Abstract
Objective
The purpose of this cross-sectional study is to compare the agreement of three diagnostic methods for maxillary transverse deficiency (MTD) across different skeletal malocclusion.
Methods
Three hundred and sixty patients were categorized into skeletal classes I, II, and III based on the ANB angle and assessed using University of Pennsylvania analysis (UPA), Yonsei transverse analysis (YTA), and Andrews Element III analysis (AEA). The intraclass correlation coefficient (ICC) was used to evaluate quantitative agreement, while Cohen's kappa was used to measure qualitative agreement.
Results
In class I, the AEA showed moderate quantitative agreement with the UPA and AEA (ICC = 0.712), but the UPA and YTA had poor agreement (ICC = 0.404). Qualitatively, UPA and AEA were highly consistent (kappa = 0.896), while YTA and UPA (kappa = 0.371), YTA and AEA (kappa = 0.330) were poor uniformity. For class II, AEA and UPA showed moderate quantitative (ICC = 0.708) and high qualitative agreement (kappa = 0.917), while YTA's qualitative agreement with UPA (kappa = 0.550)/AEA (kappa = 0.544) was moderate. In class III, the AEA again had moderate quantitative agreement with the UPA (ICC = 0.657) and YTA (ICC = 0.580), but the agreement between the UPA and YTA is poor (ICC = 0.408). UPA and YTA were similar in qualitative agreement (kappa > 0.8), and both showed substantial agreement with AEA (kappa = 0.657).
Conclusion
1. The incidence of MTD is highest in the skeletal class III group and the lowest in the skeletal class II group. 2. The results of YTA, AEA and UPA for diagnosing MTD are only consistent in patients with skeletal class III. In clinical practice, all three methods can be used to diagnose MTD in patients with skeletal class III malocclusion. 3. For patients with skeletal class I and class II malocclusion, it is recommended to use AEA and UPA for MTD diagnosis.
Keywords: Maxillary transverse discrepancy, Diagnostic methods, Qualitative agreement, Quantitative agreement, Cone beam computed tomography
Introduction
Maxillary transverse discrepancy (MTD) is an incongruous width between the upper and lower jaws [1]. It is commonly observed in various malocclusion deformities and affects approximately 30% of adult patients [2, 3]. MTD includes stenosis and a "V" arch, compensatory lingual inclination of posterior teeth, and excessive buccal corridors (Fig. 1) [4]. Some studies [5, 6] emphasize the significance of the MTD as a contributing factor to various dental and skeletal irregularities.
Fig. 1.
Symptoms of maxillary transverse deficiency. A. Compensatory lingual inclination of posterior teeth; B. "V" arch shape; C. Long buccal corridor
Several previous studies have proposed various methods for diagnosing MTD and determining the need for maxillary expansion. These methods include Andrews Element III analysis (AEA) [7], the Pont index [8], the Howes analysis method [9], the McNamara rule of thumb [10], the Batwa ratio [11], and other model analysis techniques. Moreover, radiographic measurements have also been developed to aid in the diagnosis of MTD. These include posteroanterior cephalogram (PAC) methods [12], Case Western Reserve University analysis [13], Yonsei transverse analysis (YTA) [14], University of Pennsylvania analysis (UPA) [15], and Miner analysis [16]. Among these methods, AEA, UPA and YTA are widely used by clinicians.
According to Andrews [7], the shape and size of the upper and lower dental arches should ideally match, with the distance between the mesial palatal cusps of maxillary first molars and the central fossa of mandibular first molars being equal, assuming that each root is positioned centrally in the basal bone. However, it is rare for individuals' teeth to meet these conditions. Therefore, the compensation needed to align the upper and lower first molars must be calculated using the Andrews ruler. The ideal inclination for maxillary first molars is −9° [17, 18], and for each 5° of buccal inclination, the width between the maxillary first molars should be reduced by 1 mm. Additionally, the distance between the unilateral mandibular Wala crest and the FA point of the mandibular first molars was 2 mm. The calculation method is shown in Fig. 2.
