INTRODUCTION

Several indicators of individual skeletal maturity have been proposed over the years to define treatment timing in orthodontics. The easiest indicator to record is the chronological age of the patient. Some investigators have reported that chronological age can be regarded as a reliable predictor for the adolescent growth spurt.^1,2 The estimation of the pubertal peak, however, should not be based solely on chronological age because the peak is also influenced by many factors such as secular trend, genetic factors (mediated by environmental factors), and weight (nutritional status).² The most commonly used indicators of individual skeletal maturity are increase in height,^1,3 skeletal maturation of the hand and wrist,^4,5 and the cervical vertebral maturation (CVM) method.^6–8

Several studies have demonstrated that the CVM method can detect the pubertal peak in a reliable way,^9–14 whereas other investigations have found that the CVM method is not a reliable method to identify the adolescent growth spurt.^1,15–18 Only the studies by Morris and colleagues¹⁸ and by Montasser¹⁹ have investigated the role of chronological age, sex, and CVM in predicting the pubertal peak in mandibular growth by using a multilevel logistic regression analysis. The CVM method used in study of Morris et al.¹⁸ was an older version that was based on five vertebrae as described by Franchi et al. in 2000.¹⁰ Currently, the CVM method evaluating five vertebrae is not the most commonly used method in clinical practice.⁸

Thus, the aims of the present study were to evaluate the relationship between cervical stage and the peak in mandibular growth and to develop a predictive model that combines the information derived from chronological age, sex, and the CVM method evaluating three vertebrae^7–8 to predict the pubertal spurt in mandibular growth.

MATERIALS AND METHODS

The Transparent Reporting of a Multivariable Prediction Model for Individual Prognosis or Diagnosis statement²⁰ was followed.

Subjects were selected from the records of the Fels, Iowa, Mathews, and Oregon Growth Studies that were available through the American Association of Orthodontists Foundation (AAOF) Craniofacial Growth Legacy Collection Project (www.aaoflegacycollection.org). In addition, the complete records of the University of Michigan Growth Study (after having removed the 30 subjects that were used in the previous study by Baccetti et al.⁷) and of the Denver Child Growth study were screened.

Inclusion criteria were availability of a series of at least six consecutive annual lateral cephalograms from the age of 7 years to 18 years; the bodies of the second, third, and fourth vertebrae had to be visible in all films; the interval between two consecutive cephalograms had to range from a minimum of 6 months to a maximum of 18 months; the first cephalogram of the series had to show CVM stages 1 or 2;^7,8 and the last cephalogram of the series had to show at least CVM stage 5.^7,8 Exclusion criteria were incomplete records, radiographs of poor quality, anomalies in vertebral morphology, and evident orthodontic treatment (with the exception of space maintainers).

Total mandibular length (the linear distance from Condylion to anatomical Gnathion [Co-Gn]) was measured on all cephalograms by the same examiner on the digital cephalograms using cephalometric software (Viewbox 4.0, dHal Software, Kifissia, Athens, Greece). The value of Co-Gn was standardized to 0% enlargement (life size) after adjustment of the magnification factor of the different growth studies.

The increases in Co-Gn between consecutive cephalograms taken annually were calculated for the entire series of cephalograms for each subject. Because the intervals between consecutive cephalograms were not always 12 months in duration, the increases in Co-Gn were annualized. “Mandibular pubertal growth peak” was defined as the greatest increase in the annualized value of Co-Gn between consecutive cephalograms.

The CVM method used in the present study was the one described by McNamara and Franchi.⁸ The intermediate or in-between stages (when the characteristics of two consecutive stages were present in a single image)⁸ were included in the more immature stage, that is, the intermediate CS 3–4 was classified as CS 3. All cephalograms were staged according to the CVM method by a single expert examiner. All subjects from the growth studies who met all inclusion/exclusion criteria were included in this study.

RESULTS

From a parent sample of 1151 subjects, a final sample of 50 subjects (29 females and 21 males) was selected. Six cases (5 females and 1 male) were derived from the Fels Growth Study, 2 (1 female and 1 male) from the Iowa Growth Study, 3 (1 female and 2 males) from the Mathews Growth Study, 24 (15 females and 9 males) from the Oregon Growth Study, 3 (1 female and 2 males) from the Denver Growth Study, and 12 (6 females and 6 males) from the University of Michigan Growth Study.

