Dental Age Estimation Using the Demirjian Method: Statistical Analysis Using Neural Networks

Byung-Yoon Roh; Jong-Seok Lee; Sang-Beom Lim; Hye-Won Ryu; Su-Jeong Jeon; Ju-Heon Lee; Yo-Seob Seo; Ji-Won Ryu; Jong-Mo Ahn

doi:10.7580/kjlm.2023.47.1.1

Abstract

In children and adolescents, dental age estimation is performed with the development of the teeth. Various statistical analysis methods have been used to determine the relationship between age and dental maturity and develop an accurate method of age calculation. This study attempted to apply a neural network model for the statistical analysis of dental age estimation in children and evaluated its applicability. This study used 1196 panoramic radiographs of patients aged 3-16 years, and 996 and 200 were randomly classified into training and test sets, respectively. The dental maturity of the mandibular left teeth was evaluated using Demirjian's method, the neural network model using the backpropagation algorithm was derived using training sets, and the errors were evaluated using 100 radiographs of each male and female as test sets. In addition, multiple linear regression analysis was conducted on the same training set, and the error was calculated by applying it to the test set and comparing it with the error of the neural network model. In the neural network model, the mean absolute error (MAE) and root mean squared error (RMSE) were 0.589 and 0.783 in male subjects and 0.529 and 0.760 in female subjects, respectively. In the multiple linear regression model, the MAE and RMSE were 0.600 and 0.748 in male subjects and 0.566 and 0.789 in female subjects, respectively. When applying the neural network model to the statistical analysis of the dental developmental stage, the results were as accurate as those of conventional statistical analysis methods. This study's approach is expected to be useful for estimating the ages of children.

Key Words: Age determination by teeth · Panoramic radiography · Tooth development · Neural networks

Introduction

Forensic age estimation has been used to solve various social and legal problems [1,2]. Teeth have been widely used in age estimation as an important indicator of age. In particular, dental age estimation has been conducted in recent years to solve legal problems related to minors, and many related studies have been conducted on various population groups [3,4].

In children and adolescents, dental age estimation is performed using tooth maturity and is mainly performed by evaluating the tooth developmental stage on panoramic radiographs [5]. Several studies have suggested methods for evaluating the stage of tooth development [6-10], and Demirjian's method has been widely used [5]. Subsequently, statistical analysis is performed to analyze the relationship between the tooth development stage and age, and to predict age, and many methods have been introduced in various studies, all of which have shown high accuracy [11-15].

Recently, research using neural network technology has been actively conducted in the fields of forensic science and medicine [16]. These artificial intelligence techniques make it possible to interpret complex data more accurately and automatically without human error. In particular, image analysis using convolutional neural network models has been widely utilized in pathology and radiology [16-18].

This study attempted to apply the neural network method to statistical analysis of dental age estimation in children. Using a neural network model, it was expected that accurate age prediction would be possible by calculating a model that more accurately identifies the relationship between tooth developmental stage and age. This study evaluated its accuracy and verified its applicability.

Materials and Methods

This study used 1,196 panoramic radiographs of patients aged 3-16 years who visited Chosun University Dental Hospital. Among them, 600 and 596 radiographs were obtained for male and female patients, respectively. The age and sex distributions of the participants are presented in Table 1. This study was conducted retrospectively and all patient information was processed anonymously. This study was approved by the Institutional Review Board (IRB) of the Chosun University Dental Hospital (approval No. CUDHIRB 2005001). And the informed consent was waived by the IRB, since the study was a retrospective analysis.

Table 1.

