Dentomaxillofacial Radiology (2014) 43, 20130238 ª 2014 The Authors. Published by the British Institute of Radiology http://dmfr.birjournals.org
RESEARCH ARTICLE
New software for cervical vertebral geometry assessment and its relationship to skeletal maturation—a pilot study 1
3 ´ R C Santiago, A R Cunha, 2G C Junior, N Fernandes, 2M J S Campos, 1L F M Costa, 2R W F Vitral 1 and A M Bolognese
1
Department of Pediatric Dentistry and Orthodontics, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil; 2Department of Orthodontics, Federal University of Juiz de Fora, Minas Gerais, Brazil; 3Department of Statistics, Federal University of Juiz de Fora, Minas Gerais, Brazil
Objectives: In the present study, we developed new software for quantitative analysis of cervical vertebrae maturation, and we evaluated its applicability through a multinomial logistic regression model (MLRM). Methods: Digitized images of the bodies of the second (C2), third (C3) and fourth (C4) cervical vertebrae were analysed in cephalometric radiographs of 236 subjects (116 boys and 120 girls) by using a software developed for digitized vertebrae analysis. The sample was initially distributed into 11 categories according to the Fishman’s skeletal maturity indicators and were then grouped into four stages for quantitative cervical maturational changes (QCMC) analysis (QCMC I, II, III and IV). Seven variables of interest were measured and analysed to identify morphologic alterations of the vertebral bodies in each QCMC category. Results: Statistically significant differences (p , 0.05) were observed among all QCMC categories for the variables analysed. The MLRM used to calculate the probability that an individual belonged to each of the four cervical vertebrae maturation categories was constructed by taking into account gender, chronological age and four variables determined by digitized vertebrae analysis (Ang_C3, MP_C3, MP_C4 and SP_C4). The MLRM presented a predictability of 81.4%. The weighted k test showed almost perfect agreement (k 5 0.832) between the categories defined initially by the method of Fishman and those allocated by the MLRM. Conclusions: Significant alterations in the morphologies of the C2, C3 and C4 vertebral bodies that were analysed through the digitized vertebrae analysis software occur during the different stages of skeletal maturation. The model that combines the four parameters measured on the vertebral bodies, the age and the gender showed an excellent prediction. Dentomaxillofacial Radiology (2014) 43, 20130238. doi: 10.1259/dmfr.20130238 Cite this article as: Santiago RC, Cunha AR, J´unior GC, Fernandes N, Campos MJS, Costa LFM, et al. New software for cervical vertebral geometry assessment and its relationship to skeletal maturation—a pilot study. Dentomaxillofac Radiol 2014; 43: 20130238. Keywords: cervical vertebrae; skeletal maturity; logistic regression Introduction The identification of the pubertal growth spurt has great value in dentistry. The highest response to functional orthopaedic stimuli applied to the jaw bones tend to occur during this period, and its effectiveness is directly related to bone maturation.1–4 The effectiveness of Correspondence to: Dr Rodrigo C´esar Santiago. E-mail: rodrigo_cesar_santiago@ hotmail.com Received 4 July 2013; revised 24 November 2013; accepted 2 December 2013
a biological indicator of skeletal maturity is directly related to factors such as the ability to detect and predict the growth spurt peak without the need for additional radiation exposure and the high level of agreement between examiners for the definition of the stages.5 In this context, the use of the cervical vertebrae has been suggested as an alternative, instead of the hand–wrist radiographs, in the determination of skeletal maturation.
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In the past 2 decades, several studies have analysed the applicability of lateral cephalometric radiographs to determine skeletal maturity based on the analysis of alterations in the morphology of the cervical vertebrae, especially the second (C2), third (C3) and fourth (C4) cervical vertebrae.1,2,6–11 Although many studies1,9,12–14 have validated this method through the strong correlation between the cervical vertebrae maturation (CVM) and hand and wrist skeletal maturity, recent studies have questioned its applicability.15,16 The first concerns regarding the validity of qualitative methods for identifying CVM are related to the consistency during data interpretation. These methods7,13,17–19 take into account a subjective comparison between images of the vertebrae and a reference atlas containing the CVM stages. In a previous study,20 the low reproducibility observed between clinicians of a qualitative CVM model suggested that it should not be used clinically as the only guide to define the optimal time for orthodontic treatment. The low reproducibility of a diagnostic method, in particular qualitative methods for identifying CVM,6,13,17 brings into question the accuracy of these models in the way they are proposed. Several studies21–23 have established the skeletal age of individuals from multiple regression analyses with the aim of developing quantitative methods for objective analysis of the maturation of cervical vertebrae and reducing the variability of interpretations. However, questions remain regarding the standard method used for the determination of the skeletal age24 and the lack of accuracy in the prediction of the proposed methods.25 Thus, the present study aimed to develop a new quantitative method for the identification of CVM through computer analysis by using specific software designed by the authors and to evaluate the applicability of this new method by using a multinomial logistic regression model (MLRM). Additionally, we also evaluated the predictability of an MLRM using solely chronological age or a combination of age and gender as skeletal maturation predictors. Methods and materials The data from this cross-sectional study were obtained from lateral cephalometric radiographs and hand and wrist radiographs taken as part of routine orthodontic records. The sample included 236 children—116 boys [mean (standard deviation), 146.4 (25.21) months] and 120 girls [mean (standard deviation), 146.2 (24.1) months]— consecutively selected between January and December 2011. The following selection criteria were used during the sample composition: (1) white Brazilian subjects with no history of trauma to the face and/or hand and wrist, (2) the absence of congenital and/or acquired malformations that could affect the vertebrae or the hand and wrist, (3) general good health and (4) cephalometric and hand and wrist radiographs taken on the same day and with Dentomaxillofac Radiol, 43, 20130238
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good visualization of the structures of interest, such as the C2, C3 and C4 cervical vertebrae. The study was approved by the Ethics on Research Committee of Federal University of Juiz de Fora, Brazil. The radiographs of the hands and wrists were used as the standard method for determining the degree of skeletal maturation of each individual and were analysed by a dental surgeon who specializes in image techniques with extensive experience in the method of interest. The radiographs were classified according to the skeletal maturation index (SMI) described by Fishman26 and were divided into the 11 developmental stages according to Fishman. All analyses were performed in the dark with the same light box, and the examiner was unaware of any additional information such as chronological age or gender. For reliability analysis in relation to the staging of the hand and wrist radiographs, 30 radiographs were examined twice with an interval of 2 weeks between assessments. The intraclass correlation coefficient (0.997) revealed intraobserver reproducibility and reliability in the classifications of hand–wrist maturational stages. The 11 stages of Fishman’s skeletal maturity26 can be grouped into periods of acceleration (SMI 1–3), high velocity (SMI 4–7) and deceleration (SMI 8–11).27 In the present study, the radiographs were grouped into four stages of CVM, taking into account Fishman’s indicators of skeletal maturity, but segregating the period of deceleration (SMI 8–11) into two different stages owing to significant anatomical differences between SMI 8–9 and SMI 10–11 in the morphologies of the bodies of C2, C3 and C4 cervical vertebrae. The quantitative cervical maturational changes (QCMC) comprised four stages: QCMC I (acceleration of growth), which includes Fishman’s Stages 1–3; QCMC II (high growth rate), which includes Stages 4–7; QCMC III (decelerated growth), which includes Stages 8 and 9; and QCMC IV (consummation of growth), which includes Stages 10 and 11. The radiographs were scanned using Umax Astra 2400SLT (Umax Technologies Inc, Dallas, TX) at 600 dots per inch and digitalized through the Corel PhotoPaint software v. 11.0 (Corel Photo-Paint®; Corel Corporation, Ottawa, Canada). The morphologies of the C2, C3 and C4 were analysed using software developed specifically for this study from 10 additional images. The software for digitized vertebrae analysis (DVA) was developed in Microsoft.NET Framework in the C# language to aid the specialist in the analysis of the image; this software provided measurements and proportions of the C2, C3 and C4 vertebrae based on reference points marked manually on the image (Figure 1). An important function of the software is to calculate automatically the following measures: concavity angle, width, height, square proportion (defined later) and maturity proportion (defined later). First, the user must provide reference points C, E, D for vertebrae C2 and reference points A, B, C, D and E for vertebrae C3 and C4. The software displays the radiograph-scanned image and lets the user mark the above points using his mouse.
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Figure 1 (a) Lateral cephalometric radiograph with the region of interest and the definition of the reference points (b), marked manually on the image by the digitized vertebrae analysis software. The reference points marked manually were A–E. The reference points provided automatically by the software were F, G, F9 and G9.