Fig. 2.
Elemental III analysis (AEA) of Andrews
UPA is measured based on the maxillary basal bone, which, on CBCT, intersects with the depth of the concavity in the lateral maxillary contours at the junction of the maxilla and the zygomatic buttress [15] (the intersection of the maxillary tubercle and the zygomatic buttress [19], designated point A). The measurement point (designated point B) of the mandibular basal bone is the intersection point between a straight line passing through the resistance centres of the two mandibular first molars and the outermost edge of the buccal cortical bone. Ideally, the maxilla (A-A) should be 5 mm wider than the mandible (B-B). Anatomically, the vertical position of point B is basically the same as the position of the WALA ridge [19]. The calculation method is shown in Fig. 3.
Fig. 3.
University of Pennsylvania analysis (UPA)
YTA proposed that the resistance centres of the first permanent molars remain unchanged despite variations in their position and inclination, and there is a difference between the length of the resistance centre of the maxillary first molar and the length of the resistance centre of the mandibular first molar. According to their findings, when the maxillomandibular width is in harmony, the difference should be within −0.39 ± 1.87 mm, with a threshold of less than −2.26 mm indicating the need for maxillary expansion [14]. Refer to Fig. 4 for further details on this method.
Fig. 4.
Yonsei transverse analysis (YTA)
However, the agreement in assessing maxillary transverse expansion across different diagnostic approaches has not been thoroughly investigated. This study uniquely evaluates all three methods across a diverse sample, offering insights into their reliability and real-world applicability. Unlike previous research, which often focuses on one or two methods, this study provides a comprehensive comparison of their strengths and limitations in various contexts.
Materials and methods
The diagnostic criteria for the three methods are well-established and accepted by orthodontists, with practical use in clinical settings. This is the main reason for their selection in this study. This cross-sectional study was reviewed and approved by the Institutional Review Board of Lanzhou University Dental Hospital (institutional review board no. LZUKQ-2022–021) and informed consent was obtained for all the participants under 16 years old. All CBCT images and cast data were collected from 360 patients who visited the orthodontic department of and needed 3-dimensional (3D) diagnosis for various reasons. This study obtained informed consent from the parents or legal guardians of all participants under the age of 16. The inclusion criteria were as follows: (1) aged 16 years or older with complete permanent dentitions; (2) fully erupted maxillary and mandibular first permanent molars; and (3) intact maxillomandibular casts and CBCT data. The exclusion criteria were as follows: (1) had extensive tooth defects, such as buccal caries or buccal wedge defects in any of the first permanent molars; (2) had radiographic signs of periodontal disease; (3) had missing first permanent molars; (4) had a history of systemic conditions and pathologies; and (5) had a history of orthodontic treatment. Based on the ANB angle, each sample was classified into one of three groups: skeletal class I (Group CI) for ANB angles between 0.7 and 4.7°, skeletal class II (Group CII) for ANB angles > 4.7°, and skeletal class III (Group CIII) for ANB angles < 0.7°.
