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Applicability of the third molar maturity index for assessment of age of majority in Eastern China
Journal Pre-proofs Applicability of the third molar maturity index for assessment of age of majority in Eastern China Miaochen Wang, Linfeng Fan, Shihui Shen, Xuebing Bai, Jian Wang, Fang Ji, Jiang Tao PII: DOI: Reference:
S1344-6223(19)30306-2 https://doi.org/10.1016/j.legalmed.2019.101639 LEGMED 101639
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Please cite this article as: Wang, M., Fan, L., Shen, S., Bai, X., Wang, J., Ji, F., Tao, J., Applicability of the third molar maturity index for assessment of age of majority in Eastern China, Legal Medicine (2019), doi: https://doi.org/ 10.1016/j.legalmed.2019.101639
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Applicability of the third molar maturity index for assessment of age of majority in Eastern China Miaochen Wang1a, Linfeng Fan2a, Shihui Shen1, Xuebing Bai1, Jian Wang1, Fang Ji3*, Jiang Tao1* 1. Department of General Dentistry, Shanghai Ninth People’s Hospital, College of Stomatology, Shanghai Jiao Tong University School of Medicine, National Clinical Research Center for Oral Diseases, Shanghai Key Laboratory of Stomatology & Shanghai Research Institute of Stomatology. 2. Department of Radiology, Shanghai Ninth People’s Hospital, College of Stomatology, Shanghai Jiao Tong University School of Medicine, National Clinical Research Center for Oral Diseases, Shanghai Key Laboratory of Stomatology & Shanghai Research Institute of Stomatology. 3. Department of Orthodontics, Shanghai Ninth People’s Hospital, College of Stomatology, Shanghai Jiao Tong University School of Medicine, National Clinical Research Center for Oral Diseases, Shanghai Key Laboratory of Stomatology & Shanghai Research Institute of Stomatology.
a These authors contributed equally to this work.
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All authors contact details Miaochen Wang: [email protected] Linfeng Fan: [email protected] Shihui Shen: [email protected] Xuebing Bai: [email protected] Jian Wang: [email protected]
* corresponding author: Jiang Tao. Department of General Dentistry, Shanghai Ninth People’s Hospital, College of Stomatology, Shanghai Jiao Tong University School of Medicine, National Clinical Research Center for Oral Diseases, Shanghai Key Laboratory of Stomatology & Shanghai Research Institute of Stomatology. No. 639 Zhi Zao Ju Road, Shanghai 200011, China. Tel: +862153315202 E-mail address: [email protected]
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Fang Ji. Department of Radiology, Shanghai Ninth People’s Hospital, College of Stomatology, Shanghai Jiao Tong University School of Medicine, National Clinical Research Center for Oral Diseases, Shanghai Key Laboratory of Stomatology & Shanghai Research Institute of Stomatology. No. 639 Zhi Zao Ju Road, Shanghai 200011, China. Tel: +862153315206 E-mail address: [email protected]
Authorship All authors contributed to the study conception and design. the conception and design of the study and acquisition of data were performed by Linfeng Fan and Shihui Shen. Data analysis was performed by Xuebing Bai and Jian Wang. The first draft of the manuscript was written by Miaochen Wang. Fang Ji commented on previous versions of the manuscript. Jiang Tao finally approved the version to be submitted. All authors read and approved the final manuscript.
Abstract
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From a legal and penalty point of view, it is essential to conclude if an individual has reached the legal age (also known as age of majority). Cameriere’s third molar maturity index (I3M) was used to discriminate between adults and minors. No studies have tested the applicability of I3M in the Eastern Chinese population. The aim of this study was to assess the validity of the region-specific cut-off value of I3M for discriminating minors from adults in an Eastern Chinese population. 556 samples (276 males and 280 females) aged 14-24 years were selected in this study. With the adult age and minor age as dichotomous dependent variable and I3M and gender as predictor variables, A Logstic regression analysis showed gender was not statistically significance in distinguishing adults and minors. The receiver operating curve (ROC) analysis showed the best performance of the cut-off value of I3M <0.08 in discriminating adults from minors. Diagnostic test showed the proportion of accuracy was 90.22% in males and 86.43% in females. The sensitivity and specificity for males were 88% and 94.06%, respectively. The sensitivity and specificity for females were 83.71% and 91.18%, respectively. The estimated Bayes post-test probability was 97.18% and 96.01% in males and females respectively. Above all, I3M <0.08 may be a useful tool for indicating the legal age in in Eastern Chinese population.
Keywords 4
Legal age, Age of majority, Dental age estimation Third molar maturity index, Eastern Chinese population
Declarations of interest: None
Funding: This work was supported by the National Natural Science Foundation of China (No. 81500813) and the Science and Technology Commission of Shanghai Municipality (No. 18ZR1422700).
Acknowledgements: None 5
Applicability of the third molar maturity index for assessment of age of majority in Eastern China Abstract From a legal and penalty point of view, it is essential to conclude if an individual has reached the legal age (also known as age of majority). Although Cameriere’s third molar maturity index (I3M) has been used to discriminate between adults and minors, no study has tested the applicability of I3M in the Eastern Chinese population. The aim of this study was to assess the validity of the region-specific cut-off value of I3M for discriminating minors from adults in an Eastern Chinese population. Five hundred fifty-six subjects (276 males and 280 females) aged 14–24 years participated in this study. A logistic regression analysis was conducted by considering the adult and minor ages as dichotomous dependent variables and I3M and sex as predictor variables. The results showed that sex was not statistically significant in distinguishing adults and minors. The receiver operating curve analysis showed the best performance of the cut-off value of I3M < 0.08 in discriminating adults from minors. Furthermore, the diagnostic test showed the proportion of accuracy was 90.22% in males and 86.43% in females. The sensitivity and specificity for males were 88% and 94.06%, respectively, while those for females were 83.71% and 91.18%, 6
respectively. The estimated Bayes post-test probability was 97.18% and 96.01% in males and females respectively. Therefore, I3M < 0.08 may be a useful tool for indicating the legal age in Eastern Chinese population. Keywords: Legal age, Age of majority, Dental age estimation, Third molar maturity index, Eastern Chinese population Introduction The legal age or the age of majority is the threshold of adulthood as conceptualized by law [1]. A person reaching the legal adult age implies that his decision-making no longer requires the supervision of a parent or guardian and he must bear legal responsibility alone when breaking the law [2]. According to the civil and criminal laws, the legal adult age in China is 18, which is the same as in many other countries, such as France, India, Poland, Kosovo, Japan and Africa [3–8]. Age estimation plays an important role in distinguishing between minors and adults. Misclassifications will lead to the loss of minors’ rights to protection and adults’ impunity [8, 9]. According to the Study Group on Forensic Age Diagnostics of the German Association of Forensic Medicine, three independent factors are recommended for forensic age estimation in living individuals: physical and X-ray examinations of the left wrist and the dentition. If the skeletal development of the hand is finished, an additional X-ray examination or CT scan of the clavicles can be performed [10]. However, the dental age estimation seems to be a better and more reliable assessment 7
method [11]. Compared with the skeletal development, the variability in dental development is smaller, its calcification is mainly controlled by genes, and it is less vulnerable to endocrine, nutritional, and environmental factors [5–7, 12, 13]. Between 15 and 24 years, the third molar of humans is the only tooth still in development and is important for distinguishing minors from adults [14]. Several dental age estimation methods by using the third molars have been devised do far. One of the most applied methods is to quantify the degree of the dental maturation [15]. That is, when the third molars are in stage H, implying completed development, the probability of being 18 years of age increases to 95% [16, 17]. Furthermore, in 2008, Cameriere et al. [18] developed a new dental method based on the relationship between age and the third molar maturity index (I3M) to indicate the legal adult age of 18 years. By recording ratios between measurements of apical pulp widths and tooth lengths, a threshold (cut-off) value of I3M < 0.08 was identified and used to distinguish an individual as a juvenile (<18 years) or adult (≥18 years). Because of potential ethnic differences in dental development, I3M has been used by several countries and regions [19–27]. In some research, I3M < 0.08 showed the best accurate selection of adults from minors [3, 22, 25, 27]. Other researchers recommended different I3M cut-off values to better the accurate selection in targeted study populations [12, 26]. However, no
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study has yet tested the applicability of I3M in the Eastern Chinese population. The current study aimed to apply Cameriere’s I3M method to a sample of Shanghai individuals aged 14–24 years to distinguish between adults and minors.