Age and sex distribution of sujects

Age (yr)	Male	Female
3.00-3.99	44	49
4.00-4.99	41	44
5.00-5.99	42	44
6.00-6.99	42	44
7.00-7.99	43	47
8.00-8.99	42	44
9.00-9.99	46	42
10.00-10.99	42	43
11.00-11.99	46	47
12.00-12.99	45	40
13.00-13.99	39	35
14.00-14.99	50	39
15.00-15.99	33	37
16.00-16.99	45	41
Total	600	596

The panoramic radiographs were converted into JPG files using the PiViewSTAR PACS workstation (INFINITT Healthcare Co. Ltd., Seoul, Korea), and Alsee software (ver. 8.26.0.1, ESTSoft Corp., Seoul, Korea) was used for analysis. The developmental stages of the mandibular left central incisor, lateral incisor, canine, first and second premolars, and first and second molars were determined from A to H according to Demirjian's criteria.

The training and test sets were randomly selected. The training sets comprised 500 and 496 radiographs of male and female participants, respectively, and the test sets comprised 100 radiographs of each of the male and female participants.

The model for estimating age from the stage of tooth development was derived using a neural network model with training sets. Feed-forward multilayer perceptron networks using a backpropagation algorithm with a hyperbolic tangent activation function in the hidden layer were used. There were seven neurons in the input layer, eight neurons in the hidden layer, and one neuron in the output layer (Fig. 1).

Fig. 1.

The structure of the neural networks model for age estimation using tooth developmental stage.

For comparison with this model, the development stage of each tooth was regarded as an independent variable, and multiple linear regression analysis was performed to derive an age estimation model. These models and the neural network model were applied to the test set, respectively, and in each method, the difference between the actual age and the estimated age were calculated and the results were compared.

All statistical analyses were performed using the R software (ver. 4.0.5, R Foundation for Statistical Computing, Vienna, Austria), and the Neuralnet package was used to establish the neural network model (specifications of the PC used in this study: CPU: Intel(R) Core(TM) i3-6100 @3.70GHz, GPU: Intel(R) HD Graphics 530, RAM:4.00GB, OS: Windows 10 Pro).

Results

The mean and standard deviation ages according to the developmental stage of each tooth are presented in Tables 2 and 3, respectively.

Table 2.

Means and standard deviations of age by tooth development (Demirjian's criteria) in male subjects

TDS ^a)	Tooth No. ^b)
	31		32		33		34		35		36		37
	No.	Mean±SD	No.	Mean±SD	No.	Mean±SD	No.	Mean±SD	No.	Mean±SD	No.	Mean±SD	No.	Mean±SD
A	0		0		0		9	3.2±0.2	12	3.6±0.4	0		15	4.0±0.6
B	0		0		1	3.3±0.0	25	3.5±0.3	33	4.5±0.6	0		50	4.9±0.8
C	46	3.6±0.4	53	3.6±0.4	103	4.3±0.9	67	4.6±0.7	55	5.5±0.7	7	3.4±0.2	57	6.2±0.8
D	50	4.8±0.6	54	5.0±0.6	56	6.2±0.8	61	6.2±0.6	51	6.9±0.8	47	3.7±0.5	89	7.8±0.9
E	26	5.6±0.4	42	6.1±0.6	93	8.0±1.0	109	8.3±1.0	102	8.6±1.0	53	5.0±0.6	63	9.5±0.8
F	30	6.6±0.5	33	7.0±0.7	81	9.8±1.0	60	10.0±1.2	76	10.6±1.1	34	6.1±0.6	41	10.7±0.7
G	129	8.3±1.3	137	8.9±1.2	157	12.8±1.4	142	12.4±1.2	139	13.0±1.3	188	8.6±1.5	192	13.4±1.4
H	319	13.1±2.3	281	13.6±1.9	109	15.3±1.1	127	15.2±1.2	100	15.5±1.1	271	13.6±2.0	56	15.8±1.0

SD, standard deviation.

^a) Tooth developmental stage by Demirjian's criteria;

^b) FDI (Fédération Dentaire Internationale) dental notation.

Table 3.