CBCT scans were obtained using the I-CAT Imaging System (Imaging Sciences International Inc., Hatfield, PA, USA) with the following settings: field of view (FOV) 16.0 cm × 13.0 cm, voltage = 120 kVp, filament current = 18.54 mAs, total scan time = 8.9 s, and voxel size = 0.3 mm. The CBCT data were saved as digital imaging and communications in medicine (DICOM) files in a picture archiving and communication system (KaVo Exam Vision,) at the Hospital of Stomatology,. Materialise Mimics (version 21.0.0.406, Materialise NV Technologielaan 3001, Leuven, Belgium) was used to reposition the CBCT images in the median sagittal plane and the Frankfort horizontal (FH) plane, which was perpendicular to the frontotemporal suture [20], and to analyse the maxillomandibular width (Fig. 3). For the analysis of the casts, a six-element ™ molar-measuring device (Lawrence F. Andrews Foundation, 2025 Chatsworth Boulevard, San Diego, California, USA) and electronic Vernier callipers (GREENER, 235*40* 16 mm, 0.01 mm, Yantai, Shandong) were used for measurement (Fig. 2). The centre of resistance of the first molars was positioned at the root furcation, 1–2 mm towards the root apex, based on previous studies [21]. All the data were measured twice by two operators using the three methods. The diagnostic result was determined by taking the average of the two measurements obtained by each operator. The reliability of the diagnostic outcomes from both operators was then validated using Bland‒Altman plots. To ensure data reliability, both operators received training on the three measurement methods, conducted by Professor Ren Liling. They trained for one week on 10 pre-experiment samples using the same tools and equipment. By the start of the study, both operators had fully mastered the measurement technique.
For this study, sample size calculations were conducted using PASS software (version 21.0.3; NCSS, LLC, Kaysville, Utah) to determine the required number of subjects. To evaluate kappa agreement, a sample size of at least 302 subjects was needed, considering an alpha of 0.05, power of 0.95, k1 of 0.9, and k0 of 0.8. Similarly, for the intraclass correlation coefficient (ICC) evaluation, a sample size of at least 358 subjects was needed, considering an alpha of 0.05, power of 0.9, ρ0 of 0.8, and ρ1 of 0.9. Therefore, a total of 360 subjects were included in this study. To assess the normality of the data, the Kolmogorov‒Smirnov test (K-S test) and a histogram were used due to the large sample size. The reliability of the operator measurements was evaluated using Bland‒Altman plots. For qualitative agreement, the diagnoses were recorded as "MTD" or "NOT MTD," and Cohen's kappa statistics [22] were used. The kappa values indicated the level of agreement, with ranges of 0–0.20 considered slight, 0.21–0.40 considered fair, 0.41–0.60 considered moderate, 0.61–0.80 considered substantial, and 0.81–1 considered almost perfect. The quantitative agreement was assessed using the (ICC) [23]. The ICCs were interpreted as follows: excellent (> 0.9), good (0.75–0.9), moderate (0.5–0.75), or poor (< 0.5) agreement. All analyses were performed with SPSS software (version 19.0; IBM, Armonk, NY). Normality tests were conducted to assess the distribution characteristics of the diagnostic result.
Results
Visual inspection of the histogram (Fig. 5) corroborated these findings, with the UPA and AEA results exhibiting good normality and the YTA exhibiting average normality. The absolute kurtosis values for all methods were less than 10, and the absolute skewness values were less than 3, indicating the data were basically considered a normal distribution according to Table 1 [1]. One-way analysis of variance followed by a post hoc Tukey test were used to compare the three groups, with a p value threshold of 0.05 indicating statistical significance.
Fig. 6.
Bland‒Altman plots of the three methods. A reliability of the two operators’ measurements of UPA; B reliability of two operators’ measurements of AEA; C reliability of two operators’ measurements of YTA
Table 1.
Normality test
| Skeletal classification | Kolmogorov-Smirnova | |||
|---|---|---|---|---|
| D | Df | Sig | ||
| UPA | I | .061 | 142 | .200* |
| II | .064 | 122 | .200* | |
| III | .055 | 96 | .200* | |
| YTA | I | .214 | 142 | .000 |
| II | .218 | 122 | .000 | |
| III | .215 | 96 | .000 | |
| AEA | I | .097 | 142 | .002 |
| II | .050 | 122 | .200* | |
| III | .074 | 96 | .200* | |
[*] indicates that the p-value is less than 0.05 (i.e., a 5% significance level)
All Bland‒Altman plots were examined (Fig. 6), with 95% of the data points falling within the range of plus or minus 1.96 times the standard deviation, indicating a high level of reliability for both UPA and AEA. A total of 184 males and 176 females were included in this study, with an average age of 22.96 ± 5.25 years. The distribution of skeletal classes among the participants was as follows: 142 cases of skeletal class I, 122 cases of skeletal class II, and 96 cases of skeletal class III (Table 2). The detailed results are shown in Table 3.