Material and methods 1. Subjects This study was approved by the Independent Ethics Committee of the Shanghai Ninth People’s Hospital affiliated with Shanghai Jiao Tong University School of Medicine (2017-284-T212). In addition, orthopantomograms (OPTs) were collected from the patient records database of the Oral Radiology Department of the hospital from January 1st, 2018 to March 1st, 2019. All OPTs were obtained for clinical diagnosis and treatment by using the Veraviewepocs 2D® (Morita, Tokyo, Japan). Informed consent was obtained from all study participants or participants’ parents. The general information, such as sex, confirmed date of birth, and the date the OPTs were obtained, were collected for all the subjects in this study, and have only been used for research and statistical purposes. The inclusion criteria for OPTs were as follows: 9
a. patients are aged 14–24 years; b. the presence of the left mandibular third molar (Tooth 38); c. tooth 38 with typical anatomy; d. the absence of systemic disease that may affect tooth development. Patients with systemic diseases or with orthodontic treatments were excluded from the study along with OPTs with low image quality. Overall, 556 individuals (276 males and 280 females) were selected in this study. The sample distribution according to age and sex is shown in Table 1. [Table1 inserts here]
2. Measurements Tooth 38 was assessed using I3M, which was evaluated as the ratio obtained from the sum of distances between the inner sides of two open apices divided by tooth length. If the third molars had completely developed roots with closed apices, then I3M = 0.0. 10
In case of the absence of an individual’s general information, all 556 OPTs were analyzed through Photoshop CS5 (Adobe, Inc., San Jose, CA, USA). Moreover, 50 randomly selected OPTs were analyzed four weeks after the first measuring.
3. Statistical analysis Measurement data and the general information of the individuals were recorded in an Excel spreadsheet (Microsoft Excel 2007, Microsoft Corp., Redmond, WA, USA). Chronological age (CA) was calculated as the number of days between obtaining the OPT data and the data of birth. The age of the individual was recorded as dichotomous response variable T, where T = 0 if an individual is younger than 18 years and T = 1 if an individual is at least 18 years of age or older. The data were analyzed using SPSS software (SPSS-IBM, Armonk, NY, USA). The significance threshold was set at p < 0.05, and the intraclass correlation coefficient (ICC) was calculated to estimate the intra-observer and inter-observer agreement for I3M. Further, Pearson’s correlation coefficient was calculated to test the correlation between I3M and CA. To test the effectiveness of I3M and sex in distinguishing between adults (T = 1) and minors (T = 0), a binary logistic regression with forward stepwise (Wald) was conducted. A receiver operating curve (ROC) analysis was used to determine the specific cut-off value of I3M based on the maximum Youden index, which best discriminates adults from minors. 11
An independent sample t-test was performed to show the relationships between different I3M indexes for both sexes. A two-by-two contingency table was used to evaluate the performance of the specific cut-off value of I3M to distinguish adults from minors. True positive (TP) means the number of subjects over the age of 18 whose I3M <0.08. Similarly, true negative (TN) indicates the number of individuals under the age of 18 whose I3M ≥0.08. False positive (FP) means the adult were wrongly classified as minors, and false negative (FN) means the minor were misclassified as adults. This study also calculated the accuracy, sensitivity, and specificity, which are defined as follows. Accuracy indicates the proportion of individuals correctly classified. Sensitivity implies the proportion of the individuals aged 18 years with I3M lesser than the cut-off value. Specificity implies the proportion of the individuals younger than 18 years, with I3M greater than the cut-off value. The positive likelihood ratio (LR+) and negative likelihood ratio (LR−) were also calculated to show how many times more or less likely a test result indicates an adult compared with minor individuals [28]. The larger value of LR+ and the smaller value of LR− indicates a positive screening test result [29]. The 95% confidence interval was applied to reveal the uncertainty associated with the estimates. The Bayes post-test probability (p) of the attainment of 18 years of age or more may help discriminate between individuals who are and are not aged ≥18 years. According to Bayes’ theorem, the post-test probability may be written as: 12
, where p is the post-test probability and p0 is the probability that a subject is ≥18 years, given that he or she is aged between 14 and 24 years, which represents the targeted population. In our study, p0 was calculated as the proportion of individuals between 18 and 24 years of age from a population of individuals aged 14–24 years living in Jiangsu, Zhejiang, Anhui, Jiangxi, Shandong, and Shanghai provinces of China according to demographic data from the Nation Bureau of Statistics of the People’s Republic of China (http://www.stats.gov.cn/tjsj/pcsj/). This proportion was considered to be 0.6992 and 0.7170 for males and females, respectively.
