A novel machine-learning-based model for prediction of open gingival embrasures between mandibular central incisors after clear aligners treatment: A retrospective cohort study

A novel machine-learning-based model for prediction of open gingival embrasures between mandibular central incisors after clear aligners treatment: A retrospective cohort study | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A novel machine-learning-based model for prediction of open gingival embrasures between mandibular central incisors after clear aligners treatment: A retrospective cohort study Guifeng Li, Feng Guo, Jun Chen, Houxuan Li, Lang Lei This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6663025/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 15 Oct, 2025 Read the published version in Progress in Orthodontics → Version 1 posted 8 You are reading this latest preprint version Abstract Objective To develop a machine-learning-based model and construct a nomogram that integrates ClinCheck features and clinical risk factors for accurately predicting open gingival embrasures (OGE) between mandibular central incisors after clear aligner treatment (CAT). Methods A total of 297 patients (163 normal and 134 with OGE) who underwent Invisalign® treatment were enrolled. A ClinCheck model was developed based on predicted OGE-area in the final step from initial ClinCheck treatment plan. Twenty-three clinical features were extracted from electronic medical records and ClinCheck tooth movement metrics. Predictors were selected through Least Absolute Shrinkage and Selection Operator (LASSO) regression to establish a clinical model. Additionally, a nomogram incorporating ClinCheck features and clinical predictors was constructed via logistic regression and validated with bootstrap resampling. The performances of these models were evaluated through receiver operating characteristic (ROC) curves, area under curves (AUC), and decision curve analyses (DCA). Results Six clinical features, including age, gingival papilla angle, interproximal reduction, crown morphology and two types of tooth movement, were selected through LASSO regression. The integrated model that consisted of OGE-area and clinical features demonstrated superior predictive capacity (AUC: 0.891; 95% CI : 0.850–0.927), outperforming both clinical model (AUC: 0.820; 95% CI : 0.774–0.867; P < 0.001) and ClinCheck model (AUC: 0.860; 95% CI : 0.817-0.900; P < 0.05). The corrected C-statistic of the combined nomogram was 0.889, and the calibration curve exhibited great performance with a mean absolute error of 0.015. In the DCA curve, the combined model showed higher net benefit than the clinical model when the threshold probability exceeded 0.13, and higher than the ClinCheck model between 0.13 and 0.62. Conclusion The integration of clinical features and ClinCheck in the machine-learning-based model demonstrated favorable predictive capabilities for OGE between lower central incisors. This comprehensive nomogram may contribute to precisely prediction and prevention of OGE in clinical practice. Machine-learning-based model Prediction Open gingival embrasures Clear aligner treatment Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction Open gingival embrasures (OGE), often defined by a significant reduction in the height of the gingival papillae, are a common complication of orthodontic therapy [ 1 ]. Clinically, OGE compromise both function and aesthetics by promoting food impaction, plaque accumulation, and oral hygiene difficulties, and may simultaneously induce smile anxiety and aesthetic insecurity [ 2 , 3 ]. Clear aligner treatment (CAT), while known for its aesthetic superiority, has demonstrated a higher incidence of post-treatment OGE compared to conventional fixed appliances [ 4 ]. The literature revealed a pronounced disparity in non-extraction CAT cases, with mandibular anterior OGE occurring at 2.3 times the rate of maxillary OGE [ 5 ]. Notably, extraction cases exhibited even greater prevalence, with mandibular incidence rates approaching 52.3% [ 6 ]. Given the high prevalence of