Boosting Algorithm for Optimizing Morphological Dental Age Estimation Method: A Southern China Population Study

doi:10.21203/rs.3.rs-1960389/v1

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Boosting Algorithm for Optimizing Morphological Dental Age Estimation Method: A Southern China Population Study

https://doi.org/10.21203/rs.3.rs-1960389/v1

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Age estimation based on the mineralized morphology of teeth is one of the important elements of forensic anthropology. To explore the most suitable age assessment protocol for adolescents in the South China population, 1477 panoramic radiographs images of people aged 2–18 years in the South were collected and staged by the Demirjian mineralization staging method. The dental age were estimated using the parameters of the Demirjian and Willems. Mathematical optimization and machine learning optimization were also performed in the data processing process in an attempt to obtain a more accurate model. The results show that Willems' method is more accurate in estimating the dental age of the South China population, while the model can be further optimized by re-assigning the model through a non-intercept regression method. The machine learning model presented excellent results in terms of the efficacy comparison results with the traditional mathematical model, and the machine learning model under the Boosting framework such as Gradient Boosting Decision Tree (GBDT) significantly reduced the error in dental age estimation compared to the traditional mathematical method. This machine learning processing method based on traditional assessment data can effectively reduce the error of assessment while saving arithmetic power. This study demonstrates the effectiveness of the GBDT algorithm in optimizing forensic age estimation models and provides a reference for other regions to use this scheme for age assessment model architecture, also the lightweight nature of machine learning offers the possibility of widespread forensic anthropological age estimation.

Dental Age Estimation

Demirjian Method

Non-Intercept Regression

Machine Learning

Gradient Boosting Decision Tree (GBDT)

The forensic age assessment provides important evidence for the identification and enforcement of age-related laws such as criminal responsibility identification, immigration, child adoption, and so on. With the adjustment of laws in some countries, the Age of criminal responsibility has been lowered. Under the Criminal Law of the People's Republic of China, the minimum age of criminal responsibility has been downgraded to 12 years old, these revises have led to an increase in the demand for low age identification and the higher requirements for its accuracy.

Age estimation based on the morphological process of mineralization of permanent teeth is considered a reliable means of age identification because of its highly stable mineralized morphological development, which is less susceptible to genetic^{1, 2} and environmental influences, as well as the fact that teeth are preserved longer than the average bone after death³. Various dental age estimation methods have been developed and widely practiced in different populations, among which the Demirjian method⁴ and the Willems method⁵ are the most popular. The Demirjian method divided the development of the 7 permanent teeth in the left lower jaw into 8 stages (A-H). The stages of each tooth were converted into a specific score, and the sum of the scores for all teeth represents the maturity score. Then, the maturity score was transformed into a dental age based on the conversion tables⁴. The Willems method simplifies the steps of the Demirjian method⁵, tooth development stage was divided into 8 stages according to Demirjian's definition of morphological development stage, each stage was assigned a new score, and the sum of the scores of the 7 teeth directly represents the estimation value of dental age. Currently, there are more studies⁶ on dental age estimation in northern China, but there is a lack of studies on dental age estimation for the population in southern China. And age estimation in South China is still rely mainly on bone morphology such as the knee⁷, clavicle⁸ and carpal bone.

Currently, machine learning is widely used in medical and forensic fields, such as medical image recognition⁹ and sex estimation¹⁰. Machine learning provides a considerable boost to age estimation¹¹, and as a fundamental algorithm of artificial intelligence, machine learning not only enables more accurate age estimation, but also makes age estimation more efficient¹². At the same time, machine learning can be constantly modified to iterate on the new system also brings the possibility of the application of a large amount of data that cannot be processed manually. With sufficient samples, machine learning can bring more accurate results and reduce the error of human involvement. Our study explores the appropriateness of traditional assessment methods for southern Chinese populations while also selecting several of the most common and applicable machine learning algorithms to explore their efficiency when applied to the same data.

Traditional Estimation Methods

The accuracy of the parameters of the Demirjian method with those of the Willems method in estimating the age of the South China population was compared using the same metrics. The results show that the Demirjian method significantly overestimated the age of both gender groups (Table 1), with males overestimating by 0.42 years and females by 0.31 years, and the Willems method overestimated the mean age of the male group by 0.09 years and underestimated the mean age of the female group by 0.16 years (Table 1), with the Willems method presenting results with much less error. Comparing the fit of the two to age, the results fitted by the Willems scheme also presented a better linear correlation (Fig. 1, 2). Compared to the Demirjian method, the Willems method has less error and is more suitable for age estimation in the South China population.