The intraobserver reproducibility for the CVM method and for the Co-Gn measurement was “almost perfect”²¹ (CVM method: 0.87 [95% confidence interval, CI, 0.77–0.96]; Co-Gn: 0.99 [95% CI. 0.99–1.00]). The random error for the Co-Gn measurement was 0.57 mm.

A total of 456 lateral cephalograms were analyzed. All quantitative data are expressed as mean ± standard deviation. The mean number of cephalograms per subject was 9.1 ± 1.2 (minimum 6 and maximum 12 cephalograms). In Table 1, the frequencies of the different CVM stages and the corresponding percentages are reported. The mean age at the first cephalogram was 8.2 ± 0.5 years (minimum 7.5, maximum 9.9 years), whereas the mean age at the last cephalogram was 16.5 ± 1.1 years (minimum 14.0, maximum 20.2 years). The mean interval between two consecutive cephalograms was 1.0 ± 0.1 years (minimum 0.75, maximum 1.49).

Table 1. Frequencies and Percentages of the CVM Stages

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The annualized mandibular pubertal growth peak of Co-Gn was 4.5 ± 1.2 mm for females and 5.7 ± 1.3 mm for males. The mean age at the lateral cephalogram immediately before the mandibular pubertal growth peak was 12.1 ± 1.1 years for females and 13.2 ± 0.8 years for males. Table 2 reports the frequencies and percentages of the CVM stages on the lateral cephalogram immediately before the mandibular pubertal growth peak. Interestingly, the greatest increase in mandibular length occurred after CS 3 in 78% of the cases.

Table 2. Frequencies and Percentages of the CVM Stages on the Lateral Cephalogram Immediately Before the Mandibular Pubertal Growth Peak

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As for inferential statistics (Table 3), the presence of CS 3, age, second-order age, and sex were all statistically significant. Only the interaction between age and sex was statistically significant. All other interactions were not significant, and therefore they were not included in the final model. The third-order age also was not included in the model because it was not statistically significant.

Table 3. Multilevel Logistic Model for the Prediction of the Mandibular Pubertal Growth Peak

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The logistic model is reported in both Table 3 and Figure 1.

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The predictive equation for male subjects at CS 3 was the following:

The predictive equation for male subjects presenting with a CVM stage different from CS 3 was the following:

The predictive equation for female subjects at CS 3 was the following:

The predictive equation for female subjects presenting with a CVM stage different from CS 3 was the following:

From Figure 1 and the previous equations, it can be derived that the highest probability of having the mandibular growth peak was reached for female subjects with CS 3 at 12.2 years, and it was equal to 59%. For male subjects with CS 3 the highest probability of having the mandibular growth peak was 61% at 13.2 years. In addition, the probability of having the mandibular growth peak was greater than 50% in female subjects with CS 3 between 11.3 and 13.1 years and in male subjects with CS 3 between 12.2 and 14.2 years.

The sensitivity (62%) of the model was calculated as the number of mandibular growth peaks predicted correctly by the logistic multilevel regression (31) out of the number of actual mandibular growth peaks (50). The specificity (95%) was calculated as the number of observations in which the model did not identify the mandibular growth peak (337) out of the total number of observations without the mandibular growth peak (356). The accuracy (91%) was calculated as the observations predicted correctly by the model (368) out of the total number of observations (406).

DISCUSSION

The results of the present study showed that the pubertal peak in mandibular length occurred after CS 3 in 78% of the cases. This meant that, in more than 3/4 of the subjects, the mandibular pubertal growth spurt could be expected in the year after CS 3.

As a peculiar feature of this study, chronological age was entered in the predictive model as a curvilinear variable (polynomial curve up to the third order or degree). This feature was a very important aspect when analyzing the peak in mandibular growth as a function of age. As a matter of fact, if age was entered as a linear variable, the probability of having the mandibular growth peak would increase or decrease linearly along with age. However, mandibular growth was not linear along with age but rather followed a curvilinear (nonlinear) trend that was characterized, particularly during adolescence, by an acceleration that reached a peak that was followed by a deceleration until the end of active growth.^22,23

The results of the present study were not comparable with those by Engel et al.¹⁵ and Gray et al.,¹⁶ who applied a linear mixed model analysis to identify mandibular length. In the present study, a logistic regression model to detect the presence or absence of the mandibular growth peak was applied. The regression equations found by Engel et al.¹⁵ and Gray et al,¹⁶ therefore, allowed calculation of either mandibular length or the change in mandibular length, which has limited clinical value. The regression equation that was found in the present study allows calculating the probability of having the mandibular pubertal growth peak in the subsequent year, which can be useful clinically. In addition, these previous investigations^15,16 were characterized by relatively small sample sizes (29¹⁵ and 25¹⁶ subjects).