Results The ICC for intra-observer agreement was 0.989 (95% Cl, 0.980 − 0.993), whereas it was 0.935 (95% Cl, 0.889 − 0.963) for the inter-observer agreement. The results of the intraclass correlation coefficient show that variable I3M has good repeatability. According to Fig. 1, Pearson’s correlation coefficient for the correlation between I3M and CA was better for males (−0.528; P < 0.001) than for females (−0.511; P < 0.001). As CA gradually increased, the value of I3M decreased both in males and females. [Figure 1 inserts here] 13
According to the results in Table 2, the Logistic regression model showed the significance of variable I3M (p < 0.001), whereas sex was not significant (p = 0.073). [Table 2 inserts here] Owing to the nonsignificant contribution of sex to the model, ROC analysis was performed on the whole training dataset sample.(Figure 2) The best performance of the discrimination between adults and minors or the maximum Youden index (J = 0.784) was for I3M = 0.08, which was also the highest specificity (Table S1). Thus, we determined the cut-off value as 0.08 for discriminating between adults and minors. If I3M < 0.08, an individual was considered as an adult, and if I3M ≥ 0.08, the individual was considered a minor. In the test sample, age increased gradually with the decrease of I3M in both males and females, as shown in Figure 3. Furthermore, no significant difference can be observed between sexes. And the mean ages across all I3M classes in males were lower which indicates that the faster maturation of the lower third molars was in males (Table 3). [Figure 2 inserts here] [Figure 3 inserts here] [Table 3 inserts here] 14
According to the obtained results in the two-by-two contingency tables and quantities (Tables 4 and 5), for females, the accuracy was 86.43% (95% CI, 82.42%–90.44%). The sensitivity and specificity were 83.71% (95% CI, 79.38%–88.03%) and 91.18% (95% CI, 87.85%–94.50%), respectively. The LR+ was 9.49 (95% CI, 6.66–13.51) and the LR− was 0.18 (95% CI, 0.10–0.33). The estimated Bayes post-test probability was 96.01% (95% CI, 93.71%–98.30%). [Table 4 inserts here] [Table 5 inserts here] In males, the accuracy of 90.22% (95% CI, 86.72%–93.72%), sensitivity of 88% (95% CI, 84.17%–91.83%), and specificity of 94.06% (95% CI, 91.27%–96.85%) were higher than those for females. The LR+ and LR− were 14.81(95% CI, 9.75–22.50) and 0.13 (95% CI, 0.06–0.28). The estimated Bayes post-test probability was 97.18% (95% CI, 95.23%–99.13%). Among the underage groups, the age group of 16 years for males and the age group of 18 years for females had respectively the highest error rate in determining the minors as adults. Among the adult groups, the highest error rate in determining the adult as minors was for the age group of 18 years for females (only 8 out of 25 were correctly classified), followed by the age group of 19 years with 60% of correctly selected individuals. In males, the highest error rate in determining the adult as minors was for the age group of 18 years, in which only 15 out of 25 were correctly classified (Table 6). 15
Discussion No study has tested the applicability of I3M in the Eastern Chinese population. Instead of evaluating only how well a specific cut-off value of I3M < 0.08 discriminates adults from minors, the aim of our study was to test a binary logistic regression model and evaluate if some other value of I3M makes a better differentiation. In fact, the ROC analysis showed two cut-off values of I3M, for which the Youden index was the maximal: a cut-off value of 0.09 with Youden index of 0.785 and the cut-off value of 0.08 with Youden index of 0.784 (Table S1).To select the cut-off value of I3M, we should comprehensively consider sensitivity and specificity. The classification test could lead to two types of errors: a technically unacceptable error (type I) and ethically unacceptable errors (type II). In our study, type-I errors were false negatives (FN), where individuals above 18 years were identified as below 18 years, and type-II errors were false positives (FP), where individuals younger than 18 years were identified as above 18 years. The lower the rates of FN and FP, the higher the rates of TN and TP, relatively, and thus the higher were the sensitivity and specificity values. To protect children and reduce the violation of children’s rights, the number of FP should be minimized in the medicolegal or forensic context. In short, type-I errors must be reduced to a minimum, and type-II errors must be avoided entirely; this implies that specificity plays a relatively more important role than sensitivity in determining the best cut-off value of I3M [30]. For I3M < 0.09, the sensitivity was 0.864 16
and the specificity was 0.921. For I3M < 0.08, the sensitivity was 0.858 and the specificity was 0.926 (Table S1). The specificity for I3M < 0.08 was higher than that for I3M < 0.09. Furthermore, the accuracy of classification for I3M < 0.08 (88.31%) was higher than that for I3M < 0.09 (88.13%) (Table S2). Therefore, we selected I3M < 0.08 as the best cut-off value for discriminating adults from minors in Eastern China population. Our findings show the same cut-off value of I3M proposed by Cameriere et al. [18] and are in line with the findings of some previous studies, such as the Southeastern France study by Tafrount et al. [3]. In contrast, the Northern China study by Chu et al. [12]and the Polish study by Kalinowska et al. [5] demonstrated other specific cut-off values showing better performance than 0.08 in their research population. The overall accuracy of classification was 88.31% for I3M < 0.08 in our Eastern China population, indicating the usefulness of I3M < 0.08 in discriminating adults and minors (Table S2). Our study performed better classification among males (90.22%) than among females (86.43%). Both sexes presented better specificity (91.18% for females and 94.06% for males) than sensitivity (83.71% for females and 88% for males), as shown in Table 5. Our findings are consistent with those of most studies with I3M < 0.08 [31, 32]. For example, the Sardinian study [31] demonstrated accuracy of 84% for females, with sensitivity and specificity of 79% and 100%, respectively. In contrast, for males, the accuracy, sensitivity, and specificity were 87%, 85%, and 91%, respectively. The results for the Kosovar population [32] showed better diagnosis-test performance for I3M < 0.08 in the 17
case of males. The classification accuracy was better in the case of males (96.8%) than of females (90.9%). In addition, the sensitivity was better in the case of males; this is the same as our results (96.2% for males and 82.6% for females). The specificity was slightly better in the case of females (99.1%) than for males (97.6%). The likelihood ratio combines sensitivity and specificity to determine the how much more likely the test result will reduce the uncertainty of a given diagnosis [33, 28, 29]. Generally, LR+ >10 and LR− <0.1 are considered to exert highly significant changes in probability. According to the LR+ value shown in Table 5, a positive test of I3M < 0.08 was achieved 14.81 and 9.49 times in the case of males and females, respectively, and was more likely among people who were actually aged ≥18 years than among those who were aged <18 years. The result of the LR− value indicates that a negative test of I3M ≥ 0.08 was achieved 0.13 and 0.28 times in the case of males and females, respectively, and was more likely among people aged ≥18 years than among those aged <18 years. In the Dutch study by Doğru et al. [34], the overall LR+ was 19.64 (95% CI, 6.78–76.28) and LR− was 0.28 (95% CI, 0.25–0.36). The LR+ was higher among females (19.64; 95% CI, 6.78–76.28) than among males (16.80; 95% CI, 6.97–51.09) and LR− was lower among males (0.17; 95% CI, 0.14–0.25) than among females (0.28; 95% CI, 0.25–0.36). The Kosovar study by Kelmendi et al. [32] showed higher LR+ (95.826; 95% CI, 16.69–1848.47) among females
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than among males (40.415; 95% CI, 12.962–215.592) and lower LR− among females (0.175; 95% CI, 0.166–0.223) than among males (0.039; 95% CI, 0.023–0.081). Additional findings showed that the greatest number of misclassified individuals among all age groups is in those over 18 years of age; only 46% of the 18-year-old and 66% of 19-year-old individuals were correctly classified as adults. Correct classification of individuals who are over 18 years was much better in males than in females, relatively. Only 32% and 60% of 18- and 19-year-old females and 60% and 72% of 18-and 19-year-old males, respectively, were correctly classified as adults. According to the results in Table 6, the number of correct classifications started gradually decreasing from the age of 14 until it reached its minimal at the age of 18, and then increased gradually. Similar results have been found in other studies [3, 5, 12, 32, 34, 35]. Individual differences in tooth development may explain this phenomenon. Further modifications on the I3M are necessary to reduce FPs and FNs and improve the classification accuracy in distinguishing adults and minors. As this was a retrospective study of radiographs sampled from the patient records database of the Oral Radiology Department of Shanghai Ninth People’s Hospital in Shanghai of Eastern China, our results can only be considered representative of Chinese children in this region. Furthermore, when considering the forensic and clinical literature, Chu et al. [12] studied the I3M in the Northern Chinese population. Our results are not generally in line with theirs, and they concluded that 19
the cut-off value of 0.10 showed better performance in the Northern Chinese population. Antunovic et al. [35] explained that differences exist in dental maturation between races and populations. Therefore, the accuracy of I3M requires verification in other districts of China. In addition, two other factors affect the accuracy of I3M value to some extent. Changes to position and inclination occur in the developing mandibular third molars (M3)[36, 37]. During the eruption, the inclination of M3 relative to the OPT may make it difficult to assess tooth length, and it also becomes difficult to estimate whether the root apices have been closed. On the other hand, the OPT, as a form two-dimensional radiography, possesses inherent image distortion that is also affected by aberrant head positioning[38]. In our study, the OPTs in the chosen database were captured by trained personnel who could ensure that patients maintained the correct head positioning. We also set strict inclusion and exclusion criteria to select OPTs that can clearly display the anatomical structure of the third molars. It must be acknowledged that the third molar maturity index presents limitations when it comes to assessing M3 with atypical anatomy. Because cone beam computed tomography (CBCT) is a kind of three-dimensional radiography technique, it is expected that usage of CBCT will improve the accuracy of the determined I3M value to effectively distinguish adults from minors.
