Dental Age Assessment by I2M and I3M: Portuguese Legal Age Thresholds of 12 and 14 Year Olds.

OBJECTIVE: Better understanding of dental age assessment may help in cases of age estimation in Forensic Clinics. The first aim was to provide essential information on method reliability for upcoming studies using dental age assessment by second molar index (I2M), and third molar index (I3M) for age estimation on legal ages of 12 - 14 years. The second aim was to document forensic method outcomes of the Demirjian method which has already been used in forensic clinic.
MATERIAL AND METHODS: Two samples were used for this purpose: for I2M, 633 orthopantomographs (270 females / 363 males), the age range from 7 to 17 years and for I3M, 471 orthopantomographs (253 females / 218 males), the age range from 10 to 23 years, from the database population of Lisbon North University Hospital Center, approved by the Ethic Committee.
RESULTS: The I3M cut-off point (1.133) for 12- year- olds obtained better results than the cut-off point stated by the I2M (0.135). Besides, I2M cut-off point (0.001) for 14- year- olds showed better results when compared with the cut-off point (0.705) established by the I3M. Both methods are reliable for the legal age thresholds of 12 and 14 years. However, using I2M and I3M allows us to vary the cut-off value to privilege sensitivities or specificity, depending on which is more appropriate to the intended application.
CONCLUSIONS: The accuracy (88.94%) of I3M obtained better results for the 12- year- old cut-off point (1.133) and the accuracy (90.21%) of the I2M performed better for the 14- year- old cut-off point (0.001).

Introduction

Forensic Odontology is a discipline of Forensic Sciences. The main purpose consists of proper observation, handling, examination and technical-scientific evaluation of oral evidence, which will be presented in the major interest of the justice (). The judicial system faces several difficulties regarding the identification of individuals without reliable identification, often categorizing them by physical appearance, which leads to errors and lack of equity when presented to the court (). In children and adolescents, there are several forensic issues such as minimal age for criminal responsibility and the threshold age for civil adulthood where the biological age assessment through dental evidence can help (-).

In Portugal, the legal ages, between the ages of 12 and 14 years, are covered by the Portuguese penal code which promotes the protection of juvenile individuals, giving priority to healing and prevention over individual measures of punishment. For the application of criminal law, we assume the practice of a fact qualified as a crime by a minor less than 16 years of age is not imputable. This is valid for ages between 12 and 16 years. A child below the age of 16 years cannot be held criminally liable. Children aged between 12 and 16 years can be subject to penalties under the Guardianship and Education Law, which allows for detention of children in closed educational centers. Also, this allows the application of preventing educational measures when crimes are committed by children from 12 to 16 years of age, referred to as juvenile delinquency (, ).

Within Section II of Chapter V, Book II of the Portuguese Penal Code, we are faced with the intervention area of crimes against sexual self-determination, that is, the classification of the crime, in undocumented victims, in order to blame the assailant through the action of the age estimate. According to Article 171º (Child sexual abuse), all children and young people less than 14 years of age are considered victims. In addition to this crime, article 173 refers to sexual acts with adolescents, where the victims are all children or young people between 14 and 16 years of age. If the victim is between 14 and 18 years of age, without documents, article 174 acts, resorting to the prostitution of minors. If the victim is under 18, articles 175 and 176 cover sexual exploitation of children and pornography of minors, respectively ().

Since age estimation must be as precise as possible when applied to the medico-legal field, in the best interest of justice, the use of radiographic techniques, namely orthopantomography, is preferred over any other indirect method. It is a process that is relatively time-efficient, showing to be more accurate than skeletal development for estimating chronological age (-).

Several methods, using orthopantomographs, have been introduced to estimate age through dental observation. They have been commonly used in studies of dental maturity and for age estimation (). Demirjian method is one of them, which consists in assigning one out of eight stages according to the mineralization state of the tooth (, ). However, this system is highly subjective since it depends on the stage that the observer attributes to it.