OGE, their management remains one of the most challenging and unpredictable procedures and accurate preoperative prediction is of great clinical importance. The clinical utility of OGE prediction during treatment planning is twofold. First, it aids patients in better understanding the expected treatment outcomes, thereby managing expectations and reducing post-treatment dissatisfaction [ 6 ]. Second, targeted interventions such as controlled interproximal enamel reduction and axis-adjusted tooth repositioning can be guided to minimize complications related to gingival discrepancies [ 7 , 8 ]. Furthermore, early prediction facilitates preoperatively interdisciplinary collaboration, where combined periodontal and prosthetic approaches (such as microsurgical papilla reconstruction and restorative procedures) can effectively address both aesthetic and functional concerns [ 9 ]. Although clinical risk factors for OGE (e.g., age, crowding, tooth movement) have been extensively investigated [ 5 , 10 ], predictive approaches for this condition have received little attention in the literature. Researchers of a recent in vivo study have explored the prediction of OGE through alveolar bone height assessment; however, pre-treatment crowding complicates bone height evaluation, and treatment-associated bone recession introduced additional complexity [ 11 ]. Although a previous study confirmed ClinCheck's high OGE prediction accuracy (94% in maxilla, 86% in mandible) in adult extraction CAT cases, its generalizability to non-extraction and adolescent patients remains unclear, and clinical risk factors failed to be incorporated [ 6 ]. Considering the high prevalence of OGE and the absence of simple yet sensitive predictive features, a reliable tool for precise prediction is critically needed in dental practice. As existing prediction methods rely on subjective clinician expertise, recent research has shifted toward data-driven prediction models [ 12 ]. Nowadays, nomograms serve as visual prediction tools that integrate multiple clinical parameters, including general information, treatment procedures and radiomics features, into a scoring system, enabling clinicians to calculate the risk of outcomes for patients [ 13 ]. Some researchers have developed machine-learning-based models for detection of degenerative temporomandibular joint diseases [ 14 ], prediction of fixed appliances treatment duration [ 15 ], potential design of orthodontic extraction patterns [ 16 ], etc. The user-friendly interface of nomograms offers broad clinical utility in assessing disease onset and progression; however, their clinical values in predicting OGE have never been reported. Therefore, the purposes of this study were to: (1) develop a machine-learning-based model that integrated ClinCheck features and clinical risk factors to predict OGE between mandibular central incisors after CAT; (2) validate the combined model and determine its comparative performance against simple clinical and ClinCheck model. Materials and methods Participants This retrospective cohort study received approval from the Ethics Committee (Approval Number: XXXX). All data were screened from the Orthodontic Department of XXX Hospital, during the period from July 2015 to July 2022. Informed consent was obtained from all participants. The inclusion criteria were (1) full permanent dentition with no missing teeth (excluding third molars); (2) absence of OGE or mandibular midline diastema at initial examination; (3) complete clinical records available; (4) completion of dual arch Invisalign® treatment (Align Technology, California, USA) with 22-hour daily wear and aligner changes every 7–10 days; (5) clear and high quality of intraoral photographs at pre- and post-treatment stages. The exclusion criteria were (1) concurrent use of fixed orthodontic appliances; (2) periodontitis cases with radiographic bone loss > 25% of root length and/or clinical attachment loss ≥ 2 mm; (3) planned surgical interventions (periodontal, orthognathic, or periodontally accelerated osteogenic orthodontics); (4) tooth defects of lower