2.1 Samples
The research was authorized by the Independent Ethics Committee of the Shanghai Ninth Hospital affiliated with Shanghai Jiao Tong University, School of Medicine (2017-282-T212). All methods were performed in accordance with relevant guidelines and regulations. Informed consent was obtained from all subjects or their legal guardian(s) participating in the study.
This retrospective study selected digital panoramic radiographs taken by KODAK 8000C Panoramic and Cephalometric Digital Dental X-ray Machine collected during outpatient treatment between 2000 and 2013. A total of 748 panoramic images of adolescents aged 5 to 13, including 356 females and 392 males, were included in this study. Their age and gender distributions are shown in Table 1. Since the date of birth and the date of taking the panoramic images were known for each subject, the chronological age was calculated as the difference between these two dates, rounded to two decimal places.
Table 1
Age groups and gender distribution
|
Gender
|
|
Age Group
|
female
|
male
|
Total
|
5.00-5.99
|
20
|
18
|
38
|
6.00-6.99
|
47
|
45
|
92
|
7.00-7.99
|
35
|
44
|
79
|
8.00-8.99
|
52
|
42
|
94
|
9.00-9.99
|
48
|
63
|
111
|
10.00-10.99
|
44
|
48
|
92
|
11.00-11.99
|
45
|
43
|
88
|
12.00-12.99
|
35
|
45
|
80
|
13.00-13.99
|
30
|
44
|
74
|
Total
|
355
|
392
|
748
|
The inclusion criteria for panoramic radiographs are as follows: complete mandibular permanent teeth (except third molars); clearly visible root development; no systemic disease; no history of root canal therapy; no related diseases affecting mandibular development, such as cysts or cancer.
2.2 Dental age estimation
Digital panoramic radiographs were stored on a computer and processed by computer-aided measuring software (Adobe Photoshop CC 2017). All panoramic slices were pre-processed according to the Cameriere and Demirjian methods, and the relevant data were recorded.
According to the Demirjian method, 7 mandibular teeth were classfied into eight stages from A to H according to their development and mineralization8 (Fig. 1 left). When it comes to Demirjian method, the assessment grade of the7 permanent teeth and the gender of the sample were included into the ML algorithm as variables. In the Demirjian method, we used one-hot encoding. One-Hot encoding, also known as one-bit valid encoding, essentially encodes N states using N-bit state registers, each with its own register bits, with only one bit valid at any time.
The Cameriere method, in short, divides the distance (Ai, i = 1, ..., 7) between the inner sides of the open apex of each of the seven left mandibular teeth by the length of the tooth (Li, i = 1, ...,7) to obtain the normalized value (Xi = Ai/ Li, i = 1, ...,7). Xi (i = 1, …, 7) = 0 if tooth development is complete and the apical foramen is closed (Fig. 1 right)9. The standard values (Xi, i = 1, ..., 7) of the seven permanent teeth and the gender of the sample were included into the ML algorithm as variables, when it comes to Cameriere method.
The following ML supervised regression algorithms were tested, DT, BRR and KNN model. Multiple combinations were explored by using K-fold cross-validation. In this study, we divided the data into ten groups. The image data were divided into 10 groups, 9 groups are used as training data and one for validation1718. This process was repeated 10 times until each of these 10 sets became the validation dataset.
All three ML algorithms are supervised learning. DT is a supervised learning classifier and the most powerful tool for discrete/continuous data prediction or classification19. Ridge regression is a model tuning method that is used to analyze the data that suffers from multi-collinearity20. Ridge regression is actually a Gaussian prior with mean zero. BRR differs from ordinary Ridge Regression in that it uses a Bayesian strategy to update the prior step by step. Ordinary ridge regression allows parameters to be zero because that degenerates to a linear regression, but Bayesian estimation cannot do so because the standard deviation of a Gaussian distribution cannot be infinite. KRR combines ridge regression with the kernel trick.
The method of age inference may underestimate or overestimate age, which is known as bias. An accurate method is free of biased, meaning that the average difference between dental age and chronological age will be zero or close to zero. Accuracy refers to how large the difference between the dental age (DA) and chronological age (CA). The difference between DA and CA can also be expressed in other ways, such as mean absolute error, median absolute error, etc.
The chronological age of each subject was calculated by subtracting the date of birth from the date the panoramic was taken. In this study, the mean error (ME) of dental age and chronological age was calculated to quantify the direction of error (CA-DA), where positive values indicate that dental age is underestimated and negative values conversely. The mean absolute difference (MAD) of dental age and chronological age was calculated to quantify the magnitude of the error. In addition to the above two metrics, three other indicators were used to asses accuracy, the coefficient of determination (R2), root mean square error (RMSE) and mean square error (MSE) were also used to evaluate the accuracy of age estimation.
Data analysis and related icon production were performed through SPSS 25.0 (IBM Corp. Released 2017. IBM SPSS Statistics for Windows, Version 25.0. Armonk, NY: IBM Corp.), Pycharm 2021 and Python 3.8.2. The significance level was set at 5%.