Conclusion 20
This research confirmed the usefulness of I3M to indicate legal adult age in Eastern Chinese population. I3M < 0.08 showed the best performance and the highest specificity to discriminate adults from minors in the Eastern Chinese population. Owing to potential ethnic difference among different populations, a suitable cut-off value of I3M should be tested to improve the accuracy for legal age estimation.
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a Libyan sample of living subjects. Forensic Sci Int 267:230.e1-230.e6. https://doi.org/10.1016/j.forsciint.2016.07.020 27.
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population? Study of a Sardinian sample of children and young adults. Int J Legal Med 132:1787–1794. https://doi.org/10.1007/s00414-018-1933-2 32.
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Kosovar population. Int J Legal Med 132:1151–1159. https://doi.org/10.1007/s00414-017-1761-9 33.
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radiography on mesiodistal tooth angulations. Angle Orthod 71:442–451. https://doi.org/10.1043/0003-3219(2001)0712.0.CO;2
27
Table 1. Distribution of the selected samples from Shanghai. Age (years)
Females Males
Pooled
14
26
25
51
15
26
25
51
16
25
26
51
17
25
25
50
18
25
25
50
19
25
25
50
20
25
25
50
21
25
25
50
22
26
25
51
23
27
25
52
24
25
25
50
Total
280
276
556
28
Table 2. Parameter estimates of the third molar maturity index (I3M) and sex as explanatory variables, and age (≥18 years; T = 1 and <18 years; T = 0) as the dichotomous dependent variable in the logistic regression Parameter B
Std. Error
Wald Chi-square
df
Sig.
Constant
2.192
0.210
109.245
1
<0.001
I3M
−13.025 1.137
131.331
1
<0.001
Sex
0.458
3.207
1
0.073
0.256
df: degrees of freedom
29
Table 3 Summary statistics of chronological age according to sex and third molar maturity index (I3M) classes Females
Males
P
I3M class
t (df) N
Mean
SD
Min
Q1
Med
Q3
Max
N
Mean
SD
Min
Q1
Med
Q3
value
Max
(1.31-0.40]
43 15.59 0.22 14.00 14.60 15.17 16.16 19.88 27 15.01 0.19 14.07 14.20 14.74 15.91 17.76
1.805 (68)
0.076
(0.40-0.20]
52 16.96 0.24 14.09 15.28 17.15 18.14 21.32 50 16.55 0.20 14.42 15.57 16.51 17.53 21.07 1.277 (100) 0.205
(0.20-0.08]
27 17.21 0.28 14.39 16.13 17.47 18.10 19.60 39 17.72 0.25 15.47 16.55 17.54 18.78 21.21 -1.341 (64) 0.185
(0.08-0.00] 158 21.71 0.17 15.00 20.29 21.96 23.53 24.93 160 21.59 0.17 16.26 20.02 21.91 23.46 24.93 0.479 (316) 0.633 N: number of individuals, Mean: mean age for I3M class, SD: standard deviation of mean age, Min: minimum value, Q1: first quartile, Med: median age, Q3: third quartile, Max: maximum age, t: independent sample t test, df: degrees of freedom
30
Table 4. Contingency table describing discrimination performance of the test for the cut-off value of I3M Females Test
≥18
<18
I3M < 0.08 149TP 9FN
Males Total ≥ 18 135
<18
154 TP 6 FN
Total 160
I3M ≥ 0.08 29FP
93TN 145
21 FP
95 TN 116
Total
102
175
101
178
280
TP: true positive, FN: false negative, FP: false positive, TN: true negative
31
276
Table 5. Quantities from the two-by-two contingency tables (95% confidence interval) to test the age of majority in the sample from Eastern China Quantities
Females
Males
Accuracy
86.43% (95% CI, 82.42%–90.44%)
90.22% (95% CI, 86.72%–93.72%)
Sensitivity
83.71% (95% CI, 79.38%–88.03%)
88% (95% CI, 84.17%–91.83%)
Specificity
91.18% (95% CI, 87.85%–94.50%)
94.06% (95% CI, 91.27%–96.85%)
Positive likelihood ratio (LR+)
9.49 (95% CI, 6.66–13.51)
14.81(95% CI, 9.75–22.50)
Negative likelihood ratio (LR−)
0.18 (95% CI, 0.10–0.33)
0.13 (95% CI, 0.06–0.28)
Bayes post-test probability
96.01% (95% CI, 93.71%–98.30%)
97.18% (95% CI, 95.23%–99.13%)
32
Table 6. Number and percentage of correct evaluations among all participants in each age group by using the cut-off value of I3M < 0.08. Age groups (years)
Females
Males
Total
14
26/26 (100%)
25/25 (100%)
51/51 (100%)
15
25/26 (96.15%)
25/25 (100%)
50/51 (98.04%)
16
20/25 (80%)
23/26 (88.46%)
43/51 (84.31%)
17
21/25 (84%)
22/25 (88%)
43/50 (86%)
18
8/25 (32%)
15/25 (60%)
23/50 (46%)
19
15/25 (60%)
18/25 (72%)
33/50 (66%)
20
25/25 (100%)
24/25 (96%)
49/50 (98%)
21
24/25 (96%)
23/25 (92%)
47/50 (94%)
22
26/26 (100%)
25/25 (100%)
51/51 (100%)
23
27/27 (100%)
25/25 (100%)
52/52 (100%)
24
25/25 (100%)
25/25 (100%)
50/50 (100%)
33
Total
242/280 (86.43%) 249/276 (90.22%) 491/556 (88.31%)
34
Figures Figure 1. Scatter plot of the relationship between age (years) and third molar maturity index (I3M) Figure 2. Receiver operating characteristic curve for indicating the legal adult age (≥18 years) according to I3M in the sample population from Eastern China Figure 3. Box plot of the relationship between age (years) and the third molar maturity index classes, showing the median, first, and third quartiles, while whiskers are lines extending from the box to maximum and minimum ages, including outliers.
