsuk Academic Research Fund in 2011. t requests to: Young-Seok Park, Department of Oral Anatomy, Dental rch Institute and School of Dentistry, Seoul National University, 275-1 eon-Dong, Jongro-Gu, Seoul 110-768, Korea (ROK); e-mail, ayoayo7@ c.kr. itted, August 2012; revised and accepted, January 2013. 5406/$36.00 ight 2013 by the American Association of Orthodontists. /dx.doi.org/10.1016/j.ajodo.2013.01.016
Orthodontic practice is founded on understanding the growth of the face, not only where growth occurs but also when it occurs or ceases to oc-
cur.1 The pattern of vertical growth as a component of facial growth has become a topic of great interest2-4 to orthodontists, because failure of its control often causes compromised results, and extreme vertical deficiency or excess requires surgical intervention.5-7
Vertical skeletal patterns have frequently been studied in the context of overbite in the orthodontic literature,8,9 although controversy still exists regarding the relationship between these 2 phenomena.10,11
Dentoalveolar compensations for abnormal vertical patterns have also been demonstrated.8,12,13
Skeletal open bite and skeletal deepbite—alternatively termed long-face syndrome or hyperdivergent, and short-face syndrome or hypodivergent—are 2 distinct facial morphologies associated with the most common form of vertical dysplasia.14,15 To better understand the growth patterns in patients with vertical dysplasia according to the morphologic classifications, an
Moon et al 811
analysis of adequate longitudinal samples would be particularly relevant. However, only a limited number of such longitudinal studies1,14,16-28 have evaluated vertical facial growth patterns to date, because these data are difficult to collect.1 Moreover, most study cohorts were composed of subjects of European descent.
Of the several studies mentioned above, the excellent quantification study by Nanda25 demonstrates several linear dimensions of facial vertical change in extreme facial types between childhood and early adulthood on a longitudinal basis. In this study, the subjects were recruited from the Denver Child Growth Study, which included 250 subjects. Of these, 32 were ultimately selected and divided equally into 4 groups—each with 8 subjects—of the most extreme values at both ends of the distribution: open-bite female, open-bite male, deepbite female, and deepbite male. We then statistically calculated the average values for the measured parame- ters, graphically concluding that whereas the anterior dimensions of the face have morphologically divergent patterns of development, no variation in the posterior dimension was observed between the 2 groups. Further- more, this study provided many valuable insights and meaningful clinical implications regarding vertical growth patterns.
Although longitudinal data provide significantly more information than cross-sectional counterparts, they are not easy to interpret properly. To develop a more general approach to analyzing longitudinal data with more realistic assumptions regarding the longitudinal change and the associated missing data, a wide variety of more rigorous approaches has been developed.29 Of these, the mixed-effects regression model is widely used30 because it can determine individual random variability that is not explained by conventional descriptive statistics.31,32
The aim of this study was to compare facial growth changes among patients with hypodivergent and hyperdivergent patterns. Specifically, we analyzed longitudinal cephalometric data from children with those patterns from the ages of 6 to 14 years. Moreover, unlike prior studies, we used the mixed-effects regres- sion model to analyze data from Korean adolescents.
MATERIAL AND METHODS
This study was conducted under the auspices of the Korean Dental Growth Study, which occurred from 1995 to 2003, with the exception of 1999, when the study was temporarily suspended because of financial problems. All subjects were of Korean origin and from the northern province of Gyeonggi-do. In total, 410 subjects were enrolled, of whom 223 had full sets of cephalometric radiographs during the study period.
American Journal of Orthodontics and Dentofacial Orthoped
All subjects were healthy and without systemic diseases or developmental anomalies. Lateral cephalometric radiographs from these children (107 boys, 116 girls) were made annually from the ages of 6 to 14 years, with the exception of the 10th year. No subject had received any treatment that interfered with growth or had a history of orthodontic treatment before or during the observation period. The parents or guardians of all subjects provided written informed consent. Before enrollment, the institutional review board for the protection of human subjects of the School of Dentistry, Seoul National University, reviewed and approved the re- search protocol (S-D2010013).