The reference points marked manually in this study were A and B, the most superior points of the posterior and anterior borders, respectively, of the bodies of C3 and C4; C and D, the most inferior points of the posterior and anterior borders, respectively, of the bodies of C3 and C4; E, the point of greatest concavity of the lower border of the bodies of C2, C3 and C4. The reference points provided automatically by the software were F and G, the midpoints of the lower (CD) and anterior (BD) borders, respectively; F9, the intersection point where the line from F point, parallel to the posterior border, touches the superior border and G9, the intersection point where the line from G point, parallel to the inferior border, touches the posterior border (Figure 1). After defining the points of interest, the tool used methods of linear algebra and spatial analysis to generate the dimension, proportion and angle values.
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The measurements of interest were determined as follows (Figure 2): AB and CD: superior and lower borders of the body, respectively; AC and BD: posterior and anterior borders of the body, respectively; ANG_C2, ANG_C3, and ANG_C4: internal angle formed by the intersection of the lines that connect the points CE and ED at the lower borders of C2, C3, and C4, respectively. Using the cosine formula C 2 5a2 1 b2 2 2abcosg the software calculated the cosine of angle E. Then applying the inverse cosine function we obtained the angle E. SP_C3 and SP_C4: square proportion of C3 and C4, respectively, given by the ratio between the line parallel to the lower border (CD) connecting the points G and G9 and the line parallel to the posterior border (AC) that connects points F and F9. MP_C3 and MP_C4: maturity proportion of C3 and C4, respectively, given by the ratio between the anterior border (BD) and the posterior border (AC). The sample was evaluated by one examiner for the following nine variables: (1) chronological age (months), (2) gender, (3) ANG-C2, (4) ANG_C3, (5) ANG_C4, (6) SP_C3, (7) SP_C4, (8) MP_C3 and (9) MP_C4. For the examiner variability analysis, by using the DVA software, 30 radiographs were analysed at 2 different times separated by an interval of 2 weeks. The paired t-test did not show a statistically significant difference for any of the measures analysed [p 5 0.562; mean standard error: ANG_C2 (±0.52), ANG_C3 (±0.40), ANG_C4 (±0.68), SP_C3 (±1.18), MP_C3 (±0.54), SP_C4 (±1.19), MP_C4 (±0.74)]. 30 lateral cephalograms and 30 hand–wrist radiographs were randomly selected from the 236 patients and analysed by 2 examiners to assess intra- and interobserver variability during cervical and hand–wrist assessments. The examiners received training to use the software and hand–wrist methods from a dental surgeon who had extensive experience in the methods of interest. Immediately after training, the 30 hand–wrist radiographs were analysed using light boxes, and the 30 lateral cephalograms were analysed on a personal computer in a darkened room with contrast enhancement of the bone images. The examiners did not have access to any additional information regarding the patient, such as age, gender and stage of teething. The whole procedure was repeated 2 weeks (T2) after the first evaluation (T1) with the random distribution of radiographs, and all examiners received the same training again as for the first evaluation. Statistical analysis All statistical analyses were performed using a software package (SPSS® for Windows v. 13.0; SPSS Inc., Chicago, IL). The averages and standard deviations were calculated for cervical assessments. Statistical analysis included the x 2 test, ANOVA test, weighted k test, Spearman’s rank correlation coefficient and multinomial logistic regression analysis. A significance level of p , 0.05 was used. The statistical Excel software (Microsoft Office® 2007; Microsoft, Redmond, WA) was used to analyse the data and obtain the probabilities of the multinomial regression model. dmfr.birjournals.org
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Figure 2 (a) Subject in the CVM Stage 4, according to Baccetti et al7 (b). (c) Quantitative analysis of C2, C3 and C4 maturation by the digitized vertebrae analysis software. The multinomial logistic regression model indicated a 86.6% of the probability for this patient belonged to quantitative cervical maturational changes (QCMC) IV, which is more consistent with the skeletal maturational Level 10 of Fishman,26 observed for this patient.
The logistic model enables the direct estimation of the probability of occurrence of an event, such as whether an individual belongs to a certain category.28 The logistic regression model, originally developed for binary response variables, can be extended to multinomial response variables (three or more categories), as observed in the present study, where the sample was divided into four stages of QCMC (QCMC I–IV). Although the MLRM is appropriate for nominal data, ordinal variables can be treated as nominal data, minimizing some issues such as lack of homoscedasticity, linearity and incorporating outliers.29 In this study, each of the variables analysed (chronological age, gender, hand and wrist maturity, ANG_C2, ANG_C3, ANG_C4, SP_C3, SP_C4, MP_C3 and MP_C4) were inserted individually in an MLRM that adopted the QCMC I as reference, owing to the greatest number of subjects being in this category. The variables that contributed significantly to the differentiation of the QCMC Stages II, III and IV from the reference category (QCMC I) remained in the final model. Three linear functions g(x) were generated, and Dentomaxillofac Radiol, 43, 20130238
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it was possible to calculate the conditional probabilities that each radiograph analysed belonged to a QCMC stage. Finally, the model was represented by the intercept of the independent variables that contributed significantly to the discrimination between categories and their respective B coefficients (variable coefficient). The multinomial method sought to establish a single model instead of various models, as would occur in the case of dividing the subjects according to gender or age. Moreover, the gender showed an additive effect (adding information) and non-interactive effect, which make it unnecessary to divide the sample and increased the robustness and predictability of the model because of a larger sample size. Additionally, we did evaluate the MLRM model using only chronological age or a combination of age and gender to compare the total and partial percentages of the correctness of the model obtained with the final model established in the present study. The spreadsheet generated in the Excel software by the insertion of data from the six independent variables included in the final model allowed the determination of the
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Table 1 Distributions of age, gender and means and standard deviations for the seven variables of interest for each of the quantitative cervical maturational changes (QCMC), Stages (I–IV)
Variables Age (months) Gender ANG_C2 (°) ANG_C3 (°) ANG_C4 (°) SP_C3 SP_C4 MP_C3 MP_C4
Stages QCMC I 128 ± 18 69 M/23 F 171.71 ± 7.48 176.30 ± 6.33 177.70 ± 6.16 1.61 ± 0.18 1.61 ± 0.16 0.68 ± 0.07 0.69 ± 0.07
QCMC II 144 ± 16 23 M/41 F 161.97 ± 6.31 165.46 ± 6.79 169.41 ± 6.89 1.41 ± 0.19 1.42 ± 0.18 0.80 ± 0.06 0.77 ± 0.06
QCMC III 158 ± 10 11 M/29 F 153.58 ± 8.53 157.73 ± 7.89 161.93 ± 7.47 1.22 ± 0.13 1.24 ± 0.12 0.87 ± 0.07 0.83 ± 0.04
QCMC IV 177 ± 18 13 M/27 F 147.77 ± 7.97 151.48 ± 6.82 152.43 ± 8.83 1.08 ± 0.12 1.07 ± 0.11 0.92 ± 0.06 0.89 ± 0.05
p-value 0.000a 0.000b 0.000a 0.000a 0.000a 0.000a 0.000a 0.000a 0.000a
F, female; M, male. ANG_C2, ANG_C3, and ANG_C4 are internal angle formed by the intersection of the lines that connect the points CE and ED at the lower borders of C2, C3, and C4, respectively. SP_C3 and SP_C4 are square proportion of C3 and C4, respectively. MP_C3 and MP_C4 are maturity proportion of C3 and C4, respectively. a ANOVA for mean comparison between each of the QCMC stages (p , 0.05). b 2 x test for gender distribution analysis between each of the QCMC stages (p , 0.05).
probability that each radiograph belonged to one of the four QCVM categories (QMVC I, II, III, or IV). The most likely probability for distribution of the sample in each of the categories (QMVC I, II, III or IV) was adopted. To analyse reproducibility, the overall percentage of agreement in the intra- and inter-rater variability was calculated, and the weighted k test was used for hand– wrist assessment. The paired t-test was used to analyse reliability of cervical assessment used by the DVA software. A significance level of p , 0.05 was used. Results The distributions of gender and means and standard deviations for the variables of interest are shown in Table 1. A statistically significant difference (p , 0.05) was observed in the distribution of all variables for each of the QCVM categories. For the correlation between the parameters of cervical vertebrae morphology and the SMI, all the seven parameters were significantly correlated at p , 0.01 level [Spearman rank correlation: ANG_C2 (20.826), ANG_C3 (20.836), ANG_C4 (20.818), SP_C3 (20.812), MP_C3 (10.817), SP_C4 (20.817) and MP_C4 (10.804)].