Table 2.
Demographic data of subjects
| Demographics | Skeletal Class I, n = 142(M 63, F 79) |
Skeletal Class II, n = 122(M 64, F 58) |
Skeletal Class III, n = 96(M 57, F 39) |
P |
|---|---|---|---|---|
| Age, y | 23 ± 4.9 | 23.2 ± 5.7 | 22.6 ± 5.0 | 0.672 |
| Basal bone width discrepancy, mm | ||||
| Maxilla (UPA) | 64.7015 ± 4.01271 | 65.4399 ± 3.62914 | 65.1211 ± 3.86773 | 0.248 |
| Mandible (UPA) | 62.1791 ± 4.14213 | 61.7476 ± 3.78443 | 63.2338 ± 3.95190 | < 0.05* |
| Maxilla (YTA) | 46.9487 ± 3.25103 | 48.1195 ± 3.12136 | 47.6621 ± 3.53963 | < 0.05* |
| Mandible (YTA) | 48.9965 ± 3.02212 | 48.6164 ± 2.98283 | 50.1441 ± 3.07380 | < 0.01** |
| Dental arch width discrepancy, mm | ||||
| Maxilla (AEA) | 43.8144 ± 3.98519 | 44.0680 ± 3.35473 | 43.4892 ± 3.96989 | 0.533 |
| Mandible (AEA) | 44.2914 ± 3.93161 | 44.1993 ± 3.87021 | 44.1228 ± 3.38909 | 0.943 |
Values are expressed as means ± standard deviations
M Male, F female
*P < 0.05; **P < 0.01; ***P < 0.001; One-way analysis of variance test was performed for intergroup comparison
[**] indicates that the p-value is less than 0.01 (i.e., a 1% significance level)
Table 3.
The amount of maxillary expansion
| Skeletal Class I P < 0.05* |
Skeletal Class II P < 0.01** |
Skeletal Class III P > 0.05 |
|
|---|---|---|---|
| AEA | 1.8464 ± 2.23673 | 0.9018 ± 2.23244 | 2.1732 ± 2.03599 |
| YTA | 0.8444 ± 1.60605 | 0.1251 ± 1.67495 | 1.3439 ± 2.06077 |
| UPA | 2.4665 ± 3.62884 | 1.1668 ± 3.83840 | 3.0239 ± 3.16928 |
Values are expressed as means ± standard deviations
M Male, F female
*P < 0.05; **P < 0.01; ***P < 0.001; One-way analysis of variance test was performed for intergroup comparison
[***] indicates that the p-value is less than 0.001 (i.e., a 0.1% significance level)
Figure 7 illustrates the MTD quantitative diagnosis results of the 360 patients. A value above zero indicated the presence of MTD, while a value below zero indicated the absence of MTD. Table 4 provides the corresponding proportions of MTD patients for each diagnostic method in different skeletal classes. Among skeletal class I patients, 76.76% of MTD patients used UPA, 80.28% used AEA, and 49.30% used YTA. Among skeletal class II patients, 60.66%, 63.11%, and 30.33% had MTD for UPA, AEA, and YTA, respectively. In skeletal class III patients, the proportions of MTD patients were 84.38%, 86.46%, and 53.13% for UPA, AEA, and YTA, respectively.
Fig. 7.
Diagnosis results of the three methods
Table 4.