35
Highlights I3M < 0.08 shows the best performance for discriminating adults from minors in Eastern Chinese population. A two-by-two contingency table evaluated the performance of the cut-off value of I3M The best specific I3M cut-off was determined based on maximum Youden index
36
37
38
39
S1344-6223(19)30306-2 https://doi.org/10.1016/j.legalmed.2019.101639 LEGMED 101639
To appear in:
Legal Medicine
Received Date: Revised Date: Accepted Date:
17 August 2019 30 September 2019 4 October 2019
Please cite this article as: Wang, M., Fan, L., Shen, S., Bai, X., Wang, J., Ji, F., Tao, J., Applicability of the third molar maturity index for assessment of age of majority in Eastern China, Legal Medicine (2019), doi: https://doi.org/ 10.1016/j.legalmed.2019.101639
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© 2019 Published by Elsevier B.V.
Applicability of the third molar maturity index for assessment of age of majority in Eastern China Miaochen Wang1a, Linfeng Fan2a, Shihui Shen1, Xuebing Bai1, Jian Wang1, Fang Ji3*, Jiang Tao1* 1. Department of General Dentistry, Shanghai Ninth People’s Hospital, College of Stomatology, Shanghai Jiao Tong University School of Medicine, National Clinical Research Center for Oral Diseases, Shanghai Key Laboratory of Stomatology & Shanghai Research Institute of Stomatology. 2. Department of Radiology, Shanghai Ninth People’s Hospital, College of Stomatology, Shanghai Jiao Tong University School of Medicine, National Clinical Research Center for Oral Diseases, Shanghai Key Laboratory of Stomatology & Shanghai Research Institute of Stomatology. 3. Department of Orthodontics, Shanghai Ninth People’s Hospital, College of Stomatology, Shanghai Jiao Tong University School of Medicine, National Clinical Research Center for Oral Diseases, Shanghai Key Laboratory of Stomatology & Shanghai Research Institute of Stomatology.
a These authors contributed equally to this work.
1
All authors contact details Miaochen Wang: [email protected] Linfeng Fan: [email protected] Shihui Shen: [email protected] Xuebing Bai: [email protected] Jian Wang: [email protected]
* corresponding author: Jiang Tao. Department of General Dentistry, Shanghai Ninth People’s Hospital, College of Stomatology, Shanghai Jiao Tong University School of Medicine, National Clinical Research Center for Oral Diseases, Shanghai Key Laboratory of Stomatology & Shanghai Research Institute of Stomatology. No. 639 Zhi Zao Ju Road, Shanghai 200011, China. Tel: +862153315202 E-mail address: [email protected]
2
Fang Ji. Department of Radiology, Shanghai Ninth People’s Hospital, College of Stomatology, Shanghai Jiao Tong University School of Medicine, National Clinical Research Center for Oral Diseases, Shanghai Key Laboratory of Stomatology & Shanghai Research Institute of Stomatology. No. 639 Zhi Zao Ju Road, Shanghai 200011, China. Tel: +862153315206 E-mail address: [email protected]
Authorship All authors contributed to the study conception and design. the conception and design of the study and acquisition of data were performed by Linfeng Fan and Shihui Shen. Data analysis was performed by Xuebing Bai and Jian Wang. The first draft of the manuscript was written by Miaochen Wang. Fang Ji commented on previous versions of the manuscript. Jiang Tao finally approved the version to be submitted. All authors read and approved the final manuscript.
Abstract
3
From a legal and penalty point of view, it is essential to conclude if an individual has reached the legal age (also known as age of majority). Cameriere’s third molar maturity index (I3M) was used to discriminate between adults and minors. No studies have tested the applicability of I3M in the Eastern Chinese population. The aim of this study was to assess the validity of the region-specific cut-off value of I3M for discriminating minors from adults in an Eastern Chinese population. 556 samples (276 males and 280 females) aged 14-24 years were selected in this study. With the adult age and minor age as dichotomous dependent variable and I3M and gender as predictor variables, A Logstic regression analysis showed gender was not statistically significance in distinguishing adults and minors. The receiver operating curve (ROC) analysis showed the best performance of the cut-off value of I3M <0.08 in discriminating adults from minors. Diagnostic test showed the proportion of accuracy was 90.22% in males and 86.43% in females. The sensitivity and specificity for males were 88% and 94.06%, respectively. The sensitivity and specificity for females were 83.71% and 91.18%, respectively. The estimated Bayes post-test probability was 97.18% and 96.01% in males and females respectively. Above all, I3M <0.08 may be a useful tool for indicating the legal age in in Eastern Chinese population.
Keywords 4
Legal age, Age of majority, Dental age estimation Third molar maturity index, Eastern Chinese population
Declarations of interest: None
Funding: This work was supported by the National Natural Science Foundation of China (No. 81500813) and the Science and Technology Commission of Shanghai Municipality (No. 18ZR1422700).
Acknowledgements: None 5
Applicability of the third molar maturity index for assessment of age of majority in Eastern China Abstract From a legal and penalty point of view, it is essential to conclude if an individual has reached the legal age (also known as age of majority). Although Cameriere’s third molar maturity index (I3M) has been used to discriminate between adults and minors, no study has tested the applicability of I3M in the Eastern Chinese population. The aim of this study was to assess the validity of the region-specific cut-off value of I3M for discriminating minors from adults in an Eastern Chinese population. Five hundred fifty-six subjects (276 males and 280 females) aged 14–24 years participated in this study. A logistic regression analysis was conducted by considering the adult and minor ages as dichotomous dependent variables and I3M and sex as predictor variables. The results showed that sex was not statistically significant in distinguishing adults and minors. The receiver operating curve analysis showed the best performance of the cut-off value of I3M < 0.08 in discriminating adults from minors. Furthermore, the diagnostic test showed the proportion of accuracy was 90.22% in males and 86.43% in females. The sensitivity and specificity for males were 88% and 94.06%, respectively, while those for females were 83.71% and 91.18%, 6
respectively. The estimated Bayes post-test probability was 97.18% and 96.01% in males and females respectively. Therefore, I3M < 0.08 may be a useful tool for indicating the legal age in Eastern Chinese population. Keywords: Legal age, Age of majority, Dental age estimation, Third molar maturity index, Eastern Chinese population Introduction The legal age or the age of majority is the threshold of adulthood as conceptualized by law [1]. A person reaching the legal adult age implies that his decision-making no longer requires the supervision of a parent or guardian and he must bear legal responsibility alone when breaking the law [2]. According to the civil and criminal laws, the legal adult age in China is 18, which is the same as in many other countries, such as France, India, Poland, Kosovo, Japan and Africa [3–8]. Age estimation plays an important role in distinguishing between minors and adults. Misclassifications will lead to the loss of minors’ rights to protection and adults’ impunity [8, 9]. According to the Study Group on Forensic Age Diagnostics of the German Association of Forensic Medicine, three independent factors are recommended for forensic age estimation in living individuals: physical and X-ray examinations of the left wrist and the dentition. If the skeletal development of the hand is finished, an additional X-ray examination or CT scan of the clavicles can be performed [10]. However, the dental age estimation seems to be a better and more reliable assessment 7
method [11]. Compared with the skeletal development, the variability in dental development is smaller, its calcification is mainly controlled by genes, and it is less vulnerable to endocrine, nutritional, and environmental factors [5–7, 12, 13]. Between 15 and 24 years, the third molar of humans is the only tooth still in development and is important for distinguishing minors from adults [14]. Several dental age estimation methods by using the third molars have been devised do far. One of the most applied methods is to quantify the degree of the dental maturation [15]. That is, when the third molars are in stage H, implying completed development, the probability of being 18 years of age increases to 95% [16, 17]. Furthermore, in 2008, Cameriere et al. [18] developed a new dental method based on the relationship between age and the third molar maturity index (I3M) to indicate the legal adult age of 18 years. By recording ratios between measurements of apical pulp widths and tooth lengths, a threshold (cut-off) value of I3M < 0.08 was identified and used to distinguish an individual as a juvenile (<18 years) or adult (≥18 years). Because of potential ethnic differences in dental development, I3M has been used by several countries and regions [19–27]. In some research, I3M < 0.08 showed the best accurate selection of adults from minors [3, 22, 25, 27]. Other researchers recommended different I3M cut-off values to better the accurate selection in targeted study populations [12, 26]. However, no
8
study has yet tested the applicability of I3M in the Eastern Chinese population. The current study aimed to apply Cameriere’s I3M method to a sample of Shanghai individuals aged 14–24 years to distinguish between adults and minors.