After the multinomial logistic regression analysis, six independent variables of interest (Var x1–Var x6) remained in the model (Table 2). The model provided three logit g(x) functions, one for each QCVM category (II, III and IV), which took into account the observed values for the six independent variables (Var x1–Var x6), the intercept (B0) and the coefficients for each independent variable (B1–B6). The MLRM obtained in this study showed an 81.4% of total percentage of the correctness, with partial percentages of the correctness raging from 70.3% to 93.5%, according to different QCMC stages (Table 3). The total percentage of the correctness of the model obtained with the use of chronological age was 49.5%, and 64.5% for a combination of age and gender (Table 4). The result of the weighted k test, which analysed the correlation between the categorizations established by the logistic regression model and the four QCMC stages established according to the 11 stages of Fishman’s skeletal maturity28 showed a good agreement (k 5 0.832). Regarding the reproducibility of the two examiners while using the software, the paired t test did not show a statistically significant difference for any of the measures analysed (Table 5). The percentages of agreement for intra- and interobserver variability during
Table 2 Coefficients values (B0, B1, … B6) and the six independent variables of interest (Var x1–Var x6) that remained in the model after the multinomial logistic regression analysis used to provide three logit g(x) functions 5 B0 1 (B1 Var x1) 2 (B2 Var x2) 1 (B3 Var x3) 1 (B4 Var x4) 2 (B5 Var x5) 2 (B6 Var x6), for each of quantitative cervical maturational changes (QCMC) stages, with QCMC Stage I as reference category Stages QCMC IIa QCMC IIIb QCMC IVc
Coefficients (b) and variables of interest B1 Var x1 B2 Var x2 B0 7.877 0.128 MP_C3 0.142 ANG_C3 5.565 0.162 MP_C3 0.199 ANG_C3 16.521 0.001 MP_C3 0.289 ANG_C3
B3 0.035 0.067 0.354
Var x3 MP_C4 MP_C4 MP_C4
B4 0.053 0.125 0.179
Var x4 Age Age Age
B5 0.013 0.052 0.189
Var x5 SP_C4 SP_C4 SP_C4
B6 2.374 2.784 3.301
Var x6 Genderd,e Genderd,e Genderd,e
ANG_C3 is the internal angle formed by the intersection of the lines that connect the points CE and ED at the lower borders of C3; SP_C4 is square proportion of C4; and MP_C4 is maturity proportion of C4. a Logit g(x1) function 5 7.877 1 0.128 (MP_C3) 2 0.142 (ANG_C3) 1 0.035 (MP_C4) 1 0.053 (age) 2 0.013 (SP_C4) 2 2.374 (gender). b Logit g(x2) function 5 5.565 1 0.162 (MP_C3) 2 0.199 (ANG_C3) 1 0.067 (MP_C4) 1 0.125 (age) 2 0.052 (SP_C4) 2 2.784 (gender). c Logit g(x3) function 5 16.521 1 0.001 (MP_C3) 2 0.289 (ANG_C3) 1 0.354 (MP_C4) 1 0.179 (age) 2 0.189 (SP_C4) 2 3.301 (gender). d Male. e Female.
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Table 3 Total and partial percentages of the correctness of the multinomial logistic regression model (MLRM) during skeletal stage estimation QCMC stage observed I II III IV Overall percentage (%)
MLRMa predicted I II III IV 86 6 0 0 9 45 8 2 0 11 29 0 0 1 7 32 40.3 26.7 18.6 14.4
Correctness percentage (%) 93.5 70.3 72.5 80.0 81.4
QCMC, Quantitative Cervical Maturational Changes. a Most likely probability according to the MLRM.
hand–wrist analysis were 80.00% and 66.66%, respectively. The weighted k values ranged from 0.92 (0.86–0.98) to 0.93 (0.88–0.99) for intrarater agreement, and from 0.87 (0.79–0.95) to 0.88 (0.79–0.97) for interrater agreement. The weighted k coefficients are far above those found for the percentage agreement. This is because most of the disagreements were just one stage apart.
Discussion The methodology of the present study was established while taking into consideration the criteria for assessing the quality of studies on the CVM established in a recent systematic review15 to avoid methodological flaws that could impair the validity of the presented results. Unlike other studies10,21,22 in which the measures of interest were obtained manually in individual cephalometric traces, the methodology used with the DVA software aimed to reduce the involvement of the examiner. This is particularly relevant with regard to obtaining the angular variables, where the simple identification Table 4 Total and partial percentages of the correctness of the age and a combination of age and gender during skeletal stage estimation QCMC stage observed Agea predicted I II III IV Overall percentage Age and genderb predicted I II III IV Overall percentage
III
IV
Correctness percentage (%)
I
II
67 28 1 1 40.3
21 3 1 24 5 7 26 9 4 7 6 26 26.7 18.6 14.4
73.6 36.4 23.1 65.0 49.5
79 16 2 2 40.3
11 2 0 40 7 1 16 16 6 3 7 28 26.7 18.6 14.4
86.8 60.6 41.0 70.0 64.5
QCMC, Quantitative Cervical Maturational Changes. a Most likely probability according to the chronological age. b Most likely probability according to the chronological age and gender.
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of points of interest in the vertebral bodies was enough for the software to provide all of the necessary measures. An important aspect regarding the methodology of the present study was the fact that we adopted the method proposed by Fishman26 for hand–wrist maturational staging. This method26 uses bone developmental stages associated with ossification events and defines the percentage of remaining growth, which is less susceptible to the influence of the environment and the gender and racial composition of the sample24 and is more suitable when compared with Tanner and Whitehouse methods TW230 and TW331 used in other studies that have developed quantitative CVM methods.21–23 The results obtained with the DVA analysis software revealed some interesting details. Firstly, the increase of the concavity on the lower edges of C2, C3 and C4 in advanced stages of maturation that was suggested in previous studies7,10 was consistent with the findings of the present study, where a significant reduction of the angle of the concavity of C2, C3 and C4 was observed when the degree of skeletal maturity between QCMC stages increased. Regarding the shape of the C3 and C4 vertebral bodies, mathematically, the proportion between the anterior and posterior wall is expected to be smaller in the early stages, which subsequently approaches and equates to 1 as maturity increases and the vertebral bodies become rectangular or square.7,10,17 The quantitative analysis of the present study verified this relationship through the maturity proportion and further revealed that the anterior wall remains smaller than the posterior wall on average, as this ratio increases towards 1, even in advanced stages of maturation, although significant differences exist between the QCMC stages. This observation casts uncertainty on the rectangular or square shape suggested for these vertebral bodies, which was used as the standard in the proposed atlas in previous qualitative analyses.7,13,17,19 Another observation regarding the shape of the bodies of C3 and C4 is that the ratio was .1 on average between the width and height (square proportion) in all QCMC stages in this study. This proportion was significantly reduced between the QCMC Stages I and IV, which suggests an increase in the height of the vertebral bodies in the later stages of growth and confirms the findings of another study.10 However, the present results demonstrate that the bodies of the vertebrae fail to provide a vertical rectangular shape in the later stages of growth on average, as suggested in the qualitative methods previously proposed.7,13,17,19 In summary, the weakness of the qualitative CVM methods that results in part from the difficulty in classifying the vertebral bodies of C3 and C4 as trapezoidal, rectangular horizontal, square or rectangular vertical according to another study32 did not affect the method proposed in the present study. Two major questions appear to motivate the development of an alternative method to hand–wrist radiographic assessment to determine skeletal maturity. The first issue is the complexity of identifying reference points in the hand–wrist images, which can lead to inaccurate
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Table 5 Paired Student’s t-test for intrarater and inter-rater agreement between the initial (T1) and 2-weeks time (T2) during digitized vertebrae analysis software measurements
Variables ANG_C2 ANG_C3 SP_C3 MP_C3 ANG_C4 SP_C4 MP_C4
Intrarater reliability Examiner 1 p-value Mean standard error 0.425 ±0.68 0.417 ±0.79 0.617 ±1.38 0.625 ±1.01 0.230 ±0.53 0.271 ±0.80 0.593 ±0.92
Examiner 2 p-value Mean standard error 0.237 ±0.87 0.243 ±1.07 0.414 ±1.64 0.577 ±0.82 0.159 ±0.84 0.601 ±0.94 0.379 ±0.89
Inter-rater reliability T1 p-value Mean standard error 0.462 ±0.58 0.147 ±0.48 0.331 ±1.14 0.652 ±0.73 0.789 ±0.87 0.213 ±0.94 0.257 ±0.92
T2 p-value 0.280 0.962 0.626 0.607 0.346 0.865 0.257
Mean standard error ±0.85 ±0.96 ±1.89 ±1.21 ±0.83 ±1.16 ±1.18
ANG_C2, ANG_C3, and ANG_C4 are internal angles formed by the intersection of the lines that connect the points CE and ED at the lower borders of C2, C3, and C4; SP_C3 and SP_C4 are square proportion of C3 and C4; and MP_C3 and MP_C4 are maturity proportion of C3 and C4.