central incisors; (5) history of orthodontic therapy. The workflow of this study was presented in Fig. 1 . Assessment of post-treatment OGE and predicted OGE-area Two orthodontists and one periodontist independently assessed OGE between mandibular central incisors using post-aligner-removal intraoral photos. Non-consensus assessment was excluded after discussion. The predicted area of OGE was measured from the frontal view in the final step of initial ClinCheck treatment plan. In the post-treatment digital models, the height of the OGE was defined as the distance between the interproximal papilla's uppermost margin and the lowest point of central incisors' contact area, while the base was the width of the upper margin of the interproximal papilla [ 4 ]. Therefore, the predicted OGE-area was derived as (base × height)/2 (Fig. 2 A). Measurement of clinical features The clinical features for OGE prediction included: age, gender, extraction patterns, attachment placement, interproximal reduction (IPR) design, crown morphology, gingival papilla angle (GPA) and three-dimensional predicted tooth movement. General clinical data, including age, gender and extraction patterns (non-extraction or two premolars extraction pattern), were extracted from institutional medical records, while attachment placement and IPR design were obtained from ClinCheck plans. Through linear measurements of the triangle formed by the most apical points of adjacent gingival margins and the coronal peak of the gingival papilla, the GPA was calculated based on the cosine and arccosine formula (Fig. 2 B). The crown morphology was assessed using the ratio of crown width (CW) to crown length (CL) on post-treatment digital models (Fig. 2 C). Predicted tooth movement was extracted from simulated ClinCheck metrics (Fig. 2 D). Extrusion, buccal and mesial movement were recorded as positive values. A total of 16 parameters were quantified, encompassing both absolute and differential displacement magnitudes between central incisors across eight movement categories: (1) crown extrusion/ intrusion, (2) buccolingual crown translation, (3) mesial-distal crown translation, (4) rotation, (5) angulation, (6) inclination, (7) buccolingual root translation, (8) mesial-distal root translation. The absolute magnitude was recorded as zero if incisors move in opposite direction. Interrater and Intrarater Reliability To evaluate the reproducibility of all parameters, two orthodontists traced 50 randomly selected participants, repeating the measurement after a 15-day interval. With interclass and intraclass correlation coefficients of 0.85 and 0.92, the measurements demonstrated excellent reliability. Development of ClinCheck, clinical and combined model Incorporating the predicted OGE-area as input, the ClinCheck model was constructed with univariate logistic regression. Subsequently, the Least Absolute Shrinkage and Selection Operator (LASSO) logistic regression was employed to identify the most relevant predictors from the recorded 23 clinical features. A penalty coefficient (λ) was applied in the a ten-fold cross-validated LASSO analysis to obtain features with non-zero coefficients, which were selected to develop the clinical model using multiple logistic regression. Then, the selected clinical features and OGE-area were integrated to develop a combined model for OGE prediction. This combined model was presented as a nomogram to serve as personalized and user-friendly tool for predicting the occurrence of OGE. Performance and assessments of nomograms Performance assessments were conducted for the ClinCheck, clinical, and combined models separately. Receiver operating characteristic (ROC) curves were used as evaluation metrics, with area under the curve (AUC) values exceeding 0.75 indicating favorable predictability. The differences of these models’ performance were compared using the DeLong's test. Model calibration was evaluated through calibration curves. The model’s performance was internally validated using the corrected C-statistic, derived from the bootstrapping method with 1000 