Means and standard deviations of age by tooth development (Demirjian's criteria) in female subjects

TDS ^a)	Tooth No. ^b)
	31		32		33		34		35		36		37
	No.	Mean±SD	No.	Mean±SD	No.	Mean±SD	No.	Mean±SD	No.	Mean±SD	No.	Mean±SD	No.	Mean±SD
A	0		0		0		3	3.4±0.5	32	4.0±0.8	0		19	4.1±0.5
B	0		0		0		29	3.4±0.3	24	4.3±0.6	0		42	4.7±0.6
C	44	3.5±0.4	59	3.6±0.4	98	4.0±0.7	71	4.3±0.6	53	5.4±0.9	4	3.4±0.2	60	6.1±0.8
D	50	4.3±0.4	40	4.6±0.5	49	5.7±0.6	60	6.0±0.6	67	6.6±0.7	42	3.6±0.4	99	7.7±1.0
E	36	5.6±0.3	41	5.7±0.5	90	7.2±0.8	105	7.7±0.9	86	8.4±0.9	59	4.5±0.6	50	9.2±0.7
F	33	6.3±0.6	48	6.9±0.7	74	9.1±0.8	58	9.7±0.9	72	10.4±1.1	30	5.8±0.6	48	10.6±0.7
G	126	8.1±1.0	125	8.6±1.1	161	12.0±1.5	143	12.0±1.4	131	12.5±1.4	190	8.1±1.4	192	13.4±1.6
H	307	13.0±2.3	277	13.4±2.1	124	15.0±1.5	127	15.0±1.4	105	15.4±1.2	271	13.4±2.1	43	16.1±0.8

SD, standard deviation.

^a) Tooth developmental stage by Demirjian's criteria;

^b) FDI (Fédération Dentaire Internationale) dental notation.

When the age estimation model was established using the neural network model in the training set, the standard error of estimation (SEE) was 0.469 and 0.544 in male and female subjects, respectively, and the coefficients of determination (r²) was 0.969 and 0.966 in male and female subjects, respectively. Table 4 shows the results of the model derived when multiple linear regression analysis was used. The SEE in this model was 0.749 and 0.761 for males and females, respectively, and the coefficients of determination were 0.961 and 0.951 for males and females, respectively, indicating that the neural network model showed slightly more accurate results.

Table 4.

Intercepts and coefficients of multiple linear regression model for male and female subjects

Demirjian's score	Sex	Tooth No. ^a)
Demirjian's score	Sex	31	32	33	34	35	36	37
A	M				-2.215	-0.326		0.314
	F				-2.591	-0.008		0.068
B	M				-1.985	-0.059		0.417
	F				-2.739	0.052		0.270
C	M	-1.292	-1.411	-1.855	-1.864	0.217	-0.668	0.458
	F	-1.723	-0.811	-1.491	-2.301	0.120	-0.718	0.286
D	M	-1.245	-0.841	-1.689	-1.799	0.069	-0.523	0.662
	F	-1.418	-0.714	-1.266	-2.013	-0.081	-0.869	0.356
E	M	-0.823	-0.931	-1.257	-1.108	0.192	-0.406	1.542
	F	-0.769	-0.871	-1.188	-1.630	0.609	-0.848	0.527
F	M	-0.187	-0.809	-0.946	-1.141	0.477	-0.268	1.896
	F	-0.310	-0.748	-0.590	-1.076	0.806	-0.587	1.070
G	M	-0.352	-0.338	-0.640	-1.075	0.934	-0.335	2.911
	F	-0.235	-0.510	-0.814	-1.153	0.867	-0.459	2.419
H	M					1.734		3.612
	F					1.876		3.365
Intercept	M				10.580
	F				10.880
P-value	M				<0.001
	F				<0.001

The dental age can be calculated by adding the intercept to the sum of coefficients corresponding to the tooth developmental stage on the table.

^a) FDI (Fédération Dentaire Internationale) dental notation.