analysis according to previous studies.33,34 In the present study, the percentages of inter- and intraobserver agreements show that, on average, examiners disagree in their own assessments or among themselves in one of every four evaluations during hand–wrist analysis, demonstrating some kind of variability of the hand–wrist maturational method. Since the reproducibility is also the main problem of the CVM qualitative methods, the reliability of DVA was assessed. No significant difference in the intra- and interexaminer variability was observed, indicating low level of variability by using DVA software. This was a significant diagnostic advantage when compared with the traditional qualitative methods, which can lead to accurate analysis. Apart from the question of the reliability, another issue regarding hand–wrist assessment is the additional radiographic exposure. Although cancer risk from exposure of the neck is significantly greater than the risk from exposing the hand and wrist, this can be reduced by the use of a thyroid shield during cephalometric imaging, which does not obscure the view of the bodies of C2, C3 and C4. In this case, if the answers and information about the growth status could be found in a cephalometric radiograph that is already part of the initial set of orthodontic records, why would there be a need for radiography of hand and wrist? After analysing the individual behaviour of the variables used in the software, the MLRM was applied. Unlike different regression models adopted in other quantitative studies,10,21–23 the model used in the present study does not adopt cut-offs for categorization and does not provide a specific skeletal age, which reduces the loss of information. Compared with the quantitative CVM method developed in another study,10 the method adopted in the present study seems to be more appropriate. First, by simplicity in identification of landmarks through DVA software analysis. Second, by including six variables in the final model, which formed three nonlinear equations that estimate the CVM with the accuracy of prediction. Third, gender and chronological age were included in the model. According to the results of another study,25 sexual dimorphism was found in both size and shape of cervical vertebrae bodies. In the present study, gender and
chronological age were included in the final model, and it was not necessary to segregate the sample into boys and girls because of gender differences in the process of skeletal maturation,35,36 increasing the robustness of the model. Fourth, the overall accuracy of prediction was quantified in the present study. Unfortunately, no prediction interval was reported in a previous research,10 which makes it impossible to compare their model with the system developed in the present study. The correlation coefficients between the independent variables and SMI were above 0.800 (p , 0.01). The multinomial model established in the present study took into account the correlation between one variable and another, controlled by all the other variables included in the final model, named partial correlation. The low values of partial correlation demonstrate that the present MLRM did not suffer from high collinearity. According to a previous study,25 the accuracy of the CVM methods should be compared with other evaluation systems, such as age. In the present study, the total percentage of the correctness of the model obtained with the use of chronological age solely as the independent variable was 49.5%, and 64.5% with a combination of age and gender. The best prediction (81.4%) was achieved with the combination of four cervical parameters, plus age and gender. Different from the results reported in another study,25 when the analyses of cervical vertebral shape could not predict skeletal maturation better than chronological age, the value added by the present model that used the four parameters, age and gender was 17% (81.4–64.5). In other words, the addition of the parameters of the cervical vertebrae bodies in the final model did explain almost 50% of the 35.5% of the predictability that could not be achieved with the age and gender alone. The prediction success rate of the present study was similar with those stated in another study,36 with an overall predictability of the final model of 81.4%, with a better prediction of an individual’s maturational status on QCMC Stages I and IV. In agreement with Fishman,36 it seems to be satisfactory in terms of diagnosis, especially considering that most orthodontists do not use the analysis of cervical vertebrae when determining the degree of skeletal maturity.
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Figure 2 illustrates the applicability of the MLRM. The patient’s skeletal maturational level was 10, according to Fishman’s method. The MLRM showed the most likely probability for this subject belonging to QCVM IV and agreeing with the hand–wrist skeletal age. However, the qualitative analysis of CVM showed that the patient belonged to cervical stage 4 according to Baccetti et al,7 which disagreed with the complete level of growth as shown by SMI. Apart from the results of this study, the major question regarding the reliability of the CVM method to predict the pubertal growth spurt remains unanswered. Longitudinal studies on a larger sample that analysed the sensitivity and specificity of the method proposed in this study compared with other methods, such as hand–wrist radiographs, analysis of the growth
in stature and growth hormone indicators, can help to answer that question. In conclusion, the quantitative method implemented through specific software described herein was demonstrated to be reproducible. There were significant anatomical changes observed in the bodies of C2, C3 and C4 through the DVA software analysis between the four QCMC stages. The model used here that combines the four parameters measured on the vertebral bodies, plus age and the gender showed a satisfactory prediction. Improving the DVA software with the automatic identification of the points of interest located in the bodies of C2, C3 and C4 and the inclusion of other measures of interest aimed at reducing the influence of examiner on analyses and increasing the predictability of the model could be the objectives of further research.
REFERENCES 1. Wong RW, Alkhal HA, Rabie BM. Use of cervical vertebral maturation to determine skeletal age. Am J Orthod Dentofacial Orthop 2009; 136: 484.e1–e6. doi: 10.1016/j.ajodo.2007.08.033 2. Franchi L, Baccetti T, McNamara JA Jr. Mandibular growth as related to cervical vertebral maturation and body height. Am J Orthod Dentofacial Orthop 2000; 118: 335–40. doi: 10.1067/ mod.2000.107009 3. Petrovic A, Stutzmann J, Lavergne J, Shaye R. Is it possible to modulate the growth of human mandible with a functional appliance? Int J Orthod 1991; 29: 3–8. 4. Hagg U, Pancherz H. Dentofacial orthopaedics in relation to chronological age, growth period and skeletal development. An analysis of 72 male patients with class II division 1 malocclusion with the Herbst appliance. Eur J Orthod 1988; 10: 169–76. 5. Franchi L, Baccetti T. The use of maturational indices for the identification of optimal treatment timing in dentofacial orthopedics. In: McNamara JA Jr, Kelly KA, eds. Treatment timing: orthodontics in four dimensions. Craniofacial growth series. Vol. 39. Ann Arbor, MI: Center for Human Growth and Development, University of Michigan; 2002. pp. 151–70. 6. San Rom´an P, Palma JC, Oteo MD, Nevado E. Skeletal maturation determined by cervical vertebrae development. Eur J Orthod 2002; 24: 303–11. 7. Baccetti T, Franchi L, McNamara JA, Jr. The cervical vertebral maturation (CVM) method for the assessment of optimal treatment timing in dentofacial orthopedics. Semin Orthod 2005; 11: 119–29. 8. Flores-Mir C, Burgess CA, Champney M, Jensen RJ, Pitcher MR, Major PW. Correlation of skeletal maturation stages determined by cervical vertebrae and hand–wrist evaluations. Angle Orthod 2006; 76: 1–5. doi: 10.1043/0003-3219(2006)076[0001: COSMSD]2.0.CO;2 9. Uysal T, Ramoglu SI, Basciftci FA, Sari Z. Chronologic age and skeletal maturation of the cervical vertebrae and hand–wrist: is there a relationship? Am J Orthod Dentofacial Orthop 2006; 130: 622–8. doi: 10.1016/j.ajodo.2005.01.031 10. Chen LL, Xu TM, Jiang HJ, Zhang XZ, Lin JX. Quantitative cervical vertebral maturation assessment in adolescents with normal occlusion: a mixed longitudinal study. Am J Orthod Dentofacial Orthop 2008; 134: 720.e1–e7. doi: 10.1016/j. ajodo.2008.03.014 11. Lai EHH, Liu JP, Chang JZC, Tsai SJ, Yao CC, Chen MH, et al. Radiographic assessment of skeletal maturation stages for orthodontic patients: hand–wrist bones or cervical vertebrae? J Formos Med Assoc 2008; 107: 316–25. doi: 10.1016/S0929-6646 (08)60093-5