Demographic data of subjects
| Demographics | Skeletal Class I, n = 142(M 63, F 79) |
Skeletal Class II, n = 122(M 64,F 58) |
Skeletal Class III, n = 96(M 57, F 39) |
||||||
|---|---|---|---|---|---|---|---|---|---|
| UPA | AEA | YTA | UPA | AEA | YTA | UPA | AEA | YTA | |
| MTD | 109 | 114 | 70 | 74 | 77 | 37 | 81 | 83 | 51 |
| NOT MTD | 33 | 28 | 72 | 48 | 45 | 85 | 15 | 13 | 45 |
All three methods showed that the incidence of MTD in the skeletal class III group was significantly higher than that in the class II and the class I groups
M Male, F female, MTD maxillary transverse discrepancy, NOT MTD not maxillary transverse discrepancy, UPA the Pennsylvania University analysis, AEA Andrews' Element III analysis, YTA Yonsei Transverse Analysis
The quantitative agreement among the three methods was assessed using the ICC with 95% confidence intervals, as presented in Table 5. Tables 6, 7 and Table 8 are 2*2 kappa agreement tables that assess the qualitative agreement among the methods. The results of qualitative agreement are summarized in Table 9 and illustrated in Fig. 8.
Table 5.
Intraclass correlation coefficient (ICC) results
| ICC values | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| UPA | AEA | 95%CI | UPA | YTA | 95%CI | AEA | YTA | 95%CI | |
| Skeletal Class I | 0.712 | 0.618–0.795 | 0.404 | 0.176–0.574 | 0.541 | 0.284–0.701 | |||
| Skeletal Class II | 0.708 | 0.608–0.707 | 0.405 | 0.239–0.546 | 0.480 | 0.298–0.649 | |||
| Skeletal Class III | 0.657 | 0.488–0.771 | 0.408 | 0.137–0.602 | 0.580 | 0.372–0.721 | |||
Table 6.
2 × 2 Kappa agreement table of skeletal class I
| YTA | AEA | YTA | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| AEA | MTD | NOT MTD | Total | UPA | MTD | NOT MTD | Total | UPA | MTD | NOT MTD | Total |
| MTD | 68 | 46 | 114 | MTD | 109 | 0 | 109 | MTD | 67 | 42 | 109 |
| NOT MTD | 2 | 26 | 28 | NOT MTD | 5 | 28 | 33 | NOT MTD | 3 | 30 | 33 |
| Total | 70 | 72 | 142 | Total | 114 | 28 | 142 | Total | 70 | 72 | 142 |
Table 7.
2 × 2 Kappa agreement table of skeletal class II
| YTA | AEA | YTA | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| AEA | MTD | NOT MTD | Total | UPA | MTD | NOT MTD | Total | UPA | MTD | NOT MTD | Total |
| MTD | 36 | 41 | 77 | MTD | 72 | 2 | 74 | MTD | 35 | 39 | 74 |
| NOT MTD | 1 | 44 | 45 | NOT MTD | 5 | 43 | 48 | NOT MTD | 2 | 46 | 48 |
| Total | 37 | 85 | 122 | Total | 77 | 45 | 122 | Total | 37 | 85 | 122 |
Table 8.
2 × 2 Kappa agreement table of skeletal class III
| YTA | AEA | YTA | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| AEA | MTD | NOT MTD | Total | UPA | MTD | NOT MTD | Total | UPA | MTD | NOT MTD | Total |
| MTD | 49 | 34 | 83 | MTD | 80 | 1 | 81 | MTD | 50 | 31 | 81 |
| NOT MTD | 2 | 11 | 13 | NOT MTD | 3 | 12 | 15 | NOT MTD | 1 | 14 | 15 |
| Total | 51 | 45 | 96 | Total | 83 | 13 | 96 | Total | 51 | 45 | 96 |
Table 9.
Cohen’s kappa coefficients
| UPA | AEA | UPA | YTA | AEA | YTA | |
|---|---|---|---|---|---|---|
| Skeletal class I | 0.896 | 0.371 | 0.330 | |||
| Skeletal class II | 0.917 | 0.550 | 0.544 | |||
| Skeletal class III | 0.949 | 0.657 | 0.614 | |||
Fig. 8.