Table 1

The fitting effect of different models
Method	Gender	CA^a	DA^b	AD^c	P value^d	MAE (< 18)	MAE (< 16)
Demirjian	Female	11.18(3.83)	11.49(3.72)	-0.31(1.18)	0.00	0.95	0.94
Demirjian	Male	10.68(3.76)	11.10(3.74)	-0.42(1.15)	0.00	0.96	0.96
Willems	Female	11.18(3.83)	11.02(3.78)	0.16(0.98)	0.00	0.78	0.73
Willems	Male	10.68(3.76)	10.77(3.70)	-0.09(0.98)	0.02	0.77	0.76
Modified	Female	11.18(3.83)	11.16(3.73)	0.02(0.97)	0.61	0.77	0.71
Modified	Male	10.68(3.76)	10.68(3.55)	-0.01(0.96)	0.83	0.76	0.72
a: Chronological Age

b: Dental Age

c: Age Deviation, AD = Chronological Age-Dental Age

Chronological Age, Dental Age and the Age Deviation are given as Mean (Standard Deviation)

d: Paired T-test significance of chronological age and dental age

MAE: Mean Absolute Error

Since the Willems method is more suitable for the South China population, the Willems parameters of each tooth and chronological age were fitted by linear regression with a non-intercept in each gender group to generate a model suitable for the southern China population. After the Willems scores were weighted by regression coefficients, a modified model was generated (Table 2, 3). The results of age estimation using the modified model parameters showed that the fitting effect was better than that of the Willems method. In the male group, the mean age was overestimated by 0.01 years and underestimated by 0.02 years in the female group. No statistical differences were observed between chronological age and dental age (P > 0.05).P Value improved by one notch from < 0.05 to > 0.05. However, the MAE for the male and female groups of the modified model was essentially the same as that of the Willems method. This shows that there are limited improvements to the MAE in terms of math. The modified model also adjusted MAE for each age group to the level of less than 1 year, which is more advantageous in age estimation for the large population (Table 1).

Table 2

The tooth score of the modified model (Left mandibular teeth, *Male*)
Tooth	A	B	C	D	E	F	G	H
Central incisor	-	-	0.90	0.80	0.80	1.00	1.11	1.17
Lateral incisor	-	-	0.43	0.49	0.57	0.84	1.02	1.27
Canine	-	-	-	0.03	0.24	0.37	0.85	1.48
First bicuspid	0.19	0.72	0.97	1.44	1.91	2.62	3.14	3.66
Second bicuspid	0.05	0.03	0.07	0.16	0.20	0.27	0.24	0.70
First mola	-	-	-	1.07	1.77	2.49	3.03	3.34
Second molar	0.17	0.46	0.69	0.77	1.27	1.94	2.40	4.03

Table 3

The tooth score of the modified model (Left mandibular teeth, *Female*)
Tooth	A	B	C	D	E	F	G	H
Central incisor	-	-	1.86	2.23	2.38	2.87	3.25	3.20
Lateral incisor	-	-	-	0.30	0.33	0.50	0.80	0.71
Canine	-	-	0.63	0.57	0.65	1.14	1.81	2.11
First bicuspid	-1.10	-0.17	0.19	0.47	0.69	1.47	1.83	2.53
Second bicuspid	-0.20	0.01	0.29	0.18	0.37	0.37	0.58	1.60
First mola	-	-	-	0.63	0.92	1.59	1.86	2.26
Second molar	0.11	0.09	0.17	0.26	0.54	1.05	1.71	3.30

Machine Learning results

Optimization of the model by simple mathematical fitting alone is limited and does not result in a significant improvement in the accuracy of the estimates. We put all the samples into machine learning, using the morphological staging and gender of the seven left mandibular teeth as independent variables and the actual age as the dependent variable, in an attempt to optimize the assessment of efficacy using machine learning.