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12. Gandini P, Mancini M, Andreani F. A comparison of hand–wrist bone and cervical vertebral analyses in measuring skeletal maturation. Angle Orthod. 2006; 76: 984–989. doi: 10.2319/070605-217 13. Hassel B, Farman AG. Skeletal maturation evaluation using cervical vertebrae. Am J Orthod Dentofacial Orthop 1995; 107: 58–66. 14. Stiehl J, Muller B, Dibbets J. The development of the cervical vertebrae as an indicator of skeletal maturity: comparison with the classic method of hand–wrist radiograph. J Orofac Orthop 2009; 70: 327–35. doi: 10.1007/s00056-009-9918-x 15. Santiago RC, Costa LFM, Vitral RWF, Fraga MR, Bolognese AM, Maia LC. Cervical vertebral maturation as a biologic indicator of skeletal maturity: a systematic review. Angle Orthod 2012; 82: 1123–31. doi: 10.2319/103111-673.1 16. Soegiharto BM, Moles DR, Cunningham SJ. Discriminatory ability of a skeletal maturation index and the cervical vertebrae maturation index in detecting peak pubertal growth in Indonesian and white subjects with receiver operating characteristics analysis. Am J Orthod Dentofacial Orthop 2008; 134: 227–37. 17. Baccetti T, Franchi L, McNamara JA Jr. An improved version of the cervical vertebral maturation (CVM) method for the assessment of mandibular growth. Angle Orthod 2002; 72: 316–23. doi: 10.1043/0003-3219(2002)072,0316:AIVOTC.2.0.CO;2 18. Lamparski DG. Skeletal age assessment utilizing cervical vertebrae. PhD thesis. Pittsburgh: University of Pittsburgh; 1972. 19. O’Reilly MT, Yanniello GJ. Mandibular growth changes and maturation of cervical vertebrae—a longitudinal cephalometric study. Angle Orthod 1988; 58: 179–84. doi: 10.1043/0003-3219 (1988)058,0179:MGCAMO.2.0.CO;2 20. Gabriel DB, Southard KA, Qian F, Marshall S, Franciscus R, Southard TE. Cervical vertebrae maturation method: poor reproducibility. Am J Orthod Dentofacial Orthop 2009; 136: 478. e1–e7. doi: 10.1016/j.ajodo.2007.08.028 21. Mito T, Sato K, Mitani H. Cervical vertebral bone age in girls. Am J Orthod Dentofacial Orthop 2002; 122: 380–5. 22. Caldas MP, Ambrosano GMB, Haiter Neto F. New formula to objectively evaluate skeletal maturation using lateral cephalometric radiographs. Braz Oral Res 2007; 21: 330–5. 23. Caldas MP, Ambrosano GMB, Haiter-Neto F. Computer-assisted analysis of cervical vertebral bone age using cephalometric radiographs in Brazilian subjects. Braz Oral Res 2010; 24: 120–6. 24. Flores-Mir C, Nebbe B, Major PW. Use of skeletal maturation based on hand–wrist radiographic analysis as a predictor of facial growth: a systematic review. Angle Orthod 2004; 74: 118–24. doi: 10.1043/0003-3219(2004)074,0118:UOSMBO.2.0.CO;2 25. Chatzigianni A, Halazonetis DJ. Geometric morphometric evaluation of cervical vertebral shape and its relationship to skeletal
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maturation. Am J Orthod Dentofacial Orthop 2009; 136: 481. e1–e9. doi: 10.1016/j.ajodo.2009.04.017 Fishman LS. Radiographic evaluation of skeletal maturation. A clinically oriented method based on hand–wrist films. Anlge Orthod 1982; 52: 88–112. doi: 10.1043/0003-3219(1982)052,0088: REOSM.2.0.CO;2 Kopecky GR, Fishman LS. Timing of cervical headgear treatment based on skeletal maturation. Am J Orthod Dentofacial Orthop 1993; 104: 162–9. Bitencourt HR. Multinomial logistic regression: a review and applications. Acta Scientiae 2003; 5: 77–86. Kleinbaum DG, Kupper LL, Muller KE, Nizam A. Applied regression analysis and other multivariable methods. 3rd edn. Stamford, CT: Brooks/Cole Publishing Company; 1998. pp. 656–86. Tanner JM, Whitehouse RH, Cameron N, Marshall WA, Healy MJR, Goldstein H. Assessment of skeletal maturity and prediction of adult height (TW2 method). 2nd edn. London, UK: Academic Press; 1983. pp. 22–37; 50–85.
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31. Tanner JM, Whitehouse RH, Cameron N, Marshall WA, Healy MJR, Goldstein H. Assessment of skeletal maturity and prediction of adult height (TW3 method). 3rd edn. London, UK: W.B. Saunders; 2001. 32. Nestman TS, Marshall SD, Qian F, Holton N, Franciscus RG, Southard TE. Cervical vertebrae maturation method morphologic criteria: poor reproducibility. Am J Orthod Dentofacial Orthop 2011; 140: 182–8. doi: 10.1016/j.ajodo.2011.04.013 33. Moore RN, Moyer BA, DuBois LM. Skeletal maturation and craniofacial growth. Am J Orthod Dentofacial Orthop 1990; 98: 33–40. 34. Houston WJB, Miller JC, Tanner JM. Prediction of the timing of the adolescent growth spurt from ossification events in hand–wrist films. Br J Orthod 1979; 6: 145–52. 35. Smith RJ. Misuse of hand–wrist radiographs. Am J Orthod 1980; 77: 75–8. 36. Fishman LS. Maturational patterns and prediction during adolescence. Angle Orthod 1987; 57: 178–93. doi: 10.1043/0003-3219 (1987)057,0178:MPAPDA.2.0.CO;2
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Dentomaxillofac Radiol, 43, 20130238
RESEARCH ARTICLE
New software for cervical vertebral geometry assessment and its relationship to skeletal maturation—a pilot study 1
3 ´ R C Santiago, A R Cunha, 2G C Junior, N Fernandes, 2M J S Campos, 1L F M Costa, 2R W F Vitral 1 and A M Bolognese
1
Department of Pediatric Dentistry and Orthodontics, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil; 2Department of Orthodontics, Federal University of Juiz de Fora, Minas Gerais, Brazil; 3Department of Statistics, Federal University of Juiz de Fora, Minas Gerais, Brazil
Objectives: In the present study, we developed new software for quantitative analysis of cervical vertebrae maturation, and we evaluated its applicability through a multinomial logistic regression model (MLRM). Methods: Digitized images of the bodies of the second (C2), third (C3) and fourth (C4) cervical vertebrae were analysed in cephalometric radiographs of 236 subjects (116 boys and 120 girls) by using a software developed for digitized vertebrae analysis. The sample was initially distributed into 11 categories according to the Fishman’s skeletal maturity indicators and were then grouped into four stages for quantitative cervical maturational changes (QCMC) analysis (QCMC I, II, III and IV). Seven variables of interest were measured and analysed to identify morphologic alterations of the vertebral bodies in each QCMC category. Results: Statistically significant differences (p , 0.05) were observed among all QCMC categories for the variables analysed. The MLRM used to calculate the probability that an individual belonged to each of the four cervical vertebrae maturation categories was constructed by taking into account gender, chronological age and four variables determined by digitized vertebrae analysis (Ang_C3, MP_C3, MP_C4 and SP_C4). The MLRM presented a predictability of 81.4%. The weighted k test showed almost perfect agreement (k 5 0.832) between the categories defined initially by the method of Fishman and those allocated by the MLRM. Conclusions: Significant alterations in the morphologies of the C2, C3 and C4 vertebral bodies that were analysed through the digitized vertebrae analysis software occur during the different stages of skeletal maturation. The model that combines the four parameters measured on the vertebral bodies, the age and the gender showed an excellent prediction. Dentomaxillofacial Radiology (2014) 43, 20130238. doi: 10.1259/dmfr.20130238 Cite this article as: Santiago RC, Cunha AR, J´unior GC, Fernandes N, Campos MJS, Costa LFM, et al. New software for cervical vertebral geometry assessment and its relationship to skeletal maturation—a pilot study. Dentomaxillofac Radiol 2014; 43: 20130238. Keywords: cervical vertebrae; skeletal maturity; logistic regression Introduction The identification of the pubertal growth spurt has great value in dentistry. The highest response to functional orthopaedic stimuli applied to the jaw bones tend to occur during this period, and its effectiveness is directly related to bone maturation.1–4 The effectiveness of Correspondence to: Dr Rodrigo C´esar Santiago. E-mail: rodrigo_cesar_santiago@ hotmail.com Received 4 July 2013; revised 24 November 2013; accepted 2 December 2013
a biological indicator of skeletal maturity is directly related to factors such as the ability to detect and predict the growth spurt peak without the need for additional radiation exposure and the high level of agreement between examiners for the definition of the stages.5 In this context, the use of the cervical vertebrae has been suggested as an alternative, instead of the hand–wrist radiographs, in the determination of skeletal maturation.