replications. Additionally, potential clinical utility was further quantified via decision curves to compare the net benefit among the three models. Statistical Analysis Statistical analysis was performed using SPSS software (version 23; IBM, Armonk, NY) and R (version 4.4.1; R Core Team). Multiple relevant packages, including rms, readxl, rmda, ResourceSelection, ggplot2, glmnet, caret, boot, DynNom, rsconnect and pROC were utilized in the R analysis. Continuous variables were compared using t-tests or Wilcoxon tests, whereas categorical variables were assessed via chi-square tests. All tests were two-tailed, with P < 0.05 considered statistically significant. Results Participant characteristics A total of 297 participants (63 males, 234 females, mean age of 23.12 ± 6.68 years) were eventually included to develop and validate the predictive model. The incidence of OGE was 45.12% in this study. The clinical characteristics of the OGE group (n = 134) and the Normal group (n = 163) were analyzed and compared, and the results showed that significant differences were observed in age, extraction pattern, IPR, GPA, crown morphology, D-rotation, D-angulation and inclination between patients with and without OGE (Table 1 ). Table 1 Clinical characteristics of participants and comparison of characteristics between patients with and without OGE. Characteristics Overall (n = 297) OGE (n = 134) Normal (n = 163) P Gender (male/female) 63/234 23/111 40/123 0.122 Age 23.12 ± 6.68 25.04 ± 6.14 21.54 ± 6.70 <0.001** Extraction pattern (Y/N) 117/180 64/70 53/110 0.007** Attachment design 0 (0, 0) 0 (0, 0) 0 (0, 0) 0.334 IPR (Y/N) 51/246 13/121 38/125 0.002** GPA 77.04 ± 10.50 79.20 ± 10.18 75.27 ± 10.46 0.001** Crown morphology 0.60 ± 0.08 0.57 ± 0.07 0.62 ± 0.08 <0.001** Predicted tooth movement Extrusion/intrusion -2.00 (-3.30, -1.05) -2.10 (-3.33, -1.08) -2.00 (-3.10, -1.00) 0.665 D-extrusion/intrusion 0.20 (0.10, 0.45) 0.30 (0.10, 0.50) 0.20 (0.10, 0.40) 0.110 B/L crown translation 0.00 (-1.50, 0.80) 0.00 (-1.83, 0.80) 0.00 (-1.20, 1.00) 0.178 D-B/L crown translation 0.50 (0.30, 1.10) 0.50 (0.30, 1.30) 0.60 (0.20, 1.00) 0.282 M/D-crown translation 0.00 (-0.10, 0.00) 0.00 (-0.13, 0.00) 0.00 (-0.10, 0.00) 0.082 D-M/D crown translation 0.90 (0.40, 2.00) 0.90 (0.40, 2.40) 0.80 (0.40, 1.60) 0.262 Rotation -1.60 (-9.40, 0.00) 0.00 (-8.63, 0.00) -2.80 (-9.80, 0.00) 0.237 D-rotation 9.90 (4.55, 17.00) 13.00 (7.08, 21.90) 7.40 (4.10, 12.80) <0.001** Angulation 0.00 (0.00, 0.00) 0.00 (0.00, 0.00) 0.00 (0.00, 0.00) 0.107 D-angulation 4.10 (1.90, 7.75) 4.65 (2.00, 9.70) 3.50 (1.80, 6.90) 0.011* Inclination 1.30 (0.00, 5.80) 0.30 (0.00, 4.68) 2.20 (0.00, 7.80) 0.014* D-inclination 3.60 (1.80, 6.85) 4.00 (2.00, 7.05) 3.30 (1.60, 6.80) 0.209 B/L root translation -0.70 (-2.80, 0.00) -0.60 (-2.33, 0.00) -0.80 (-3.00, 0.00) 0.456 D-B/L root translation 0.70 (0.30, 1.20) 0.70 (0.30, 1.20) 0.70 (0.30, 1.10) 0.915 M/D root translation 0.00 (-0.40, 0.00) 0.00 (-0.33, 0.00) 0.00 (-0.40, 0.00) 0.382 D-M/D root translation 1.00 (0.50, 1.90) 1.00 (0.50, 1.90) 1.10 (0.50, 1.90) 0.782 Data with a normal distribution were presented as mean ± SD, while data with a non-normal distribution were presented as median (25%, 75%). IPR, interproximal reduction; GPA, gingival papilla angle; D-Extrusion/intrusion, differential movement of extrusion/intrusion; B/L crown translation, buccolingual crown translation; D-B/L crown translation, differential movement of buccolingual crown translation; M/D-crown translation, mesial-distal crown translation; D-M/D crown translation, differential movement of mesial-distal crown translation; D-rotation, differential movement of rotation; D-angulation, differential movement of angulation; D-inclination, differential movement of inclination; B/L root translation, buccolingual root translation; D-B/L root translation, differential movement of buccolingual root translation; M/D root translation, mesial-distal root translation; D-M/D root translation, differential movement of mesial-distal root translation. P value < 0.05 was considered significant given in bold. * P < 