## Introduction

Currently, a standard of reference for longitudinal facial growth parameters for South American mestizos is lacking. Therefore, in this study, we describe an 18-year follow-up of craniofacial growth from 6 to 24 years of age in a Colombian mestizo population, and an analysis of facial growth beyond 18 years of age.

## Methods

This 18-year follow-up longitudinal study was conducted in Medellín, Colombia. The study sample consisted of 49 mestizo subjects with normal facial features and no history of orthodontic treatment. Measurements of cranial base length, maxillary and mandibular length, posterior and anterior facial height, lower anterior facial height, and mandibular plane angle were documented at an X-ray magnification of 10%. Data were subjected to linear mixed model analysis.

## Results

Changes in cephalometric measurements were detected during the 18-year follow-up and were significantly affected by age and sex. Pubertal growth spurts were between 12 and 14 years for females, and between 14 and 16 years of age for males. Mandibular plane angle decreased in both females and males during the 18-year follow-up.

## Conclusions

Age and sex significantly affect craniofacial growth in mestizos in Columbia. Beyond 18 years of age, craniofacial growth is important. Our data do not support sexual dimorphism in mandibular rotation in young adults.

## Highlights

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All facial dimensions changed during the 18-year follow-up period in Colombian mestizos.

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Facial growth beyond 18 years of age was important.

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Pubertal growth spurts were between 12 and 14 years for females and between 14 and 16 years of age for males.

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There was no sexual dimorphism in mandibular rotation after 18 years of age.

An understanding of the timing, magnitude, and direction of craniofacial growth is fundamental for a comprehensive diagnosis and treatment. Several studies have reported craniofacial variations among races suggesting the use of specific normative data for each population, sex, and age. Studies of cephalometric trends and facial growth of different populations have been reported since the 1970s, including studies from the University of Michigan in 1974, University of Ohio in 1975, and University of Iowa in 1985. Studies of other populations have also been reported, from Denmark in 1963, as well as from the University of Toronto in 1968, ^{,} University of Montreal in 1979, ^{,} and more recently from Turkey in 2005, Sweden in 2005, and Iceland in 2006.

A comparison between studies is challenging because of methodological differences, including sample selection criteria and variations in the radiographic magnification factor, which ranges from 0% to 13.2% and thus affects linear measurements. In addition, study design and statistical analysis may also affect comparisons. For instance, in a previous study performed at the University of Michigan, annual evaluations were conducted in subjects between 6 and 16 years of age; 83 subjects were initially enrolled in the study at age 6, and 32 finished the study at age 16, and an X-ray magnification factor of 12.7% was used. In a study from Ohio with annual follow-ups from 1 to 18 years of age in 16 males and 16 females, the X-ray magnification factor ranged from 5.2% to 5.9%. Other cephalometric measurements from the Ohio study retracing x-rays and using a magnification factor of 8% yielded different results, thus contributing to the current lack of consensus in the literature. The Burlington growth study at the University of Toronto was initiated in 1951 with 1200 children and included 2 longitudinal samples and 1 cross-sectional sample. The Burlington linear measurements presented in the literature decreased at 20 years of age because of a combination of 2 different samples, including the longitudinal one that enrolled participants to 17 years of age, and the cross-sectional ones that enrolled participants at 20 years of age. In these cases, lateral x-rays had a magnification factor of 10.9%.

Mixed longitudinal studies have combined subjects from different groups, making the comparisons more complicated. For instance, a Swedish study had 1 group in which individuals were followed-up from 5 to 13 years of age and another group in which patients were followed-up from 13 to 31 years of age, with observations at 16, 19, and 31 years. In this study, the X-ray magnification factor was 10%.

This study, referred to as the CES-Colombia study, was designed to follow up on the same subjects beyond 20 years of age. Three main ethnic groups contribute to Latin American genetic composition: Amerindians, Africans, and Europeans. Each person has a different contribution of these ethnicities in their genetic makeup. ^{,} From Mexico to Argentina, there is a mestizo ethnic group, shaped since colonial times before the 19th century, by extensive mixture ruled by the European genetic influence in the context of social stratification and economic activity. Growth data from Latin American subjects is scarce, and there is currently no standard of reference for cephalometric longitudinal facial growth normative data for mestizos from South America. Therefore, this study describes facial growth in a Colombian mestizo population based on longitudinal craniofacial data and analyzes facial growth beyond 18 years of age.