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In the past 2 decades, several studies have analysed the applicability of lateral cephalometric radiographs to determine skeletal maturity based on the analysis of alterations in the morphology of the cervical vertebrae, especially the second (C2), third (C3) and fourth (C4) cervical vertebrae.1,2,6–11 Although many studies1,9,12–14 have validated this method through the strong correlation between the cervical vertebrae maturation (CVM) and hand and wrist skeletal maturity, recent studies have questioned its applicability.15,16 The first concerns regarding the validity of qualitative methods for identifying CVM are related to the consistency during data interpretation. These methods7,13,17–19 take into account a subjective comparison between images of the vertebrae and a reference atlas containing the CVM stages. In a previous study,20 the low reproducibility observed between clinicians of a qualitative CVM model suggested that it should not be used clinically as the only guide to define the optimal time for orthodontic treatment. The low reproducibility of a diagnostic method, in particular qualitative methods for identifying CVM,6,13,17 brings into question the accuracy of these models in the way they are proposed. Several studies21–23 have established the skeletal age of individuals from multiple regression analyses with the aim of developing quantitative methods for objective analysis of the maturation of cervical vertebrae and reducing the variability of interpretations. However, questions remain regarding the standard method used for the determination of the skeletal age24 and the lack of accuracy in the prediction of the proposed methods.25 Thus, the present study aimed to develop a new quantitative method for the identification of CVM through computer analysis by using specific software designed by the authors and to evaluate the applicability of this new method by using a multinomial logistic regression model (MLRM). Additionally, we also evaluated the predictability of an MLRM using solely chronological age or a combination of age and gender as skeletal maturation predictors. Methods and materials The data from this cross-sectional study were obtained from lateral cephalometric radiographs and hand and wrist radiographs taken as part of routine orthodontic records. The sample included 236 children—116 boys [mean (standard deviation), 146.4 (25.21) months] and 120 girls [mean (standard deviation), 146.2 (24.1) months]— consecutively selected between January and December 2011. The following selection criteria were used during the sample composition: (1) white Brazilian subjects with no history of trauma to the face and/or hand and wrist, (2) the absence of congenital and/or acquired malformations that could affect the vertebrae or the hand and wrist, (3) general good health and (4) cephalometric and hand and wrist radiographs taken on the same day and with Dentomaxillofac Radiol, 43, 20130238
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good visualization of the structures of interest, such as the C2, C3 and C4 cervical vertebrae. The study was approved by the Ethics on Research Committee of Federal University of Juiz de Fora, Brazil. The radiographs of the hands and wrists were used as the standard method for determining the degree of skeletal maturation of each individual and were analysed by a dental surgeon who specializes in image techniques with extensive experience in the method of interest. The radiographs were classified according to the skeletal maturation index (SMI) described by Fishman26 and were divided into the 11 developmental stages according to Fishman. All analyses were performed in the dark with the same light box, and the examiner was unaware of any additional information such as chronological age or gender. For reliability analysis in relation to the staging of the hand and wrist radiographs, 30 radiographs were examined twice with an interval of 2 weeks between assessments. The intraclass correlation coefficient (0.997) revealed intraobserver reproducibility and reliability in the classifications of hand–wrist maturational stages. The 11 stages of Fishman’s skeletal maturity26 can be grouped into periods of acceleration (SMI 1–3), high velocity (SMI 4–7) and deceleration (SMI 8–11).27 In the present study, the radiographs were grouped into four stages of CVM, taking into account Fishman’s indicators of skeletal maturity, but segregating the period of deceleration (SMI 8–11) into two different stages owing to significant anatomical differences between SMI 8–9 and SMI 10–11 in the morphologies of the bodies of C2, C3 and C4 cervical vertebrae. The quantitative cervical maturational changes (QCMC) comprised four stages: QCMC I (acceleration of growth), which includes Fishman’s Stages 1–3; QCMC II (high growth rate), which includes Stages 4–7; QCMC III (decelerated growth), which includes Stages 8 and 9; and QCMC IV (consummation of growth), which includes Stages 10 and 11. The radiographs were scanned using Umax Astra 2400SLT (Umax Technologies Inc, Dallas, TX) at 600 dots per inch and digitalized through the Corel PhotoPaint software v. 11.0 (Corel Photo-Paint®; Corel Corporation, Ottawa, Canada). The morphologies of the C2, C3 and C4 were analysed using software developed specifically for this study from 10 additional images. The software for digitized vertebrae analysis (DVA) was developed in Microsoft.NET Framework in the C# language to aid the specialist in the analysis of the image; this software provided measurements and proportions of the C2, C3 and C4 vertebrae based on reference points marked manually on the image (Figure 1). An important function of the software is to calculate automatically the following measures: concavity angle, width, height, square proportion (defined later) and maturity proportion (defined later). First, the user must provide reference points C, E, D for vertebrae C2 and reference points A, B, C, D and E for vertebrae C3 and C4. The software displays the radiograph-scanned image and lets the user mark the above points using his mouse.
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Figure 1 (a) Lateral cephalometric radiograph with the region of interest and the definition of the reference points (b), marked manually on the image by the digitized vertebrae analysis software. The reference points marked manually were A–E. The reference points provided automatically by the software were F, G, F9 and G9.
The reference points marked manually in this study were A and B, the most superior points of the posterior and anterior borders, respectively, of the bodies of C3 and C4; C and D, the most inferior points of the posterior and anterior borders, respectively, of the bodies of C3 and C4; E, the point of greatest concavity of the lower border of the bodies of C2, C3 and C4. The reference points provided automatically by the software were F and G, the midpoints of the lower (CD) and anterior (BD) borders, respectively; F9, the intersection point where the line from F point, parallel to the posterior border, touches the superior border and G9, the intersection point where the line from G point, parallel to the inferior border, touches the posterior border (Figure 1). After defining the points of interest, the tool used methods of linear algebra and spatial analysis to generate the dimension, proportion and angle values.
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The measurements of interest were determined as follows (Figure 2): AB and CD: superior and lower borders of the body, respectively; AC and BD: posterior and anterior borders of the body, respectively; ANG_C2, ANG_C3, and ANG_C4: internal angle formed by the intersection of the lines that connect the points CE and ED at the lower borders of C2, C3, and C4, respectively. Using the cosine formula C 2 5a2 1 b2 2 2abcosg the software calculated the cosine of angle E. Then applying the inverse cosine function we obtained the angle E. SP_C3 and SP_C4: square proportion of C3 and C4, respectively, given by the ratio between the line parallel to the lower border (CD) connecting the points G and G9 and the line parallel to the posterior border (AC) that connects points F and F9. MP_C3 and MP_C4: maturity proportion of C3 and C4, respectively, given by the ratio between the anterior border (BD) and the posterior border (AC). The sample was evaluated by one examiner for the following nine variables: (1) chronological age (months), (2) gender, (3) ANG-C2, (4) ANG_C3, (5) ANG_C4, (6) SP_C3, (7) SP_C4, (8) MP_C3 and (9) MP_C4. For the examiner variability analysis, by using the DVA software, 30 radiographs were analysed at 2 different times separated by an interval of 2 weeks. The paired t-test did not show a statistically significant difference for any of the measures analysed [p 5 0.562; mean standard error: ANG_C2 (±0.52), ANG_C3 (±0.40), ANG_C4 (±0.68), SP_C3 (±1.18), MP_C3 (±0.54), SP_C4 (±1.19), MP_C4 (±0.74)]. 30 lateral cephalograms and 30 hand–wrist radiographs were randomly selected from the 236 patients and analysed by 2 examiners to assess intra- and interobserver variability during cervical and hand–wrist assessments. The examiners received training to use the software and hand–wrist methods from a dental surgeon who had extensive experience in the methods of interest. Immediately after training, the 30 hand–wrist radiographs were analysed using light boxes, and the 30 lateral cephalograms were analysed on a personal computer in a darkened room with contrast enhancement of the bone images. The examiners did not have access to any additional information regarding the patient, such as age, gender and stage of teething. The whole procedure was repeated 2 weeks (T2) after the first evaluation (T1) with the random distribution of radiographs, and all examiners received the same training again as for the first evaluation. Statistical analysis All statistical analyses were performed using a software package (SPSS® for Windows v. 13.0; SPSS Inc., Chicago, IL). The averages and standard deviations were calculated for cervical assessments. Statistical analysis included the x 2 test, ANOVA test, weighted k test, Spearman’s rank correlation coefficient and multinomial logistic regression analysis. A significance level of p , 0.05 was used. The statistical Excel software (Microsoft Office® 2007; Microsoft, Redmond, WA) was used to analyse the data and obtain the probabilities of the multinomial regression model. dmfr.birjournals.org
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Figure 2 (a) Subject in the CVM Stage 4, according to Baccetti et al7 (b). (c) Quantitative analysis of C2, C3 and C4 maturation by the digitized vertebrae analysis software. The multinomial logistic regression model indicated a 86.6% of the probability for this patient belonged to quantitative cervical maturational changes (QCMC) IV, which is more consistent with the skeletal maturational Level 10 of Fishman,26 observed for this patient.