Diagnosis results of the three methods
Among patients with skeletal class I, the kappa value was 0.896 (> 0.8) for UPA and AEA, indicating almost perfect agreement. The kappa value was 0.371 (> 0.2) for UPA and YTA, suggesting fair agreement, and 0.330 (> 0.2) for AEA and YTA, also indicating fair agreement. The quantitative agreement between AEA and UPA was moderate (ICC > 0.5), as was the quantitative agreement between AEA and YTA. However, the quantitative agreement between the UPA and YTA was poor (ICC < 0.5).
In the skeletal class II group, the kappa value was 0.917 (> 0.8) for UPA and AEA, indicating almost perfect agreement. The kappa value was 0.550 (> 0.4) for UPA and YTA, suggesting moderate agreement, and 0.544 (> 0.4) for AEA and YTA, also indicating moderate agreement. The quantitative agreement between the AEA and PTA was moderate (ICC > 0.5), while the quantitative agreement between the remaining analyses was poor (ICC < 0.5).
Among patients with skeletal class III, the kappa value was 0.949 (> 0.8) for UPA and AEA, indicating almost perfect agreement. The kappa value was 0.657 (> 0.6) for UPA and YTA, suggesting substantial agreement, and 0.614 (> 0.6) for AEA and YTA, also indicating substantial agreement. The AEA demonstrated moderate quantitative agreement with both the UPA and YTA (ICC > 0.5), but the UPA showed poor quantitative agreement with the YTA (ICC < 0.5).
Discussion
MTD is a common clinical issue. Due to the lack of a gold standard, the transverse diagnosis has always been controversial in clinical practice [16, 24]. AEA, UPA, and YTA are widely used for diagnosing MTD in practice. However, differences often existed in diagnostic results. This study explored the consistency of using these three methods to diagnosis MTD in patients with different sagittal skeletal pattern.
The main factors influencing basal bone width include gender, age, osteo-facial type and race. With a longer development period, the maxillary basal bone width of males tends to be larger than that of females [25]. But it was unnecessary to conduct a gender-based grouping study because the agreement of MTD diagnosis results were not affected. Studies have shown that basal bone width stabilizes before puberty, therefore, to exclude the influence of growth and development as much as possible, the youngest sample in this study was set at 16 years old [26].
Existing research has revealed that patients with different sagittal skeletal patterns show differences in transverse compensation [27]. In this study, all the methods showed that the incidence of MTD in the skeletal class III group was significantly higher than that in the class II and the class I groups (Table 4). Moreover, the incidence of MTD in the class II group being the lowest (Table 4), which was consistent with the findings of the study conducted by Hwang [28].
In our study, the UPA and YTA utilize CBCT for measurement, while AEA employs plaster models for measurement. Due to the complexity of the anatomical structure of the zygomatic alveolar ridge, the UPA requires more time for landmark identification compared to the other two methods. In order to ensure more accurate positioning when diagnosing MTD with UPA, the coronal plane in CBCT was recommended to identify the left and right concave points of the maxilla, then, adjusting to the horizontal section to locate the intersection of the zygomatic and maxillary tuberosity. The agreement results indicate that all diagnostic methods are valid through statistical analysis. In clinical practice, for accurate assessment of width, the choice of methods should be made based on the specific conditions. Also, it can be observed that the proportion of MTD is highest in the AEA group among the three methods. AEA is based on Andrews six key elements of craniofacial harmony, the system's focus on the three-dimensional coordination of teeth, jawbones, and facial features ensures a stricter match of maxillofacial width. Furthermore, the Bland‒Altman plot results demonstrated high reliability across all three analyses, confirming Liu's findings [29] (Fig. 6). Due to the lack of a gold standard, selecting diagnostic methods with high agreement will allow clinical transverse diagnosis results to corroborate each other. Therefore, for skeletal class I and II patients, the use of AEA and UPA for MTD is recommended, but for skeletal class III, all of the three methods can be used.