The effectiveness of each machine learning algorithm in optimizing the model was compared, and the results showed that Light GBM, XG Boost, Extra Trees, Decision Tree, Cat Boost and GBDT were effective in improving the estimation of the model, with XG Boost, Cat Boost and GBDT all being algorithms under the Boosting framework. The GBDT algorithm had the greatest improvement on the estimation effect (Fig. 3). The evaluation results using the GBDT algorithm in the overall population showed that the MAE decreased to below 0.441 for females and below 0.495 for males (Table 4, 5). Also, its assessment effectiveness was optimized for each age group, with the MAE dropping below 0.25 for all age groups in the test set (Fig. 4, 5). The above results show that machine learning algorithms, particularly the Boosting algorithm, can significantly improve the estimation efficiency of the model and improve the accuracy of age prediction. This successful optimization shows that the efficacy of the dental age estimation model can be optimized by the machine learning algorithm to generate a dental age estimation model that is more suitable for a specific regional population. The optimized model can provide more accurate results for forensic age estimation and can better meet the needs of age estimation in actual forensic identification.

Table 4

The result of Machine learning algorithm model for female and male
	Set	MSE		RMSE		MAE		R²
		female	male	female	male	female	male	female	male
Decision Tree	Training	0.799	0.865	0.894	0.93	0.684	0.679	0.933	0.938
Decision Tree	Testing	0.668	0.659	0.817	0.812	0.643	0.602	0.948	0.954
Random forests	Training	0.674	0.789	0.821	0.888	0.565	0.654	0.946	0.94
Random forests	Testing	1.495	1.244	1.223	1.115	0.868	0.834	0.866	0.924
Ada Boost	Training	1.15	1.172	1.072	1.082	0.78	0.796	0.907	0.916
Ada Boost	Testing	1.255	1.123	1.12	1.06	0.828	0.815	0.891	0.921
GBDT	Training	0.604	0.654	0.777	0.809	0.523	0.534	0.951	0.952
GBDT	Testing	0.426	0.628	0.652	0.793	0.441	0.495	0.963	0.957
Extra Trees	Training	0.74	0.809	0.86	0.899	0.655	0.665	0.942	0.943
Extra Trees	Testing	0.786	0.702	0.887	0.838	0.682	0.626	0.923	0.947
Cat boost	Training	0.578	0.747	0.76	0.864	0.56	0.613	0.953	0.945
Cat boost	Testing	0.683	0.584	0.827	0.764	0.594	0.545	0.944	0.961
KNN	Training	1.268	1.065	1.126	1.032	0.795	0.748	0.896	0.923
KNN	Testing	1.458	1.134	1.207	1.065	0.862	0.792	0.88	0.922
BPNN	Training	2.117	2.632	1.455	1.622	1.105	1.268	0.827	0.817
BPNN	Testing	2.107	2.403	1.452	1.55	1.16	1.182	0.827	0.813
SVR	Training	4.096	2.816	2.024	1.678	1.659	1.29	0.677	0.798
SVR	Testing	2.945	2.794	1.716	1.672	1.437	1.3	0.727	0.8
Light GBM	Training	0.76	0.801	0.872	0.895	0.634	0.67	0.937	0.943
Light GBM	Testing	0.676	0.839	0.822	0.916	0.642	0.648	0.947	0.938
MSE: Mean Square Error

RMSE: Root Mean Squared Error

MAE: Mean Absolute Error

Overall, the statistical results showed that the age of the southern China population was significantly overestimated by the Demirjian method, while the Willems method overestimated the age of males and underestimated the age of females both to a lesser degree. The linear regression model without an intercept based on the Willems method could better fit the age of both gender groups and has been proved to be one of the available optimization methods. The machine learning algorithm significantly improves the accuracy of predicting the age of the population in South China, which is more valuable for practical application (Fig. 4, 5). GBDT as a well-known algorithm in the Boosting framework, has also excelled in reducing age estimation errors.

The sample selection did have some bias in each group, but the broad baseline was not problematic and would not affect the study results. And the total sample size and the sample size of each group were completely adequate.

Demirjian method shows a trend of overestimating chronological age in both male and female groups of Southern China population, and the error was large, so it is considered not suitable for the age estimation of southern China population. This result is consistent with many studies in China^{6, 13, 14} or Asian region¹⁵. Demirjian method was developed for age estimation of French-Canadians children, and the overestimation of the results in and around China suggests that the results of the age estimation are probably matched by the geographical proximity of the population. The poor linear relationship between the two may be the reason why this method cannot give a good estimation result, which is fundamentally the difference between the development patterns. The Willems method had a smaller margin of error than the Demirjian method. The Willems parameter modification was also due to the Demirjian method's unsatisfactory estimation effect in Belgian children, so the overall estimation results were revised down, and thus showed a corresponding better estimation performance in the population of southern China. Similarly, the results of the Willems method are similar in China^{6, 16} and its neighboring regions¹⁷.