The logistic model enables the direct estimation of the probability of occurrence of an event, such as whether an individual belongs to a certain category.28 The logistic regression model, originally developed for binary response variables, can be extended to multinomial response variables (three or more categories), as observed in the present study, where the sample was divided into four stages of QCMC (QCMC I–IV). Although the MLRM is appropriate for nominal data, ordinal variables can be treated as nominal data, minimizing some issues such as lack of homoscedasticity, linearity and incorporating outliers.29 In this study, each of the variables analysed (chronological age, gender, hand and wrist maturity, ANG_C2, ANG_C3, ANG_C4, SP_C3, SP_C4, MP_C3 and MP_C4) were inserted individually in an MLRM that adopted the QCMC I as reference, owing to the greatest number of subjects being in this category. The variables that contributed significantly to the differentiation of the QCMC Stages II, III and IV from the reference category (QCMC I) remained in the final model. Three linear functions g(x) were generated, and Dentomaxillofac Radiol, 43, 20130238
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it was possible to calculate the conditional probabilities that each radiograph analysed belonged to a QCMC stage. Finally, the model was represented by the intercept of the independent variables that contributed significantly to the discrimination between categories and their respective B coefficients (variable coefficient). The multinomial method sought to establish a single model instead of various models, as would occur in the case of dividing the subjects according to gender or age. Moreover, the gender showed an additive effect (adding information) and non-interactive effect, which make it unnecessary to divide the sample and increased the robustness and predictability of the model because of a larger sample size. Additionally, we did evaluate the MLRM model using only chronological age or a combination of age and gender to compare the total and partial percentages of the correctness of the model obtained with the final model established in the present study. The spreadsheet generated in the Excel software by the insertion of data from the six independent variables included in the final model allowed the determination of the
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Table 1 Distributions of age, gender and means and standard deviations for the seven variables of interest for each of the quantitative cervical maturational changes (QCMC), Stages (I–IV)
Variables Age (months) Gender ANG_C2 (°) ANG_C3 (°) ANG_C4 (°) SP_C3 SP_C4 MP_C3 MP_C4
Stages QCMC I 128 ± 18 69 M/23 F 171.71 ± 7.48 176.30 ± 6.33 177.70 ± 6.16 1.61 ± 0.18 1.61 ± 0.16 0.68 ± 0.07 0.69 ± 0.07
QCMC II 144 ± 16 23 M/41 F 161.97 ± 6.31 165.46 ± 6.79 169.41 ± 6.89 1.41 ± 0.19 1.42 ± 0.18 0.80 ± 0.06 0.77 ± 0.06
QCMC III 158 ± 10 11 M/29 F 153.58 ± 8.53 157.73 ± 7.89 161.93 ± 7.47 1.22 ± 0.13 1.24 ± 0.12 0.87 ± 0.07 0.83 ± 0.04
QCMC IV 177 ± 18 13 M/27 F 147.77 ± 7.97 151.48 ± 6.82 152.43 ± 8.83 1.08 ± 0.12 1.07 ± 0.11 0.92 ± 0.06 0.89 ± 0.05
p-value 0.000a 0.000b 0.000a 0.000a 0.000a 0.000a 0.000a 0.000a 0.000a
F, female; M, male. ANG_C2, ANG_C3, and ANG_C4 are internal angle formed by the intersection of the lines that connect the points CE and ED at the lower borders of C2, C3, and C4, respectively. SP_C3 and SP_C4 are square proportion of C3 and C4, respectively. MP_C3 and MP_C4 are maturity proportion of C3 and C4, respectively. a ANOVA for mean comparison between each of the QCMC stages (p , 0.05). b 2 x test for gender distribution analysis between each of the QCMC stages (p , 0.05).
probability that each radiograph belonged to one of the four QCVM categories (QMVC I, II, III, or IV). The most likely probability for distribution of the sample in each of the categories (QMVC I, II, III or IV) was adopted. To analyse reproducibility, the overall percentage of agreement in the intra- and inter-rater variability was calculated, and the weighted k test was used for hand– wrist assessment. The paired t-test was used to analyse reliability of cervical assessment used by the DVA software. A significance level of p , 0.05 was used. Results The distributions of gender and means and standard deviations for the variables of interest are shown in Table 1. A statistically significant difference (p , 0.05) was observed in the distribution of all variables for each of the QCVM categories. For the correlation between the parameters of cervical vertebrae morphology and the SMI, all the seven parameters were significantly correlated at p , 0.01 level [Spearman rank correlation: ANG_C2 (20.826), ANG_C3 (20.836), ANG_C4 (20.818), SP_C3 (20.812), MP_C3 (10.817), SP_C4 (20.817) and MP_C4 (10.804)].
After the multinomial logistic regression analysis, six independent variables of interest (Var x1–Var x6) remained in the model (Table 2). The model provided three logit g(x) functions, one for each QCVM category (II, III and IV), which took into account the observed values for the six independent variables (Var x1–Var x6), the intercept (B0) and the coefficients for each independent variable (B1–B6). The MLRM obtained in this study showed an 81.4% of total percentage of the correctness, with partial percentages of the correctness raging from 70.3% to 93.5%, according to different QCMC stages (Table 3). The total percentage of the correctness of the model obtained with the use of chronological age was 49.5%, and 64.5% for a combination of age and gender (Table 4). The result of the weighted k test, which analysed the correlation between the categorizations established by the logistic regression model and the four QCMC stages established according to the 11 stages of Fishman’s skeletal maturity28 showed a good agreement (k 5 0.832). Regarding the reproducibility of the two examiners while using the software, the paired t test did not show a statistically significant difference for any of the measures analysed (Table 5). The percentages of agreement for intra- and interobserver variability during
Table 2 Coefficients values (B0, B1, … B6) and the six independent variables of interest (Var x1–Var x6) that remained in the model after the multinomial logistic regression analysis used to provide three logit g(x) functions 5 B0 1 (B1 Var x1) 2 (B2 Var x2) 1 (B3 Var x3) 1 (B4 Var x4) 2 (B5 Var x5) 2 (B6 Var x6), for each of quantitative cervical maturational changes (QCMC) stages, with QCMC Stage I as reference category Stages QCMC IIa QCMC IIIb QCMC IVc
Coefficients (b) and variables of interest B1 Var x1 B2 Var x2 B0 7.877 0.128 MP_C3 0.142 ANG_C3 5.565 0.162 MP_C3 0.199 ANG_C3 16.521 0.001 MP_C3 0.289 ANG_C3
B3 0.035 0.067 0.354
Var x3 MP_C4 MP_C4 MP_C4
B4 0.053 0.125 0.179
Var x4 Age Age Age
B5 0.013 0.052 0.189
Var x5 SP_C4 SP_C4 SP_C4
B6 2.374 2.784 3.301
Var x6 Genderd,e Genderd,e Genderd,e
ANG_C3 is the internal angle formed by the intersection of the lines that connect the points CE and ED at the lower borders of C3; SP_C4 is square proportion of C4; and MP_C4 is maturity proportion of C4. a Logit g(x1) function 5 7.877 1 0.128 (MP_C3) 2 0.142 (ANG_C3) 1 0.035 (MP_C4) 1 0.053 (age) 2 0.013 (SP_C4) 2 2.374 (gender). b Logit g(x2) function 5 5.565 1 0.162 (MP_C3) 2 0.199 (ANG_C3) 1 0.067 (MP_C4) 1 0.125 (age) 2 0.052 (SP_C4) 2 2.784 (gender). c Logit g(x3) function 5 16.521 1 0.001 (MP_C3) 2 0.289 (ANG_C3) 1 0.354 (MP_C4) 1 0.179 (age) 2 0.189 (SP_C4) 2 3.301 (gender). d Male. e Female.
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Table 3 Total and partial percentages of the correctness of the multinomial logistic regression model (MLRM) during skeletal stage estimation QCMC stage observed I II III IV Overall percentage (%)
MLRMa predicted I II III IV 86 6 0 0 9 45 8 2 0 11 29 0 0 1 7 32 40.3 26.7 18.6 14.4
Correctness percentage (%) 93.5 70.3 72.5 80.0 81.4
QCMC, Quantitative Cervical Maturational Changes. a Most likely probability according to the MLRM.
hand–wrist analysis were 80.00% and 66.66%, respectively. The weighted k values ranged from 0.92 (0.86–0.98) to 0.93 (0.88–0.99) for intrarater agreement, and from 0.87 (0.79–0.95) to 0.88 (0.79–0.97) for interrater agreement. The weighted k coefficients are far above those found for the percentage agreement. This is because most of the disagreements were just one stage apart.
Discussion The methodology of the present study was established while taking into consideration the criteria for assessing the quality of studies on the CVM established in a recent systematic review15 to avoid methodological flaws that could impair the validity of the presented results. Unlike other studies10,21,22 in which the measures of interest were obtained manually in individual cephalometric traces, the methodology used with the DVA software aimed to reduce the involvement of the examiner. This is particularly relevant with regard to obtaining the angular variables, where the simple identification Table 4 Total and partial percentages of the correctness of the age and a combination of age and gender during skeletal stage estimation QCMC stage observed Agea predicted I II III IV Overall percentage Age and genderb predicted I II III IV Overall percentage
III
IV
Correctness percentage (%)
I
II
67 28 1 1 40.3
21 3 1 24 5 7 26 9 4 7 6 26 26.7 18.6 14.4
73.6 36.4 23.1 65.0 49.5
79 16 2 2 40.3
11 2 0 40 7 1 16 16 6 3 7 28 26.7 18.6 14.4
86.8 60.6 41.0 70.0 64.5
QCMC, Quantitative Cervical Maturational Changes. a Most likely probability according to the chronological age. b Most likely probability according to the chronological age and gender.