The most appropriate statistical approach that appears to answer this question is a multilevel logistic regression model in which the outcome variable is the presence or absence of the pubertal growth spurt (measured as the greatest annual increase in the length Co-Gn), and the predictive variables were presence or absence of CS 3, sex, chronological age at each film, and interactions among these variables. Only the studies of Morris et al.¹⁸ and Montasser¹⁹ applied this statistical approach. The CVM method that was used by Morris et al.,¹⁸ however, was the version based on the evaluation method of the older five vertebrae.¹⁰ Montasser used the CVM method proposed by Hassel and Farman.⁶ In addition, these studies^18,19 used chronological age only as a linear predictive variable without considering that, after a given age, the probability of finding the pubertal peak should decrease.

The present study, therefore, was the first to apply a multilevel logistic model to investigate the role of chronological age (up to third order), sex, and CVM method on three cervical vertebrae for the prediction of the pubertal peak in mandibular growth. The limitations of the present study were the lack of validation of the prediction model and the fact that the same examiner evaluated both the increments in Co-Gn and the CVM stages. Unfortunately, it was not possible to validate the prediction model on a different sample because all eligible subjects available through the AAOF Craniofacial Growth Legacy Collection Project, the University of Michigan Growth Study, and of the Denver Child Growth study were included in this study. No other growth study was available.

Another limitation was the secular trend of the chronological age at which the pubertal growth spurt occurs. In general, the secular trend is toward the earlier onset of puberty with an earlier maturation of the mandible.^24,25 Therefore the results of the present study should be analyzed with caution because they were based on radiographs collected about 40 to 50 years ago. For ethical reasons it is impossible to collect a contemporary sample of untreated subjects with lateral cephalograms taken annually.

Interestingly, CS 3, chronological age, second-order age, sex, and the age × sex interaction were all significant predictors for the presence of the pubertal peak in mandibular growth. This result disagreed with that of Morris et al.,¹⁸ who found that only chronological age was a significant predictor. This difference in results could be explained by the fact that Morris et al.¹⁸ restricted their analysis only to the age groups from 10 through 14 years. In addition, as emphasized previously, they staged the vertebrae by using the CVM method on five vertebrae,¹⁰ whereas the CVM method on three vertebrae was used in the current study.^7,8 On the contrary, Montasser¹⁹ reported that presence of CS 3 would indicate the peak of the growth spurt.

Figure 1 can be used to assess the probability of having the mandibular pubertal growth peak in the year following the lateral cephalogram (y-axis) as a function of chronological age (x-axis), sex, and CS 3. The maximum probability of having the mandibular pubertal growth peak in the year following the lateral cephalogram for subjects at CS 3 was 12.2 years (59%) for females and 13.2 years (61%) for males. At the same age for non-CS 3 subjects, the probabilities of having the mandibular pubertal growth peak were only 13% and 14% for females and males, respectively. Therefore, it was confirmed that CS 3 can be a useful predictor for the mandibular growth peak. From a practical standpoint, if a female subject is between 11 and 13 years of age (considering the secular trend in the onset of the pubertal growth spurt)^24,25 and shows a CS 3 on the lateral cephalogram, she has a probability greater than 50% of having the mandibular pubertal peak during the following year. Similarly, a male subject between 12 and 14 years at CS 3 has a probability greater than 50% of showing the mandibular pubertal peak during the following year. During the same age interval, if the subject does not show a CS 3 stage, the probability of the mandibular pubertal peak occurring during the following year is only between 10% and 15%.

In the future, the addition of other predictors, such as the presence of secondary sexual characteristics or the age at menarche in females, could help in improving the predictive capabilities of the mandibular growth peak of CS 3 in CVM.

CONCLUSIONS

The present study showed the following:

• The greatest increase in mandibular length occurred after CS 3 in 78% of the subjects.

• CS 3, chronological age, and sex were significant predictors for the presence of the pubertal peak in mandibular growth.