The new model proposed new weights, has eliminated deviations between chronological age and dental age in the total sample and has shown good results in improving the accuracy of estimation. This suggests that the reconstruction of a linear model can effectively improve the accuracy of estimation when the original linear correlation is good, to propose a more accurate model for the population in each region. At the same time, this study also proves that morphology-based dental age estimation is an effective method to estimate the chronological age of young children and adolescents.

Optimization of the model by machine learning resulted in a significant reduction in MAE for each age group, with the GBDT algorithm performing best in the optimization. Possible reasons for this optimization include (1) Machine learning eliminates the use of transformation tables, reducing the error in the model process. (2) The Boosting algorithm is first trained on the full sample set, and the training produces a series of weak learners. In the next round of training, the training set is kept constant but the weights of the correct samples are reduced and the weights of the incorrect samples from the previous round are increased. A function is found to fit the residuals from the previous round, generating a strong learner until the residuals are sufficiently small or a set maximum number of iterations is reached to stop the iterations. As tooth development is not completely linear and teeth tend to develop faster and then slower, such a general, non-linear estimation method may be more suitable for age assessment based on the developmental pattern of tooth mineralization.

The GBDT scheme is flexible enough to handle various types of data, including continuous and discrete values, and also takes full account of the weights of each classifier. GBDT has been shown to excel in a number of areas^{12, 18, 19}, but our study is the first to apply GBDT to dental age estimation.Our study also demonstrates that GBDT can break the accuracy limits of traditional dental age estimation and lead to better results for forensic age estimation. The GBDT algorithm in the Boosting framework can estimate the age of the population more accurately, suggesting that machine learning can effectively improve the accuracy of dental age estimation models for all age groups, and with a sufficient number of prior samples, a model with higher accuracy can be proposed for each region. Compared to traditional dental age estimation methods, the age estimation models obtained by machine learning algorithms are more easily applied in other regions and are simpler to implement However, it is noteworthy that seemingly large enough datasets and enough learning algorithms have existed for decades, yet despite thousands of papers applying machine learning algorithms to medical data, few papers have made meaningful contributions to solving practical problems. This study proposes a practical age estimation scheme to facilitate the application of dental estimation in population forensics in South China, and the conclusion that GBDT is effective in improving the efficacy of age estimation, as demonstrated in this study, also provides a reference for the development of forensic dental age assessment schemes in other regions.

Unlike end-to-end estimation schemes with no human intervention and automatic extraction of dental features for age estimation using CNN algorithms²⁰, this study manually determines the staging and then uses machine learning algorithms to continuously iterate to obtain the most appropriate age estimation model, and this estimation process can be accomplished using a lightweight computer terminal, which eliminates the tediousness of using a large server for model training. In comparison, the MAE obtained by the GBDT algorithm (< 0.5) is also lower than that of the end-to-end solution (0.83). Machine learning algorithms bring more possibilities for the wide application of age estimation in forensic science.

We compared the validity of traditional age assessment programs with machine learning programs for age estimation in a South China population. The results show that the Demirjian method is less accurate than the Willems method in assessing age, and that some improvement in the accuracy of age assessment can be achieved by re-weighting the parameters. Training the same data using an machine learning scheme can effectively improve the accuracy of age assessment, with several algorithms under the Boosting framework performing well and GBDT leading to the most accurate estimates. This Boosting-based model architecture model gets rid of the tedious steps of traditional models, while the lightweight machine learning model architecture can be implemented more easily across institutions. We demonstrate that schemes such as GBDT can effectively optimize forensic age estimation accuracy and can provide a reference for model architectures for age assessment in various regions.

Sample Collection and Screening

This study was approved by the Ethics Committee of Nanfang Hospital, Southern Medical University (NFEC-2022-298) and we confirm that all methods were performed in accordance with the relevant guidelines and regulations. A total of 1477 panoramic radiographs images were collected from the Department of Stomatology, Nanfang Hospital, Southern Medical University, including 644 male samples and 833 female samples. The age of the sample is ranged from 2.00 to 17.99 years old. According to the chronological age, the samples of different genders are divided into 15 groups with a distance of 1 year (Table 5). All the images were taken for diagnosis and treatment. The machine that took the panoramic radiographs was the Kodak 8000-8000C X-ray machine. Samples were collected and stored in DICOM format.