All radiographs were traced by 1 observer (Y.S.P.) to eliminate interexaminer variability and were analyzed us- ing Vceph (version 6.0; Osstem, Seoul, Korea). As in the study of Nanda,25 a total of 5 linear distances were mea- sured for use as discriminators of vertical facial dysplasia. The measured distance parameters were defined as fol- lows (Fig 1): (1) total anterior face height, nasion to men- ton; (2) upper anterior face height, nasion, to anterior nasal spine; (3) lower anterior face height, anterior nasal spine to menton; (4) total posterior face height, sella to gonion; and (5) ramal height, articulare to gonion.
In selecting hypodivergent (deepbite) and hyperdi- vergent (open bite) subjects, the protocol from a previous study was followed with some modification.25 We selected the records at age 14 years and then looked back to see how early the growth pattern was established. One radiograph obtained at 14 years of age was used for the final measurements, since it represented each subject's most mature state. All
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812 Moon et al
subjects were selected from the aforementioned cohort of 223 subjects on the basis of the ratio of lower anterior face height to total anterior face height, with some exhibiting the most extreme values at both ends of the distribution (ie, .1 SD from the mean) were selected to create 4 groups, instead of 8 subjects in each group as in the previous study.25 In the end, 11 boys with open bite, 14 girls with open bite, 14 boys with deepbite, and 12 girls with deepbite were selected for this study. The terms “open” and “deep” were used for the sake of comparison with the study of Nanda,25 although these do not indicate dental open bite or deepbite but, rather, the skeletal tendency.
All data were analyzed by both graphic and statistical methods to present individual as well as group findings (Fig 2). Descriptive statistics for each group were calculated at each age to characterize yearly absolute values and relative percentages to the final measurements of the 5 dimensions and 1 ratio between the ages of 6 and 14 years. Since the serial measurements were correlated according to the individual subjects, a mixed-effects regression model was used for the following analysis model: yijk 5 m 1 b1 sexi 1 b2 groupij 1 b3 ageijk 1 b4 sexi * groupij 1 b5 sexi * ageijk 1 b6 groupij * ageijk 1 b7 sexi * groupij * ageijk 1 bij 1 bij2 * ageij 1 eijk, where m represents total mean; b1, sex effect; b2, group effect; b3, age effect; b4, interaction effect between sex and group; b5, interaction effect between sex and age; b6, interaction effect be- tween group and age; b7, interaction effect among sex, group, and age; and bi (i5 1, 2, . . ., 51), the random effect by each subject. Comparisons between sexes and groups at each age were performed. All statistical analy- ses were performed using the language R, and P values less than 0.05 were predetermined as statistically signif- icant, although they were also assessed at the 0.01 level of confidence.
RESULTS
Intraexaminer reliability coefficients ranged from 0.965 to 0.983. In terms of root mean square values, the random errors of estimation were less than 0.42 mm. No variables were significantly different between the test and retest measurements.
The means, standard deviations, and ranges of the ratio of lower anterior face height to total anterior face height at the age of 14 years are shown in Table I for the entire cohort of 223 subjects and the 4 selected groups. From the 4 groups, statistically significant differences were observed between the same-sex groups, although not between the opposite sexes within each group. Descriptive statistics at each age regarding the
June 2013 Vol 143 Issue 6 American
5 measured distance variables as well as the ratio of lower anterior face height to total anterior face height are reported in Tables II-IV.
A graphic representation of the mean absolute growth curves for the 6 variables is given in Figure 2, with the ratio of lower anterior face height to total anterior face height growth curve exhibiting some fluctuations. Morphologic differences clearly evident at the first measurement became more pronounced with age. Except at the age of 8 years, there were no statisti- cally significant differences between the sexes. However, there were significant differences between groups at all ages (Table IV). The male and female open-bite curves were nearly congruent during the entire study period, whereas the male and female deepbite curves came together at the end.
In contrast to the ratio of lower anterior face height to total anterior face height curve, the total anterior face height curves exhibited classic sexual dimorphism. There were significant differences between the sexes and between the groups at all ages (Table II). The differ- ences between the sexes were greater in the open-bite groups than in deepbite groups. Between the ages of 8 and 12 years, the female open-bite curve was positioned higher than the male deepbite curve, suggesting that morphologic factors are more pronounced than a normal sexual difference.