## Material and methods

This was an 18-year follow-up longitudinal study conducted in Medellín, Colombia. In 1992, 55 participants, aged 5-8 years, attending first grade at a community public school, joined our study. Throughout the study, 6 individuals were excluded because they developed Class III or open bite malocclusions. Thus, 49 individuals with normal facial appearance and no history of orthodontic treatment were evaluated. X-ray magnification was kept constant at 10%. Normal facial and dental characteristics and cephalometric superimpositions in the plane sella–ethmoidal, sphenoidal intersection of 10 of the subjects are shown in Figures 1-4 .

The ethics committee at CES University approved this study. A signed informed consent form was obtained from participants’ parents or legal guardians before enrolling in the study. Once participants reached 18 years of age, an additional signed informed consent form was obtained from each participant.

Participants were subjected to annual follow-up that included preventive measures such as plaque control, prophylaxis, topical fluoride applications, oral hygiene instruction, and supragingival scaling. Between 1992 and 2002, control and maintenance examinations of the mestizo sample population were subjected to numerous logistic challenges because of the critical social period in Colombia.

All equipment for lateral cephalic radiographs (analog and digital) was adjusted to give a 10% magnification. In our analysis, cephalometric landmarks and planes were defined based on the Growth and Development Atlas of the University of Michigan, including the following points: sella (S), nasion (N), condylion, A point (A), gnathion (Gn), gonion (Go), gonial intersection (Goi), menton (Me), B point (B), and anterior nasal spine. Measurements were obtained for the following: cranial base length (S-N distance), maxillary length (Co-A distance) and mandibular length (Co-Gn distance), posterior facial height (PFH; defined as the distance in millimeters from S to Go), anterior facial height (AFH; defined as the distance in millimeters from N to Me), lower anterior facial height (LAFH; defined as the distance in millimeters from anterior nasal spine and Me), and the angle between sella-nasion and the mandibular plane (SN-MP; defined as the angle formed between SN and the plane from menton [Me] to gonial intersection). The same member of our research team performed all measurements; all cephalograms of each subject were traced at once to verify the image of each point ( Fig 5 ).

Intraclass correlation coefficients were calculated for interobserver and intraobserver variation. For interobserver variation, 2 observers performed measurements in 15 blinded radiographs. The intraobserver correlation was calculated by having 1 of the researchers perform measurements on the same radiographs after a 2-week interval.

## Statistical analysis

A linear mixed model for comparing measurements of craniofacial growth over time, the ideal for longitudinal data, was applied. Previous studies have reported that linear mixed models also allow individual growth profiles to be built through the use of polynomial functions. ^{,} An important feature of these models is that they take into account both within-subject and between-subject variability, while traditional models, such as linear regression models, only take into account between-subject variability.

A linear mixed model with a random intercept for the PFH was considered as the response variable and both sex and age as explanatory variables. By using the following equation, we can express the effect of sex and age on the PFH:

Yij=β0+b0i+β1Gender+β2Age+β3(Gender⋅Age)+εij

where *Y* _{ij }is the analyzed craniofacial variable (PFH in this case) for subject *i* at age *j* . *β* _{0} is the intercept, *β* _{1} is the fixed effect of sex on the PFH, *β* _{2} is the fixed effect of age on the PFH and *β* _{3} is the effect of the interaction between sex and age, *ε* _{ij }is a measurement error specific to the subject *i* at time *j* which is assumed to be normally distributed. Finally, *b* _{0 i }is a specific random intercept for subject *i* , which is also assumed normally distributed and independent of the random variable *ε* _{ij }. Observe that this intercept ( *b* _{0 i }) randomly modifies the population intercept *β* _{0} , and therefore, it incorporates the individual heterogeneity that could be seen as random deviations of the subjects from the population trend. These models can be adjusted using standard statistical software such as SPSS, R, or SAS.

Because of the nature of longitudinal growth studies, it was not always possible to record information for some of the subjects, and for this reason, one needs to implement processes such as imputation of missing data because missing data may have a significant negative effect on the conclusions drawn from the data. This imputation process is usually done with summary statistics and linear regression models. ^{,} SAS version 9.4 (SAS Institute, Cary, NC) was used to fit both models and perform calculations.