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of points of interest in the vertebral bodies was enough for the software to provide all of the necessary measures. An important aspect regarding the methodology of the present study was the fact that we adopted the method proposed by Fishman26 for hand–wrist maturational staging. This method26 uses bone developmental stages associated with ossification events and defines the percentage of remaining growth, which is less susceptible to the influence of the environment and the gender and racial composition of the sample24 and is more suitable when compared with Tanner and Whitehouse methods TW230 and TW331 used in other studies that have developed quantitative CVM methods.21–23 The results obtained with the DVA analysis software revealed some interesting details. Firstly, the increase of the concavity on the lower edges of C2, C3 and C4 in advanced stages of maturation that was suggested in previous studies7,10 was consistent with the findings of the present study, where a significant reduction of the angle of the concavity of C2, C3 and C4 was observed when the degree of skeletal maturity between QCMC stages increased. Regarding the shape of the C3 and C4 vertebral bodies, mathematically, the proportion between the anterior and posterior wall is expected to be smaller in the early stages, which subsequently approaches and equates to 1 as maturity increases and the vertebral bodies become rectangular or square.7,10,17 The quantitative analysis of the present study verified this relationship through the maturity proportion and further revealed that the anterior wall remains smaller than the posterior wall on average, as this ratio increases towards 1, even in advanced stages of maturation, although significant differences exist between the QCMC stages. This observation casts uncertainty on the rectangular or square shape suggested for these vertebral bodies, which was used as the standard in the proposed atlas in previous qualitative analyses.7,13,17,19 Another observation regarding the shape of the bodies of C3 and C4 is that the ratio was .1 on average between the width and height (square proportion) in all QCMC stages in this study. This proportion was significantly reduced between the QCMC Stages I and IV, which suggests an increase in the height of the vertebral bodies in the later stages of growth and confirms the findings of another study.10 However, the present results demonstrate that the bodies of the vertebrae fail to provide a vertical rectangular shape in the later stages of growth on average, as suggested in the qualitative methods previously proposed.7,13,17,19 In summary, the weakness of the qualitative CVM methods that results in part from the difficulty in classifying the vertebral bodies of C3 and C4 as trapezoidal, rectangular horizontal, square or rectangular vertical according to another study32 did not affect the method proposed in the present study. Two major questions appear to motivate the development of an alternative method to hand–wrist radiographic assessment to determine skeletal maturity. The first issue is the complexity of identifying reference points in the hand–wrist images, which can lead to inaccurate
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Table 5 Paired Student’s t-test for intrarater and inter-rater agreement between the initial (T1) and 2-weeks time (T2) during digitized vertebrae analysis software measurements
Variables ANG_C2 ANG_C3 SP_C3 MP_C3 ANG_C4 SP_C4 MP_C4
Intrarater reliability Examiner 1 p-value Mean standard error 0.425 ±0.68 0.417 ±0.79 0.617 ±1.38 0.625 ±1.01 0.230 ±0.53 0.271 ±0.80 0.593 ±0.92
Examiner 2 p-value Mean standard error 0.237 ±0.87 0.243 ±1.07 0.414 ±1.64 0.577 ±0.82 0.159 ±0.84 0.601 ±0.94 0.379 ±0.89
Inter-rater reliability T1 p-value Mean standard error 0.462 ±0.58 0.147 ±0.48 0.331 ±1.14 0.652 ±0.73 0.789 ±0.87 0.213 ±0.94 0.257 ±0.92
T2 p-value 0.280 0.962 0.626 0.607 0.346 0.865 0.257
Mean standard error ±0.85 ±0.96 ±1.89 ±1.21 ±0.83 ±1.16 ±1.18
ANG_C2, ANG_C3, and ANG_C4 are internal angles formed by the intersection of the lines that connect the points CE and ED at the lower borders of C2, C3, and C4; SP_C3 and SP_C4 are square proportion of C3 and C4; and MP_C3 and MP_C4 are maturity proportion of C3 and C4.
analysis according to previous studies.33,34 In the present study, the percentages of inter- and intraobserver agreements show that, on average, examiners disagree in their own assessments or among themselves in one of every four evaluations during hand–wrist analysis, demonstrating some kind of variability of the hand–wrist maturational method. Since the reproducibility is also the main problem of the CVM qualitative methods, the reliability of DVA was assessed. No significant difference in the intra- and interexaminer variability was observed, indicating low level of variability by using DVA software. This was a significant diagnostic advantage when compared with the traditional qualitative methods, which can lead to accurate analysis. Apart from the question of the reliability, another issue regarding hand–wrist assessment is the additional radiographic exposure. Although cancer risk from exposure of the neck is significantly greater than the risk from exposing the hand and wrist, this can be reduced by the use of a thyroid shield during cephalometric imaging, which does not obscure the view of the bodies of C2, C3 and C4. In this case, if the answers and information about the growth status could be found in a cephalometric radiograph that is already part of the initial set of orthodontic records, why would there be a need for radiography of hand and wrist? After analysing the individual behaviour of the variables used in the software, the MLRM was applied. Unlike different regression models adopted in other quantitative studies,10,21–23 the model used in the present study does not adopt cut-offs for categorization and does not provide a specific skeletal age, which reduces the loss of information. Compared with the quantitative CVM method developed in another study,10 the method adopted in the present study seems to be more appropriate. First, by simplicity in identification of landmarks through DVA software analysis. Second, by including six variables in the final model, which formed three nonlinear equations that estimate the CVM with the accuracy of prediction. Third, gender and chronological age were included in the model. According to the results of another study,25 sexual dimorphism was found in both size and shape of cervical vertebrae bodies. In the present study, gender and
chronological age were included in the final model, and it was not necessary to segregate the sample into boys and girls because of gender differences in the process of skeletal maturation,35,36 increasing the robustness of the model. Fourth, the overall accuracy of prediction was quantified in the present study. Unfortunately, no prediction interval was reported in a previous research,10 which makes it impossible to compare their model with the system developed in the present study. The correlation coefficients between the independent variables and SMI were above 0.800 (p , 0.01). The multinomial model established in the present study took into account the correlation between one variable and another, controlled by all the other variables included in the final model, named partial correlation. The low values of partial correlation demonstrate that the present MLRM did not suffer from high collinearity. According to a previous study,25 the accuracy of the CVM methods should be compared with other evaluation systems, such as age. In the present study, the total percentage of the correctness of the model obtained with the use of chronological age solely as the independent variable was 49.5%, and 64.5% with a combination of age and gender. The best prediction (81.4%) was achieved with the combination of four cervical parameters, plus age and gender. Different from the results reported in another study,25 when the analyses of cervical vertebral shape could not predict skeletal maturation better than chronological age, the value added by the present model that used the four parameters, age and gender was 17% (81.4–64.5). In other words, the addition of the parameters of the cervical vertebrae bodies in the final model did explain almost 50% of the 35.5% of the predictability that could not be achieved with the age and gender alone. The prediction success rate of the present study was similar with those stated in another study,36 with an overall predictability of the final model of 81.4%, with a better prediction of an individual’s maturational status on QCMC Stages I and IV. In agreement with Fishman,36 it seems to be satisfactory in terms of diagnosis, especially considering that most orthodontists do not use the analysis of cervical vertebrae when determining the degree of skeletal maturity.
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Figure 2 illustrates the applicability of the MLRM. The patient’s skeletal maturational level was 10, according to Fishman’s method. The MLRM showed the most likely probability for this subject belonging to QCVM IV and agreeing with the hand–wrist skeletal age. However, the qualitative analysis of CVM showed that the patient belonged to cervical stage 4 according to Baccetti et al,7 which disagreed with the complete level of growth as shown by SMI. Apart from the results of this study, the major question regarding the reliability of the CVM method to predict the pubertal growth spurt remains unanswered. Longitudinal studies on a larger sample that analysed the sensitivity and specificity of the method proposed in this study compared with other methods, such as hand–wrist radiographs, analysis of the growth
in stature and growth hormone indicators, can help to answer that question. In conclusion, the quantitative method implemented through specific software described herein was demonstrated to be reproducible. There were significant anatomical changes observed in the bodies of C2, C3 and C4 through the DVA software analysis between the four QCMC stages. The model used here that combines the four parameters measured on the vertebral bodies, plus age and the gender showed a satisfactory prediction. Improving the DVA software with the automatic identification of the points of interest located in the bodies of C2, C3 and C4 and the inclusion of other measures of interest aimed at reducing the influence of examiner on analyses and increasing the predictability of the model could be the objectives of further research.
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