In the upper anterior face height curve, the value of the deepbite in male subjects exceeded that of the open bite in males, resulting in a cross between their open-bite and deepbite curves. However, the female groups exhibited a distinct difference from the first measurement that became more pronounced with age.
The lower anterior face height curves also exhibited both morphologic and sexual differences clearly in the graph, although the former were greater than the latter and became more so with advancing age.
In contrast to the anterior facial dimensions aforementioned, the total posterior face height curves were not segregated by type for either sex; only sexual differences were evident. The ramus height curves were well clustered and lacked prominent morphologic or sexual differences. There were no significant differences between the sexes or between the groups (Table III). Descriptive statistics of the relative percentages to the final measurements for each group at each age were basically similar to the absolute values.
The results of the mixed-effects regression model analysis are summarized in Tables V and VI. As components of the fixed effects, statistically significant differences in the initial values and increases with age in all 6 variables were observed, with the exception of an increase with age in the ratio of lower anterior face
Journal of Orthodontics and Dentofacial Orthopedics
Fig 2. Graphic representation of mean absolute curves of growth for the 6 measured variables for subjects with open bite and deepbite segregated by sex.
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American Journal of Orthodontics and Dentofacial Orthopedics June 2013 Vol 143 Issue 6
Table I. Comparison of the ratio of lower anterior facial height to total anterior facial height for the open-bite and deepbite groups of 14-year-old subjects
Boys Girls
n Mean SD Range n Mean SD Range Deepbite 14 0.537 0.017 0.523-0.542 12 0.539 0.010 0.526-0.553 Open bite 11 0.588 0.007 0.581-0.601 14 0.588 0.006 0.580-0.603 Total subjects 107 0.561 0.018 0.523-0.601 116 0.561 0.018 0.526-0.603
There were statistically significant differences between the morphologic groups in the sexes (P\0.01) and no statistically significant differences between the sexes in the same morphologic group.
Table II. Descriptive statistics regarding anterior facial height dimensions (mm) according to age and group
Group Male open bite Female open bite Male deepbite Female deepbite
Age Mean SD Mean SD Mean SD Mean SD Total anterior facial height 6*,y 113.60 5.48 108.34 3.82 108.39 3.38 105.51 2.57 7*,y 116.09 5.51 110.06 4.27 110.22 4.42 108.46 3.57 8z,§ 118.36 6.39 112.97 4.28 112.91 4.66 110.76 3.40 9*,y 121.08 6.35 115.30 4.45 114.76 4.45 113.20 3.55 11*,§ 126.79 6.87 122.39 5.09 120.06 5.36 118.94 4.64 12*,y 130.26 7.68 124.50 4.86 123.52 5.53 120.11 3.78 13y,z 133.28 8.64 126.89 5.82 127.54 5.58 122.65 3.71 14*,y 137.54 8.96 128.08 5.11 131.64 5.50 123.54 3.54
Upper anterior facial height 6 48.86 3.75 46.59 1.57 48.84 1.69 49.19 1.99 7 50.48 2.48 47.84 2.34 50.12 2.68 50.51 2.37 8 52.36 2.74 49.19 2.60 51.42 2.08 52.34 1.85 9 53.67 2.39 50.67 2.26 52.56 1.67 53.50 1.99 11 55.94 3.15 52.86 2.95 55.11 1.81 56.16 1.88 12 57.33 2.48 53.69 3.13 57.41 3.08 57.03 1.81 13*,y 58.37 2.90 54.45 3.37 60.03 2.75 58.71 1.35 14*,y 59.41 3.27 54.84 2.72 62.15 3.34 59.45 1.17
Lower anterior facial height 6*,y 66.85 2.76 63.47 2.91 61.16 2.83 58.02 1.93 7*,y 67.82 3.78 63.92 2.80 61.88 3.41 59.18 2.13 8*,y 68.93 4.28 65.39 2.73 63.05 3.56 59.51 2.30 9*,y 70.29 4.24 66.53 3.23 64.03 4.00 61.30 2.36 11*,§ 73.13 4.63 71.06 3.32 65.70 4.23 63.43 2.89 12*,y 75.94 5.06 72.52 3.12 67.78 4.20 64.47 2.68 13*,y 77.48 6.20 74.16 3.56 69.12 4.23 65.28 3.34 14*,y 80.94 5.77 75.26 3.27 70.71 3.77 66.55 2.66
*Statistically significant differences between groups (P\0.01); ystatistically significant differences between sexes (P\0.01); zstatistically signif- icant differences between groups (P\0.05); §statistically significant differences between sexes (P\0.05).