On the other hand, there is Cameriere’s method with a regressive formula in which it is established that the ratio given by the sum of the distances from the inner sides of the open apices and the height of the developing of second and third molars (second molar maturity index – I2M and third molar maturity index - I3M) is a reliable method to discriminate, regardless of geographic origin and socio-economic status (, ).

The aim of this study was to assess the cut-off points for the Portuguese legal ages of 12 and 14 years, important according to the Portuguese Penal Code, through the second molar maturity index (I2M) and third molar maturity index (I3M) and to compare this method to the Demirjian’s stages already applied in the forensic community for dental age assessment.

Material and methods

Sample

To assess the cut-off points through the I2M, 633 orthopantomographs (270 females and 363 males) were selected between 7 and 17 year olds and to assess the cut off points through the I3M. We selected 471 orthopantomographs (253 females and 218 males) between 10 and 23 years old (Table 1). The samples were taken as a random basis from the X-ray database of the Stomatology Department at Hospital Santa Maria, targeting patients from the Lisbon North University Hospital Center.

Table 1

Age distribution by sex

	Sample for I2M			Sample for I3M
Age (years)	Sex		Total	Sex		Total
	Male	Female		Male	Female
7	38	25	63	-	-	-
8	48	36	84	-	-	-
9	60	41	101	-	-	-
10	54	39	93	26	35	61
11	45	29	74	23	37	60
12	35	38	73	22	30	52
13	28	22	50	27	19	46
14	23	17	40	23	24	47
15	7	6	13	16	13	29
16	8	10	18	13	13	26
17	17	7	24	8	22	30
18	-	-	-	10	9	19
19	-	-	-	15	13	28
20	-	-	-	11	5	16
21	-	-	-	10	10	20
22	-	-	-	8	13	21
23	-	-	-	6	10	16
Total	363	270	633	218	253	471

Selection criteria were healthy subjects of Portuguese origin, presence of the second and third molar in all lower quadrants, absence of congenital dental anomalies in shape or/and position, including root canal treatment, caries or restorations in the left mandibular permanent teeth. Heavily rotated, impacted, and unclear orthopantomographs were excluded from the analysis.

The subject’s sex, date of birth, and the date of the orthopantomography were recorded. The chronological age (CA) for each subject was computed by subtracting the date of the X-rays from the date of birth.

The study was performed in accordance with the ethical standards laid down by Faculty of Dental Medicine, University of Lisbon Health Ethics Committee, under the number 911105 and 911106.

Measurements

As proposed by Cameriere et al. in the original study, the maturity index was assessed as follows: a ratio between the sum of the inner side’s width of the open apices (A1 and A2) in the left and right lower third molar and the tooth’s length (L) when more than one root were presented, or a ratio between the width of the open apex (A) and the tooth’s length (L1) when a single root was present (Figure 1, Figure 2) ().

Figure 1

Measurement of second molar index, according to the molar index proposed by Cameriere

Figure 2

Measurement of the third molar index, according to de third molar index proposed by Cameriere

X-ray images in JPG format were analyzed by a software program, ImageJ ®. The orthopantomographs were scaled at 400% and afterwards the measurement was changed from pixels to millimeters.

Mineralization of permanent teeth on the lower left mandible was also assessed according to the Demirjian () classification for later comparison with Cameriere’s molar maturity index.

Statistical analysis

The intra-class correlation coefficient (ICC) was applied to quantify intra- and inter-observer agreement. Weighted Cohen’s kappa was used to evaluate intra and inter-observer agreement in Demirjian’s stages classification. Spearman ρ rank correlation was also used to evaluate the order relation between two measurements. For this purpose, 10% of the sample was randomly selected 3 months following the initial scoring process to determine percentage of agreement, for both intra- and inter-observer agreement analyses.