Fig. 5.
Histograms of the three methods
The quantitative diagnosis results of YTA and the other two methods showed obvious differences in class I and II patients. This could be attributed to their different approaches. UPA and AEA utilize fixed values to define the normal width, whereas YTA employs a relative range of −0.39 ± 1.87 mm, which inherently reduces its sensitivity to MTD diagnosis. However, in skeletal class III patients, the compensatory lingual inclination of the mandibular first molars leads to an increased distance between their centers of resistance [30]. This, in turn, magnifies the diagnostic result, thereby enhancing YTA's sensitivity to MTD in skeletal class III cases. This is why YTA shows poorer diagnostic agreement with the other two methods in skeletal class I and II, but better agreement in skeletal class III.
This study has several limitations. There are inter-operator differences in the localization of anatomical structures, such as the maxillary tuberosity and the impact of operator bias on the results requires further validation. There are differences in maxillofacial width characteristics across different racial groups, and the generalizability of the findings needs to be assessed. Additionally, due to the lack of a gold standard for diagnosing MTD, comparing the agreement of different methods is an attempt and exploration in the field of transverse diagnosis research, if a gold standard were available, the primary focus would be on evaluating the validity and accuracy of these methods. Therefore, the conclusions of this study are derived through statistical analysis currently.
In the end, large sample studies on MTD are crucial for establishing future diagnostic consensus. Artificial intelligence models, such as convolutional neural networks (CNN) [31], could be used to automatically identify landmarks and measure based on those three methods, improving diagnostic efficiency and enabling large-scale collection, storage, and analysis of data.
Conclusion
The incidence of MTD is highest in patients with skeletal class III malocclusion and the lowest in that skeletal class II malocclusion.
All three methods (YTA, AEA, UPA) show consistent diagnostic agreement for skeletal Class III malocclusion and can be reliably used in such cases.
For patients with skeletal class I and class II malocclusion, UPA and AEA exhibit good agreement, in clinical practice, to corroborate the diagnostic results and enhance relative reliability, it is recommended to use AEA and UPA for MTD diagnosis.
Acknowledgements
Not applicable
Abbreviations
- AEA
Andrews Element III Analysis
- UPA
University of Pennsylvania Analysis
- YTA
Yonsei Transverse Analysis
- ICC
Intraclass Correlation Coefficient
- MTD
Maxillary Transverse Discrepancy
- PAC
Posteroanterior Cephalogram
- CNN
Convolutional Neural Networks
- CBCT
Cone Beam Computed Tomography
- DICOM
Digital Imaging and Communications in Medicine
Authors’ contributions
Li-ling Ren: conceptualization, methodology, supervision, writing—review & editing, and validation; Ning-bo Zhang: methodology, data curation, formal analysis, and writing-original draft; Tian-xiao Wang: resources and software; Yan Feng: statistical analysis; Chen Rui: resources and software; Xin-yu Fu: investigation and data curation. All authors reviewed the manuscript.
Funding
This work was supported by:
- Lanzhou University Scientific Research Projects (LZUKQKY-2022-T01, LZUKQKY-2022-P05).
- Clinical Medical Research Center for Dental and Maxillary Diseases, Shaanxi Province (2020YHZB10).
- National Center for Clinical Medical Research of Oral Diseases (LCA202009).
Data availability
The datasets used or analysed during the current study are available from the corresponding author on reasonable request.
Declarations
Ethics approval and consent to participate
Approved by the Institutional Review Board of Lanzhou University Dental Hospital (no. LZUKQ-2022–021). Informed consent was obtained for all the participants under 16 years old.
Consent for publication
Not Applicable.
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
The datasets used or analysed during the current study are available from the corresponding author on reasonable request.