Material and methods 1. Subjects This study was approved by the Independent Ethics Committee of the Shanghai Ninth People’s Hospital affiliated with Shanghai Jiao Tong University School of Medicine (2017-284-T212). In addition, orthopantomograms (OPTs) were collected from the patient records database of the Oral Radiology Department of the hospital from January 1st, 2018 to March 1st, 2019. All OPTs were obtained for clinical diagnosis and treatment by using the Veraviewepocs 2D® (Morita, Tokyo, Japan). Informed consent was obtained from all study participants or participants’ parents. The general information, such as sex, confirmed date of birth, and the date the OPTs were obtained, were collected for all the subjects in this study, and have only been used for research and statistical purposes. The inclusion criteria for OPTs were as follows: 9
a. patients are aged 14–24 years; b. the presence of the left mandibular third molar (Tooth 38); c. tooth 38 with typical anatomy; d. the absence of systemic disease that may affect tooth development. Patients with systemic diseases or with orthodontic treatments were excluded from the study along with OPTs with low image quality. Overall, 556 individuals (276 males and 280 females) were selected in this study. The sample distribution according to age and sex is shown in Table 1. [Table1 inserts here]
2. Measurements Tooth 38 was assessed using I3M, which was evaluated as the ratio obtained from the sum of distances between the inner sides of two open apices divided by tooth length. If the third molars had completely developed roots with closed apices, then I3M = 0.0. 10
In case of the absence of an individual’s general information, all 556 OPTs were analyzed through Photoshop CS5 (Adobe, Inc., San Jose, CA, USA). Moreover, 50 randomly selected OPTs were analyzed four weeks after the first measuring.
3. Statistical analysis Measurement data and the general information of the individuals were recorded in an Excel spreadsheet (Microsoft Excel 2007, Microsoft Corp., Redmond, WA, USA). Chronological age (CA) was calculated as the number of days between obtaining the OPT data and the data of birth. The age of the individual was recorded as dichotomous response variable T, where T = 0 if an individual is younger than 18 years and T = 1 if an individual is at least 18 years of age or older. The data were analyzed using SPSS software (SPSS-IBM, Armonk, NY, USA). The significance threshold was set at p < 0.05, and the intraclass correlation coefficient (ICC) was calculated to estimate the intra-observer and inter-observer agreement for I3M. Further, Pearson’s correlation coefficient was calculated to test the correlation between I3M and CA. To test the effectiveness of I3M and sex in distinguishing between adults (T = 1) and minors (T = 0), a binary logistic regression with forward stepwise (Wald) was conducted. A receiver operating curve (ROC) analysis was used to determine the specific cut-off value of I3M based on the maximum Youden index, which best discriminates adults from minors. 11
An independent sample t-test was performed to show the relationships between different I3M indexes for both sexes. A two-by-two contingency table was used to evaluate the performance of the specific cut-off value of I3M to distinguish adults from minors. True positive (TP) means the number of subjects over the age of 18 whose I3M <0.08. Similarly, true negative (TN) indicates the number of individuals under the age of 18 whose I3M ≥0.08. False positive (FP) means the adult were wrongly classified as minors, and false negative (FN) means the minor were misclassified as adults. This study also calculated the accuracy, sensitivity, and specificity, which are defined as follows. Accuracy indicates the proportion of individuals correctly classified. Sensitivity implies the proportion of the individuals aged 18 years with I3M lesser than the cut-off value. Specificity implies the proportion of the individuals younger than 18 years, with I3M greater than the cut-off value. The positive likelihood ratio (LR+) and negative likelihood ratio (LR−) were also calculated to show how many times more or less likely a test result indicates an adult compared with minor individuals [28]. The larger value of LR+ and the smaller value of LR− indicates a positive screening test result [29]. The 95% confidence interval was applied to reveal the uncertainty associated with the estimates. The Bayes post-test probability (p) of the attainment of 18 years of age or more may help discriminate between individuals who are and are not aged ≥18 years. According to Bayes’ theorem, the post-test probability may be written as: 12
, where p is the post-test probability and p0 is the probability that a subject is ≥18 years, given that he or she is aged between 14 and 24 years, which represents the targeted population. In our study, p0 was calculated as the proportion of individuals between 18 and 24 years of age from a population of individuals aged 14–24 years living in Jiangsu, Zhejiang, Anhui, Jiangxi, Shandong, and Shanghai provinces of China according to demographic data from the Nation Bureau of Statistics of the People’s Republic of China (http://www.stats.gov.cn/tjsj/pcsj/). This proportion was considered to be 0.6992 and 0.7170 for males and females, respectively.