Apart from the accuracy, the sensitivity and the specificity, other measures to assess misclassification were computed, such as the positive predictive value (PPV), the negative predictive value (NPV), and the positive and negative likelihood ratios (LR+ and LR−). Moreover, the post-test probabilities (Bayes PTP) were computed using Bayes’s theorem in order to generalize the results of the Portuguese population, using data extracted from the Statistics Portugal data base (https://www.ine.pt/xportal/xmain?xpid=INE&xpgid=ine_main), ().

Finally, the Receiver Operating Characteristic (ROC) curves were obtained and the areas under the ROC curves (AUC) were computed.

Results

The results of Cohen’s kappa and ICC for second molar are showed in Tables 2 and 3. Intra-observer validation for I2M varies between 0.608 and 0.943. The weighted Cohen's kappa for intra-observer validation of Demirjian stadiums is equal to 0.834. In terms of inter-observer validation, kappa coefficients were equal to 0.834 and to 1.000. The computed Spearman correlations have values greater than 0.95. Thus, the obtained values denote, in most cases, excellent results both in precision and in reproducibility.

Table 2

CCI values of intra-observer validation (I2M)

	Measure	Intra
		Observer 1
37	A1	0.922
	A2	0.918
	L	0.926
	A	0.810
	L1	0.608
47	A1	0.927
	A2	0.918
	L	0.943
	A	0.793
	L1	0.653

Notes: A1, Width of the mesial open apex of the multiradicular tooth; A2, Width of the distal open apex of the multiradicular tooth; L, Maximum tooth length; A, Width of the open apex of the monoradicular tooth; L1, Maximum monoradicular tooth length

Table 3

Weighted Cohen’s kappa coefficient values of intra and inter-observer validation (Demirjian)

Method	Validation	κ	ρ
Demirjian	Intra	0.834	0.953
	Inter 1	0.834	0.953
	Inter 2	1.000	1.000

On the other hand, for the third molars, the results of Cohen’s kappa and ICC are showed in Tables 4 and 5. The intra-observer validation for I3M varies between 0.852 and 0.998 for observer 1 and between 0.966 and 0.996 for observer 2. The inter observer validation varies between 0.964 and 0.999. The weighted Cohen’s kappa for intra-observer validation of Demirjian stadiums was 0.969, while intra-observer varies between 0.919 and 0.930. All values showed excellent results regarding precision and repeatability.

Table 4

CCI values of Intra-observer validation (I3M)

	Measure	Intra		Inter
		Observer 1	Observer 2
38	A1	0.978	0.978	0.996
	A2	0.985	0.966	0.996
	L	0.852	0.994	0.985
	A	0.991	0.996	0.998
	L1	0.998	0.993	0.998
48	A1	0.991	0.992	0.964
	A2	0.989	0.991	0.998
	L	0.985	0.994	0.997
	A	0.980	0.993	0.999
	L1	0.981	0.988	0.993

Notes: A1, Width of the mesial open apex of the multiradicular tooth; A2, Width of the distal open apex of the multiradicular tooth; L, Maximum tooth length; A, Width of the open apex of the monoradicular tooth; L1, Maximum monoradicular tooth length

Table 5

Weighted Cohen’s kappa coefficient values of Intra and Inter-observer validation (Demirjian)

Method	Validation	κ	Ρ
Demirjian	Intra	0.969	0.990
	Inter 1	0.919	0.980
	Inter 2	0.930	0.986

The Spearman’s correlation was used to understand the relationship between chronological age and I2M and Demirjian stadiums. The correlation between the real age and the I2M was 0.875, whereas with the Demirjian stadiums it was 0.861. Thus, both reveal a significant order relationship with chronological age. For the third molar, the Spearman correlation between real age and I3M was 0.902, and the correlation between chronological age and Demirjian stadiums was 0.902, showing that both methods are equally reliable.