For each measure, the mean and standard deviation were estimated using a linear mixed model with random intercepts as described by Verveke and Molenberghs. These values are reported in all tables and figures. Statistical significance was considered significant at *P* <0.05, very significant at *P* <0.01, and highly significant at *P* <0.001.

## Results

Of the 49 subjects enrolled at the start of the study (30 females and 19 males), 33 remained at the 18-year follow-up (23 females and 10 males); 14 dropped out of the study because of death (n = 1), inability to contact (n = 3), undergoing orthodontic treatment (n = 10), and not being 24 years of age at the time of last evaluation (n = 2). Evaluation of measurement of error of cephalometric tracings established a high and reliable interobserver and intraobserver intraclass correlation coefficient of 0.981-0.998 and 0.969-0.996, respectively. Cephalometric measurements and graphs of cumulative length changes with age, as well as the growth velocity curves ( Figs 6-13 ). Tables I-IV included the least square means, standard deviation, and *P* values for the 7 skeletal measurements by age and sex. As shown in Tables I-IV , sex was significantly associated with the differences in craniofacial growth.

Age | S-N | Co-A | Co-Gn | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Female | Male | Female | Male | P |
Female | Male | P |
Female | Male | P |
|||||||

n | n | Mean | SD | Mean | SD | Mean | SD | Mean | SD | Mean | SD | Mean | SD | ||||

6 | 30 | 19 | 64.4 ^{a } |
3.5 | 64.6 ^{a } |
3.5 | NS | 76.6 ^{a } |
4.2 | 78.1 ^{a } |
4.2 | NS | 95.2 ^{a } |
4.8 | 95.7 ^{a } |
4.8 | NS |

8 | 30 | 19 | 65.6 ^{b } |
3.5 | 66.2 ^{b } |
3.5 | NS | 79.0 ^{b } |
4.2 | 80.4 ^{b } |
4.2 | NS | 99.2 ^{b } |
4.8 | 99.9 ^{b } |
4.8 | NS |

10 | 30 | 19 | 66.9 ^{c } |
3.5 | 67.7 ^{c } |
3.5 | NS | 82.1 ^{c } |
4.2 | 82.8 ^{c } |
4.2 | NS | 103.5 ^{c } |
4.8 | 104.1 ^{c } |
4.8 | NS |

12 | 30 | 18 | 68.1 ^{d } |
3.5 | 68.8 ^{d } |
3.4 | NS | 85.3 ^{d } |
4.2 | 85.8 ^{d } |
4.1 | NS | 107.6 ^{d } |
4.8 | 108.1 ^{d } |
4.7 | NS |

14 | 30 | 18 | 69.2 ^{e } |
3.5 | 70.5 ^{e } |
3.4 | NS | 88.0 ^{e } |
4.2 | 87.9 ^{e } |
4.1 | NS | 111.9 ^{e } |
4.8 | 112.1 ^{e } |
4.7 | NS |

16 | 30 | 18 | 70.0 ^{f } |
3.5 | 72.4 ^{f } |
3.4 | * | 88.9 ^{f } |
4.2 | 91.9 ^{f } |
4.1 | * | 113.8 ^{f } |
4.8 | 118.4 ^{f } |
4.7 | † |

18 | 28 | 17 | 70.8 ^{g } |
3.4 | 74.1 ^{g } |
3.4 | * | 90.0 ^{g } |
4.1 | 93.8 ^{g } |
4.0 | † | 115.3 ^{g } |
4.6 | 122.2 ^{g } |
4.6 | ‡ |

20 | 27 | 17 | 70.9 ^{g } |
3.4 | 74.3 ^{g } |
3.4 | † | 90.5 ^{g } |
4.0 | 94.9 ^{h } |
4.0 | ‡ | 116.2 ^{h } |
4.6 | 124.1 ^{h } |
4.6 | ‡ |

22 | 25 | 11 | 71.3 ^{g } |
3.3 | 74.6 ^{g } |
2.8 | † | 90.9 ^{gh } |
3.9 | 95.9 ^{h,i } |
3.4 | ‡ | 117.0 ^{h,i } |
4.4 | 124.7 ^{h,i } |
3.9 | ‡ |

24 | 23 | 10 | 72.0 ^{h } |
3.1 | 75.0 ^{g } |
2.7 | † | 91.5 ^{h } |
3.8 | 96.7 ^{i } |
3.3 | ‡ | 118.1 ^{i } |
4.3 | 125.9 ^{i } |
3.8 | ‡ |