Comparing the results of applying the neural network model and the multiple linear regression model to test sets (Table 5, Fig. 2), the mean error in the neural network model was 0.038 and 0.039 for each male and female subject, and in the multiple linear regression model, it was -0.014 and 0.014 for each male and female subject, showing slightly lower error values, but the mean absolute error (MAE) in the neural network model was 0.589 and 0.529 for male and female subjects, respectively; in the multiple linear regression model, it was 0.600 and 0.566 for male and female subjects, respectively, and the neural network model showed slightly more accurate results. However, the results of the two models showed no significant differences. The root mean squared error (RMSE) in the neural network model was 0.783 and 760 for males and females, respectively, and in the multiple linear regression, it was 0.748 and 0.789 for male and female, respectively. The neural network model in female subjects and the regression model in male subjects showed slightly more accurate results (Table 5).

Table 5.

The prediction errors of the developed models in the test sets

	Sex	Neural networks model	Multiple linear regression model	P-value
Mean error	M	0.038	-0.014	0.753
	F	0.039	0.014	0.828
MAE	M	0.589	0.600	0.598
	F	0.529	0.566	0.888
RMSE	M	0.783	0.748
	F	0.760	0.789

MAE, mean absolute error; RMSE, root mean squared error.

Fig. 2.

Comparison of the participants’ real ages and predicted ages using the neural network model (NNM) and the multiple linear regression model (MLRM): (A) male, (B) female.

Discussion

Recently, machine learning or deep learning technology using neural networks has been introduced in the fields of medicine and forensic science and has been widely used; many related studies have been actively conducted [16-20]. Automated image analysis technology using a convolution neural network has also been applied to age estimation, and several studies have reported more accurate results compared to previous studies [16,19,20]. However, this requires high-spec computer, programmer participation, or complex programming skills. Therefore, this study evaluated the stage of tooth development using an observer, as in the conventional method, and attempted to apply neural network technology for statistical analysis. Compared to the method of automating the entire process, this approach has the advantage of being able to perform relatively simple and fast without complex programming skills or high-spec computer equipment.

Regression analysis using neural networks, attempted in this study, also has the advantage of automatically determining the weights of variables and automatically establishing a regression model, even if the relationship is not linear. The model of body growth over time does not show a simple linear relationship, and the relationship between the tooth development stage and age also shows the shape of the curve [8]. In addition, the classification of developmental stages according to Demirjian's criteria is divided based on what is easy for observers to distinguish, and the time change according to these stage changes is not regular. Many statistical analyses have attempted to accurately identify the relationship between tooth developmental stage and age. To accurately predict ages, we must determine the weighted value of the variable and model the relationship between age and tooth maturity. However, they can be calculated automatically using a neural network model.

Considering these results, it can be confirmed that using neural network models can produce results that are as accurate as conventional statistical methods; however, it is difficult to confirm that they have produced more accurate results. Comparing the neural network model with the conventional statistical analysis method, it appears that the results in the training set showed higher accuracy. However, neural network models can cause overfitting problems [21]. Therefore, we checked the prediction error in the test sets. When the neural network model was applied to the test set, the MAE was slightly lower in both men and women, but the value of RMSE in male subjects was slightly higher than when the multiple linear regression model was applied. It is believed that these discrepancies were due to overfitting, and a follow-up study is needed to find a more suitable neural network model using more data.

Comparing this study with the results of a previous study on Korean population, Lee et al. in 2008 [22] reported that the coefficient of determination was 0.9721 and 0.9740 in men and women, which were higher than in this study, but SEE was 0.63 and 0.62 in men and women, and the result value using neural network model was lower. Considering that 28 teeth were used in Lee et al.'s study [22], it is believed that the research results of this study predicted relatively accurate values. Compared with Lee et al.'s study in 2011 [14], the mean squared error in Lee at al.'s study [14] was 0.381 and 0.632, and the mean squared error in the training set of this study was 0.220 and 0.296, showing lower values in this study. Although there are some limitations in comparing the results accurately owing to differences in research design, it is thought that the neural network model is as accurate as existing methods.

This study attempted to apply a neural network model to the statistical analysis of the tooth developmental stage and evaluated its applicability. It showed acceptable prediction performance as a conventional statistical method; therefore, it can be useful for dental age estimation in children. To improve this model, a follow-up study using more data is required.