Based on the maturity indices and Demirjian stages, it was intended to classify a person as under 12- year- old or at least 12 year- old, as well as classify him/her as under 14- year-old or at least 14- year- old. To perform these classifications, the cut-off points for I2M and for the I3M were computed using binary logistic regression, minimizing the occurrence of misclassifications. For the Demirjian stadiums, the individuals were classified using the most similar age group for each stage since all individuals in the same stadium are classified in the same age group. In these procedures, the sex variable was used as an explanatory variable, but Wald’s test shows that this explanatory variable should be removed from the model (in all cases the p-value was greater than 0.05). Therefore, all results obtained measured the entire sample without distinguishing males from females.

The reliability measures of these classifications are shown in Table 6 for the second molar and in Table 7 for the third molar. Figure 3 shows the ROC curves for I2M, and Figure 4 shows the ROC curves for I3M.

Table 6

Reliability Measures for the cut-off points for the ages of 12 and 14 (I2M and Demirjian)

12 years	I2M <0.135	Demirjian (G, H)
Sensitivity	81.19%	88.53%
Specificity	90.36%	85.30%
Accuracy	87.20%	86.41%
PPV	81.57%	75.98%
NPV	90.14%	93.40%
LR+	8.42	6.02
LR-	0.21	0.13
Bayes PTP	91.57%	88.60%
AUC	0.93	-
14 years	I2M <0.001	Demirjian (H)
Sensitivity	90.53%	90.53%
Specificity	90.15%	90.15%
Accuracy	90.21%	90.21%
PPV	61.87%	61.87%
NPV	98.18%	98.18%
LR+	9.19	9.19
LR-	0.11	0.11
Bayes PTP	85.07%	85.07%
AUC	0.938	-

Table 7

Reliability Measures for the cut-off points for the ages of 12 and 14 (I3M and Demirjian)

12 years	I3M <1.133	Demirjian (D, E, F, G, H)
Sensitivity	93.98%	94.56%
Specificity	74.38%	80.99%
Accuracy	88.94%	91.06%
PPV	91.36%	93.48%
NPV	81.08%	83.76%
LR+	3.67	4.97
LR-	0.08	0.07
Bayes PTP	96.00%	97.02%
AUC	0.959	-
14 years	I3M <0.705	Demirjian (E, F, G, H)
Sensitivity	86.85%	88.25%
Specificity	88.13%	92.69%
Accuracy	87.45%	89.96%
PPV	89.34%	95.06%
NPV	85.40%	83.20%
LR+	7.32	12.08
LR-	0.15	0.13
Bayes PTP	95.26%	97.07%
AUC	0.95	-

Figure 3

ROC curves for I2M

Figure 4

ROC curves for I3M

Discussion

Over the years, estimating age through dental methods has become crucial in the juvenile criminal justice. For that same reason, several studies have been conducted over the years to estimate the age accurately, mainly by considering the population affinity.

In this present study, the first one for the Portuguese legal age thresholds of 12 and 14 year- olds, we tested the discriminatory potential of a specific cut-off value of I2M and I3M in discriminating children aged 12 and 14. Secondly, we compared those quantitative dental age assessment methods with the qualitative dental age assessment method, the Demirjian classification, which has already been used in the Portuguese population.

The intra and inter-observer results (Tables 2 to 5) mostly represent excellent results both on precision and on reproducibility for the I2M, I3M and Demirjian’s stadiums, which is consistent with the existing literature regarding both methods (, -).

Spearman’s correlation results show that all methods (I2M, I3M and Demirjian’s stadiums from the second and the third molar) reveal significant correlation with real age, which is consistent with the available literature (, ).