814 Moon et al
height to total anterior face height. Statistical significance was also reached in the morphologic differences of annual increases in the ratio of lower anterior face height to total anterior face height and lower anterior face height (P \0.01), both annual increases with regard to sexual difference and the interaction of sexual and morphologic difference for upper anterior face height (P \0.05). In terms of the effect of individual random variability, this was relatively large when compared with the annual
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change over time for all variables (minimum, 7.62; maximum, 16.24 times greater).
DISCUSSION
In our study, the sexual and morphologic differences of 6 distance-related variables were evaluated from 9 years of longitudinal cephalometric data from subjects with skeletal open bites and deepbites. Since it is difficult to collect eligible samples for longitudinal studies related to human growth, there is a shortage of pure
Journal of Orthodontics and Dentofacial Orthopedics
Table III. Descriptive statistics regarding posterior facial height dimensions (mm) according to age and group
Group Male open bite Female open bite Male deepbite Female deepbite
Age Mean SD Mean SD Mean SD Mean SD Total anterior facial height 6* 70.75 4.12 67.45 3.09 70.29 3.01 67.26 2.70 7* 72.21 4.12 68.28 3.17 71.44 2.60 69.35 2.87 8y 73.41 4.93 70.15 3.43 72.73 2.48 71.17 2.92 9y 75.56 5.30 71.91 3.77 74.84 2.91 73.51 3.71 11y 79.46 6.02 77.49 5.01 79.11 3.97 78.75 4.51 12y 82.96 5.54 80.10 4.97 82.56 4.58 80.85 3.69 13* 86.82 7.47 81.49 4.76 86.26 4.70 82.17 4.51 14* 89.36 6.47 82.47 4.41 89.69 4.59 83.03 4.42
Ramus height 6 41.49 2.87 39.51 3.15 40.75 2.52 40.11 2.56 7 41.96 2.53 40.26 2.57 41.94 2.55 41.29 2.87 8 42.90 2.77 41.11 2.87 42.72 2.48 41.76 3.24 9 44.47 3.44 41.87 2.72 44.43 3.08 42.91 3.01 11 46.24 3.39 45.66 3.77 46.44 3.07 47.11 4.36 12 48.09 3.34 47.28 3.39 48.90 3.80 48.65 4.27 13 51.35 4.15 49.20 3.89 51.41 4.26 50.06 6.05 14y 52.09 4.28 49.77 3.59 53.86 4.75 50.99 5.79
*Statistically significant differences between sexes (P\0.01); ystatistically significant differences between sexes (P\0.05).
Table IV. Descriptive statistics regarding the ratio of lower anterior facial height to total anterior facial height accord- ing to age and group
Group Male open bite Female open bite Male deepbite Female deepbite
Age Mean SD Mean SD Mean SD Mean SD 6* 0.589 0.014 0.586 0.014 0.564 0.016 0.550 0.013 7* 0.584 0.014 0.581 0.012 0.561 0.018 0.546 0.010 8*,y 0.583 0.027 0.579 0.015 0.558 0.014 0.537 0.014 9* 0.580 0.013 0.577 0.013 0.558 0.020 0.542 0.014 11* 0.576 0.015 0.581 0.012 0.547 0.017 0.533 0.012 12* 0.583 0.014 0.583 0.014 0.549 0.021 0.536 0.011 13* 0.581 0.016 0.58 0.015 0.542 0.017 0.532 0.016 14* 0.588 0.008 0.59 0.006 0.537 0.017 0.538 0.010
*Statistically significant differences between groups (P\0.01); ystatistically significant differences between sexes (P\0.05).
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longitudinal reports.33 In the case of cephalometric radiographs, repeated radiologic exposures of healthy subjects could be considered unethical despite the abundant information they can provide. On the other hand, once they have been taken, it would be unethical not to use them for the good of the orthodontic community worldwide. The data used in this study were gathered from 1995 to 2003.
Although a mixed-effects regression model has the advantage of being able to analyze data with missing values, data with missing values were excluded from this…
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