Results The ICC for intra-observer agreement was 0.989 (95% Cl, 0.980 − 0.993), whereas it was 0.935 (95% Cl, 0.889 − 0.963) for the inter-observer agreement. The results of the intraclass correlation coefficient show that variable I3M has good repeatability. According to Fig. 1, Pearson’s correlation coefficient for the correlation between I3M and CA was better for males (−0.528; P < 0.001) than for females (−0.511; P < 0.001). As CA gradually increased, the value of I3M decreased both in males and females. [Figure 1 inserts here] 13
According to the results in Table 2, the Logistic regression model showed the significance of variable I3M (p < 0.001), whereas sex was not significant (p = 0.073). [Table 2 inserts here] Owing to the nonsignificant contribution of sex to the model, ROC analysis was performed on the whole training dataset sample.(Figure 2) The best performance of the discrimination between adults and minors or the maximum Youden index (J = 0.784) was for I3M = 0.08, which was also the highest specificity (Table S1). Thus, we determined the cut-off value as 0.08 for discriminating between adults and minors. If I3M < 0.08, an individual was considered as an adult, and if I3M ≥ 0.08, the individual was considered a minor. In the test sample, age increased gradually with the decrease of I3M in both males and females, as shown in Figure 3. Furthermore, no significant difference can be observed between sexes. And the mean ages across all I3M classes in males were lower which indicates that the faster maturation of the lower third molars was in males (Table 3). [Figure 2 inserts here] [Figure 3 inserts here] [Table 3 inserts here] 14
According to the obtained results in the two-by-two contingency tables and quantities (Tables 4 and 5), for females, the accuracy was 86.43% (95% CI, 82.42%–90.44%). The sensitivity and specificity were 83.71% (95% CI, 79.38%–88.03%) and 91.18% (95% CI, 87.85%–94.50%), respectively. The LR+ was 9.49 (95% CI, 6.66–13.51) and the LR− was 0.18 (95% CI, 0.10–0.33). The estimated Bayes post-test probability was 96.01% (95% CI, 93.71%–98.30%). [Table 4 inserts here] [Table 5 inserts here] In males, the accuracy of 90.22% (95% CI, 86.72%–93.72%), sensitivity of 88% (95% CI, 84.17%–91.83%), and specificity of 94.06% (95% CI, 91.27%–96.85%) were higher than those for females. The LR+ and LR− were 14.81(95% CI, 9.75–22.50) and 0.13 (95% CI, 0.06–0.28). The estimated Bayes post-test probability was 97.18% (95% CI, 95.23%–99.13%). Among the underage groups, the age group of 16 years for males and the age group of 18 years for females had respectively the highest error rate in determining the minors as adults. Among the adult groups, the highest error rate in determining the adult as minors was for the age group of 18 years for females (only 8 out of 25 were correctly classified), followed by the age group of 19 years with 60% of correctly selected individuals. In males, the highest error rate in determining the adult as minors was for the age group of 18 years, in which only 15 out of 25 were correctly classified (Table 6). 15
Discussion No study has tested the applicability of I3M in the Eastern Chinese population. Instead of evaluating only how well a specific cut-off value of I3M < 0.08 discriminates adults from minors, the aim of our study was to test a binary logistic regression model and evaluate if some other value of I3M makes a better differentiation. In fact, the ROC analysis showed two cut-off values of I3M, for which the Youden index was the maximal: a cut-off value of 0.09 with Youden index of 0.785 and the cut-off value of 0.08 with Youden index of 0.784 (Table S1).To select the cut-off value of I3M, we should comprehensively consider sensitivity and specificity. The classification test could lead to two types of errors: a technically unacceptable error (type I) and ethically unacceptable errors (type II). In our study, type-I errors were false negatives (FN), where individuals above 18 years were identified as below 18 years, and type-II errors were false positives (FP), where individuals younger than 18 years were identified as above 18 years. The lower the rates of FN and FP, the higher the rates of TN and TP, relatively, and thus the higher were the sensitivity and specificity values. To protect children and reduce the violation of children’s rights, the number of FP should be minimized in the medicolegal or forensic context. In short, type-I errors must be reduced to a minimum, and type-II errors must be avoided entirely; this implies that specificity plays a relatively more important role than sensitivity in determining the best cut-off value of I3M [30]. For I3M < 0.09, the sensitivity was 0.864 16
and the specificity was 0.921. For I3M < 0.08, the sensitivity was 0.858 and the specificity was 0.926 (Table S1). The specificity for I3M < 0.08 was higher than that for I3M < 0.09. Furthermore, the accuracy of classification for I3M < 0.08 (88.31%) was higher than that for I3M < 0.09 (88.13%) (Table S2). Therefore, we selected I3M < 0.08 as the best cut-off value for discriminating adults from minors in Eastern China population. Our findings show the same cut-off value of I3M proposed by Cameriere et al. [18] and are in line with the findings of some previous studies, such as the Southeastern France study by Tafrount et al. [3]. In contrast, the Northern China study by Chu et al. [12]and the Polish study by Kalinowska et al. [5] demonstrated other specific cut-off values showing better performance than 0.08 in their research population. The overall accuracy of classification was 88.31% for I3M < 0.08 in our Eastern China population, indicating the usefulness of I3M < 0.08 in discriminating adults and minors (Table S2). Our study performed better classification among males (90.22%) than among females (86.43%). Both sexes presented better specificity (91.18% for females and 94.06% for males) than sensitivity (83.71% for females and 88% for males), as shown in Table 5. Our findings are consistent with those of most studies with I3M < 0.08 [31, 32]. For example, the Sardinian study [31] demonstrated accuracy of 84% for females, with sensitivity and specificity of 79% and 100%, respectively. In contrast, for males, the accuracy, sensitivity, and specificity were 87%, 85%, and 91%, respectively. The results for the Kosovar population [32] showed better diagnosis-test performance for I3M < 0.08 in the 17
case of males. The classification accuracy was better in the case of males (96.8%) than of females (90.9%). In addition, the sensitivity was better in the case of males; this is the same as our results (96.2% for males and 82.6% for females). The specificity was slightly better in the case of females (99.1%) than for males (97.6%). The likelihood ratio combines sensitivity and specificity to determine the how much more likely the test result will reduce the uncertainty of a given diagnosis [33, 28, 29]. Generally, LR+ >10 and LR− <0.1 are considered to exert highly significant changes in probability. According to the LR+ value shown in Table 5, a positive test of I3M < 0.08 was achieved 14.81 and 9.49 times in the case of males and females, respectively, and was more likely among people who were actually aged ≥18 years than among those who were aged <18 years. The result of the LR− value indicates that a negative test of I3M ≥ 0.08 was achieved 0.13 and 0.28 times in the case of males and females, respectively, and was more likely among people aged ≥18 years than among those aged <18 years. In the Dutch study by Doğru et al. [34], the overall LR+ was 19.64 (95% CI, 6.78–76.28) and LR− was 0.28 (95% CI, 0.25–0.36). The LR+ was higher among females (19.64; 95% CI, 6.78–76.28) than among males (16.80; 95% CI, 6.97–51.09) and LR− was lower among males (0.17; 95% CI, 0.14–0.25) than among females (0.28; 95% CI, 0.25–0.36). The Kosovar study by Kelmendi et al. [32] showed higher LR+ (95.826; 95% CI, 16.69–1848.47) among females
18
than among males (40.415; 95% CI, 12.962–215.592) and lower LR− among females (0.175; 95% CI, 0.166–0.223) than among males (0.039; 95% CI, 0.023–0.081). Additional findings showed that the greatest number of misclassified individuals among all age groups is in those over 18 years of age; only 46% of the 18-year-old and 66% of 19-year-old individuals were correctly classified as adults. Correct classification of individuals who are over 18 years was much better in males than in females, relatively. Only 32% and 60% of 18- and 19-year-old females and 60% and 72% of 18-and 19-year-old males, respectively, were correctly classified as adults. According to the results in Table 6, the number of correct classifications started gradually decreasing from the age of 14 until it reached its minimal at the age of 18, and then increased gradually. Similar results have been found in other studies [3, 5, 12, 32, 34, 35]. Individual differences in tooth development may explain this phenomenon. Further modifications on the I3M are necessary to reduce FPs and FNs and improve the classification accuracy in distinguishing adults and minors. As this was a retrospective study of radiographs sampled from the patient records database of the Oral Radiology Department of Shanghai Ninth People’s Hospital in Shanghai of Eastern China, our results can only be considered representative of Chinese children in this region. Furthermore, when considering the forensic and clinical literature, Chu et al. [12] studied the I3M in the Northern Chinese population. Our results are not generally in line with theirs, and they concluded that 19
the cut-off value of 0.10 showed better performance in the Northern Chinese population. Antunovic et al. [35] explained that differences exist in dental maturation between races and populations. Therefore, the accuracy of I3M requires verification in other districts of China. In addition, two other factors affect the accuracy of I3M value to some extent. Changes to position and inclination occur in the developing mandibular third molars (M3)[36, 37]. During the eruption, the inclination of M3 relative to the OPT may make it difficult to assess tooth length, and it also becomes difficult to estimate whether the root apices have been closed. On the other hand, the OPT, as a form two-dimensional radiography, possesses inherent image distortion that is also affected by aberrant head positioning[38]. In our study, the OPTs in the chosen database were captured by trained personnel who could ensure that patients maintained the correct head positioning. We also set strict inclusion and exclusion criteria to select OPTs that can clearly display the anatomical structure of the third molars. It must be acknowledged that the third molar maturity index presents limitations when it comes to assessing M3 with atypical anatomy. Because cone beam computed tomography (CBCT) is a kind of three-dimensional radiography technique, it is expected that usage of CBCT will improve the accuracy of the determined I3M value to effectively distinguish adults from minors.