Table 5

Sample Distribution
Age group (years)	Female	Male	Both
2.00-2.99	5	1	6
3.00-3.99	19	11	30
4.00-4.99	33	39	72
5.00-5.99	49	45	94
6.00-6.99	59	52	111
7.00-7.99	53	43	96
8.00-8.99	41	38	79
9.00-9.99	37	34	71
10.00-10.99	37	38	75
11.00-11.99	64	51	115
12.00-12.99	123	94	217
13.00-13.99	111	73	184
14.00-14.99	60	40	100
15.00-15.99	69	42	111
16.00-16.99	36	28	64
17.00-17.99	37	15	52
Total	833	644	1477

Panoramic radiographs that are clear enough to evaluate the tooth mineralized morphology were brought into the study. The sample was excluded when the patient had (1) orthodontic history or was in orthodontics, (2) multiple mandibular teeth missing more than three or more; (3) extra teeth appeared; (4) mandibular disease; (5) systemic diseases, and (6) history of medication affecting tooth development.

Morphological Classification

Before the morphological grading, the patient's name, gender, age, and other information were hidden, and a randomly generated ID that matched the patient information was used as the only identification index. The birth date and shooting date of the patient were automatically extracted in the system and the chronological age data of the patient were generated.

Qualified medical practitioners evaluated panoramic radiographs without gender and age information randomly according to the Demirjian staging method. All the mandibular teeth in the panoramic radiograph were evaluated, and in the final grading results, the tooth stage data of the left mandible were used. A week later, the evaluators re-evaluated 10% of the panoramic radiographs to make sure the results were consistent between the two tests. All images were evaluated in DICOM format using grayscale displays in the Forensic Science Center of Southern Medical University.

Machine Learning Methods

After trying various ratios, the data was randomly sliced into a training set and a test set in a 3-to-1 ratio. The training set was about 984 image slices and the test set was about 493 images. Machine learning was performed using several simple machine learning algorithms, with age as the dependent variable and gender and Demirjian mineralization morphological staging of seven teeth as independent variables, to complete the architecture of the age estimation model. The following machine learning supervised regression algorithms were tested in the study: Support Vector Regression (SVR), back-propagation neural network (BPNN), Random Forest, AdaBoost, K-nearest neighbor (KNN), Light Gradient Boosting Machine (Light GBM), XGboost, Extra Trees, Decision Trees, Gradient Boosting Decision Tree (GBDT), Cat Boost. The results of machine learning were evaluated using the same metrics.

Statistical Analysis

The inter-observer agreement passed the Kappa coefficient test. The dental ages estimated by the Demirjian method and the Willems method were compared to the chronological age, respectively. A positive result designated an overestimation, and a negative one indicated an underestimation of age. The deviation between dental age and chronological age and the mean absolute error (MAE) were used as indicators of the estimation effect in this study. MAE indicates the mean of individual errors in age estimation. The lower the MAE, the higher the reliability of age estimation. P < 0.05, < 0.01, and < 0.001 were determined as three levels of significance. All statistical procedures and data visualization were done using R (4.1.0).

Acknowledgments

Thanks are due to Mr. Cheng Le (South China Normal University) and Mr. Yu Chenhao (School of Public Health, Shanghai Jiao Tong University School of Medicine) for assistant with the data analysis and valuable discussion.

Funding information: This work was supported by College Students' Innovative Entrepreneurial Training Plan Program of Southern Medical University (Grant No. 202112121265) and Teaching quality and teaching reform project of Southern Medical University (Grant No. JG2021070).

Author contributions

WJ Shan, X Yue and QL Chen contributed to the study conception and design. Data collection was performed by Y Zhang, ZK Zhang, M Huo and YT Lei. Data analysis and statistical analysis was done by WJ Shan, LY Hu and YS Sun. The manuscript was written by WJ Shan, LY Hu and YS Sun.. All authors have read and approved the final version of the manuscript.

Competing interests

The authors declare no competing interests.

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Ethics declarations

Ethical Approval:

This research study was conducted retrospectively from data obtained for clinical purposes. This study was approved by the Ethics Committee of Nanfang Hospital, Southern Medical University (NFEC-2022-298).

Approval for animal and/or human experiments:

The material use was reviewed and approved by the Ethics Committee of Nanfang Hospital, Southern Medical University.

Informed consent:

Informed consent for this study was waived by the Ethics Committee of Nanfang Hospital, Southern Medical University.

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No competing interests reported.

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Boosting Algorithm for Optimizing Morphological Dental Age Estimation Method: A Southern China Population Study

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Machine Learning Methods

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