In Portugal, the legal ages of 12 and 14 years are covered in the Portuguese penal code which promotes the protection of the juvenile individuals, giving priority to healing and prevention over punishment. Consequently, the determination of the cut-off points is very important in order to determine if an individual is younger than 12 or 14 years, or at least if the individual is 12 or 14- year- old (). Regarding the cut-off points for 12 year olds (I3M = 1.133 and I2M = 0.135), I3M shows better sensitivity (93.98%) but lower specificity (74.38%) than I2M (sensitivity = 81.19% and specificity = 90.36%). For the Portuguese cut-off points for 14- year- olds (I2M = 0.001 and I3M = 0.705), I2M has higher values of sensitivity and specificity (90.53% and 90.15%) than I3M (sensitivity = 86.85% and specificity = 88.13%). The results of our study are consistent with the results obtained by Cameriere in 2018 (). Although, the area under the ROC curve of I3M for both ages (AUC 12 years = 0.959 and AUC 14 years = 0.95) is greater than the area under the ROC curve of I2M (AUC 12 years = 0.93 and AUC 14 years = 0.938), both indexes obtain excellent results for the area under the ROC curve (greater than 0.9), ().

The accuracy is measured under the ROC curve. The area of 1 represents a perfect method. The area measures discrimination, that is, the ability of the method to correctly classify those who are, or are not, 12 and 14- year- old (). Hence, the areas under the ROC curves obtained in this study for 12- and 14-year- olds reveal that the use of I2M and I3M is a suitable methodology to classify the age of the analyzed individuals. However, when compared I2M to I3M, the latter shows better results regarding age estimation. The value of AUC obtained in this study is higher than in other studies (, ).

The sensitivity obtained by Cameriere and Ferrante using dental age assessment by the 7 teeth regression, bone age assessment by hand-wrist bones or using the combination of both, biological indicators for the cut points of 12 and 14- year- olds were lower than the sensitivity obtained for the cut-points using only the dental parameters I2M or I3M for the Portuguese population (). This means that it is better to use only dental age assessment for these Portuguese legal ages. The Bayes post-test probabilities with highest value were obtained using only the I3M for the cut points determining for the legal age threshold 12- year- old (Bayes PTP = 96%) and 14 year- old (Bayes PTP = 95.26%). Bayes post-test probability of being 12 and 14- year- old is computed to discriminate between those who are not 12- year- old and 14- year-old or over 14. Accurate age estimation is crucial to ensure that children and adolescents are identified and treated adequately in the Portuguese criminal field.

For the I2M results, there are no studies to sustain the results regarding the cut-off point for 12- year olds. Nevertheless, the obtained results are very reasonable. For the cut-off point for the 14- year-olds, some studies assume I2M = 0 which is equal to the cut-off point obtained in this study by the binary logistic regression (the only cases in which I2M < 0.001 were I2M = 0). Thus, the reliability measures are similar to the ones obtained in those studies (, , ).

When comparing the Demirjian with Cameriere method, the results are quite similar. For 14- year-olds using the second molar, the results are identical because all individuals have obtained the same age classification in both methods since I2M = 0 implies Demirjian stadium equals to H. However, Cameriere’s method is better because the age group classification is based on a quantitative variable and, consequently, the cut-off point can be adjusted to improve one measure in relation to another (sensitivity or specificity), whereas this is not possible if Demirjian stadium is used.

Conclusions

This is the first study in Portugal to validate the reliability and the medico-legal application of I2M and I3M for the legal thresholds ages 12 and 14 years in the Portuguese population. Regarding our results for the cut-off points for Portuguese population for the 12 year-olds, I3M is better and for 14- year- olds, I2M has performed better. When comparing the age classification by I2M or I3M and the Demirjian stages, it is possible to conclude that there are no significant differences between the precision obtained by these methods. However, the use of I2M and I3M allows us to vary the cut-off value to privilege sensitivities or specificity, depending on which is more appropriate to the intended application. Thus, the I2M and I3M indexes provide reliable classification by each Portuguese legal age threshold of 12 and 14 year- olds. In medico-legal circumstances, a successful discrimination method must produce a smaller number of false positives than false negatives in order to legally protect the children’s rights.