Conclusion 20
This research confirmed the usefulness of I3M to indicate legal adult age in Eastern Chinese population. I3M < 0.08 showed the best performance and the highest specificity to discriminate adults from minors in the Eastern Chinese population. Owing to potential ethnic difference among different populations, a suitable cut-off value of I3M should be tested to improve the accuracy for legal age estimation.
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Table 1. Distribution of the selected samples from Shanghai. Age (years)
Females Males
Pooled
14
26
25
51
15
26
25
51
16
25
26
51
17
25
25
50
18
25
25
50
19
25
25
50
20
25
25
50
21
25
25
50
22
26
25
51
23
27
25
52
24
25
25
50
Total
280
276
556
28
Table 2. Parameter estimates of the third molar maturity index (I3M) and sex as explanatory variables, and age (≥18 years; T = 1 and <18 years; T = 0) as the dichotomous dependent variable in the logistic regression Parameter B
Std. Error
Wald Chi-square
df
Sig.
Constant
2.192
0.210
109.245
1
<0.001
I3M
−13.025 1.137
131.331
1
<0.001
Sex
0.458
3.207
1
0.073
0.256
df: degrees of freedom
29
Table 3 Summary statistics of chronological age according to sex and third molar maturity index (I3M) classes Females
Males
P
I3M class
t (df) N
Mean
SD
Min
Q1
Med
Q3
Max
N
Mean
SD
Min
Q1
Med
Q3
value
Max
(1.31-0.40]
43 15.59 0.22 14.00 14.60 15.17 16.16 19.88 27 15.01 0.19 14.07 14.20 14.74 15.91 17.76
1.805 (68)
0.076
(0.40-0.20]
52 16.96 0.24 14.09 15.28 17.15 18.14 21.32 50 16.55 0.20 14.42 15.57 16.51 17.53 21.07 1.277 (100) 0.205
(0.20-0.08]
27 17.21 0.28 14.39 16.13 17.47 18.10 19.60 39 17.72 0.25 15.47 16.55 17.54 18.78 21.21 -1.341 (64) 0.185
(0.08-0.00] 158 21.71 0.17 15.00 20.29 21.96 23.53 24.93 160 21.59 0.17 16.26 20.02 21.91 23.46 24.93 0.479 (316) 0.633 N: number of individuals, Mean: mean age for I3M class, SD: standard deviation of mean age, Min: minimum value, Q1: first quartile, Med: median age, Q3: third quartile, Max: maximum age, t: independent sample t test, df: degrees of freedom
30
Table 4. Contingency table describing discrimination performance of the test for the cut-off value of I3M Females Test
≥18
<18
I3M < 0.08 149TP 9FN
Males Total ≥ 18 135
<18
154 TP 6 FN
Total 160
I3M ≥ 0.08 29FP
93TN 145
21 FP
95 TN 116
Total
102
175
101
178
280
TP: true positive, FN: false negative, FP: false positive, TN: true negative
31
276
Table 5. Quantities from the two-by-two contingency tables (95% confidence interval) to test the age of majority in the sample from Eastern China Quantities
Females
Males
Accuracy
86.43% (95% CI, 82.42%–90.44%)
90.22% (95% CI, 86.72%–93.72%)
Sensitivity
83.71% (95% CI, 79.38%–88.03%)
88% (95% CI, 84.17%–91.83%)
Specificity
91.18% (95% CI, 87.85%–94.50%)
94.06% (95% CI, 91.27%–96.85%)
Positive likelihood ratio (LR+)
9.49 (95% CI, 6.66–13.51)
14.81(95% CI, 9.75–22.50)
Negative likelihood ratio (LR−)
0.18 (95% CI, 0.10–0.33)
0.13 (95% CI, 0.06–0.28)
Bayes post-test probability
96.01% (95% CI, 93.71%–98.30%)
97.18% (95% CI, 95.23%–99.13%)
32
Table 6. Number and percentage of correct evaluations among all participants in each age group by using the cut-off value of I3M < 0.08. Age groups (years)
Females
Males
Total
14
26/26 (100%)
25/25 (100%)
51/51 (100%)
15
25/26 (96.15%)
25/25 (100%)
50/51 (98.04%)
16
20/25 (80%)
23/26 (88.46%)
43/51 (84.31%)
17
21/25 (84%)
22/25 (88%)
43/50 (86%)
18
8/25 (32%)
15/25 (60%)
23/50 (46%)
19
15/25 (60%)
18/25 (72%)
33/50 (66%)
20
25/25 (100%)
24/25 (96%)
49/50 (98%)
21
24/25 (96%)
23/25 (92%)
47/50 (94%)
22
26/26 (100%)
25/25 (100%)
51/51 (100%)
23
27/27 (100%)
25/25 (100%)
52/52 (100%)
24
25/25 (100%)
25/25 (100%)
50/50 (100%)
33
Total
242/280 (86.43%) 249/276 (90.22%) 491/556 (88.31%)
34
Figures Figure 1. Scatter plot of the relationship between age (years) and third molar maturity index (I3M) Figure 2. Receiver operating characteristic curve for indicating the legal adult age (≥18 years) according to I3M in the sample population from Eastern China Figure 3. Box plot of the relationship between age (years) and the third molar maturity index classes, showing the median, first, and third quartiles, while whiskers are lines extending from the box to maximum and minimum ages, including outliers.
35
Highlights I3M < 0.08 shows the best performance for discriminating adults from minors in Eastern Chinese population. A two-by-two contingency table evaluated the performance of the cut-off value of I3M The best specific I3M cut-off was determined based on maximum Youden index
36
37
38
39