0.05, ** P < 0.01. Development and nomogram of OGE prediction models A ClinCheck model was constructed using the virtual OGE-area. Twenty-three clinical features were standardized (z-score) and included in the LASSO regression analysis for predictor selection. Through ten-fold cross-validation, the optimal regularization parameter (λ) was determined to be 0.051 with one standard error (Fig. 3 A). Following this criterion, six clinical features with nonzero coefficients were selected (Fig. 3 B), including crown morphology, IPR, inclination, age, D-rotation, and GPA (Fig. 3 C). Subsequently, the six features were included as predictors to construct a clinical model by multivariable logistic regression (Table 2 ). In this clinical model, all features except inclination were significantly associated with the occurrence of OGE ( P < 0.05). Table 2 Description of predictors in the clinical and combined models. Predictors Clinical model Combined model OR (95%CI) P OR (95%CI) P IPR 0.20 (0.09, 0.45) < 0.001** 0.58 (0.22, 1.47) 0.261 Crown morphology 0.00 (0.00, 0.00) < 0.001** 0.00 (0.00, 0.01) < 0.001** Inclination 0.96 (0.92, 1.01) 0.121 0.98 (0.92, 1.03) 0.428 GPA 1.07 (1.04, 1.10) < 0.001** 1.03 (0.99, 1.06) 0.126 D-rotation 1.06 (1.03, 1.09) < 0.001** 1.04 (1.01, 1.08) 0.024* Age 1.08 (1.03, 1.13) 0.001** 1.06 (1.00, 1.11) 0.036* OGE-area NA NA 4.78 (3.00, 8.14) < 0.001** NA, not available. IPR, interproximal reduction; GPA, gingival papilla angle; D-rotation, differential movement of rotation; D-B/L root translation, differential movement of buccolingual root translation; OR, odds ratio; CI, confidence interval. P value < 0.05 was considered significant given in bold. * P < 0.05, ** P < 0.01. A combined model incorporating OGE-area and clinical predictors was developed with multivariable logistic regression analysis. Four indicators, including OGE-area, crown morphology, age and differential movement of rotation, were all significantly correlated with OGE (Table 2 ). The combined model was visualized in a nomogram for individual risk estimation (Fig. 4 ). Each factor was assigned a score based on a point scale axis. The total score was calculated by summing the individual scores. By projecting this total score onto the bottom risk scale axis, the probability of OGE could be estimated. To facilitate implementation of the model in clinical settings, a user-friendly R-Shiny web application was developed and shared at: https://fenguo4863364.shinyapps.io/DynNomapp/ . Validation and performances of the models Through 1000 bootstrap resamples, the corrected C-statistic of the combined nomogram was 0.889, demonstrating favorable internal validation performance. The calibration curve showed strong concordance between predicted and observed values, with a mean absolute error of 0.015 (Fig. 5 ). Additionally, the Hosmer-Lemeshow test confirmed the acceptable fit of this combined model ( P = 0.737). In this study, the combined nomogram demonstrated superior predictive performance with an AUC of 0.891 (95% CI: 0.850–0.927), significantly outperforming both the ClinCheck model (AUC = 0.860; 95% CI: 0.817–0.900; P < 0.05) and the clinical model (AUC = 0.820; 95% CI: 0.774–0.867; P < 0.01) (Fig. 6 A). However, according to DeLong's test, no significant difference was observed between the ClinCheck and clinical models. The DCA curves exhibited clinical utility in all three prediction models. In the DCA curve, the combined model showed higher net benefit than the clinical model when the threshold probability exceeded 0.13, and higher than the ClinCheck model between 0.13 and 0.62 (Fig. 6 B). Discussion A novel nomogram, integrating ClinCheck OGE-area with clinical predictors, was firstly developed and validated in this study to quantify the risk of OGE between mandibular incisors. The combined nomogram demonstrated superior predictive performance (AUC: 0.891), significantly outperforming both the independent ClinCheck model and conventional clinical models. Decision curve analysis further confirmed the enhanced clinical utility of the integrated model. These findings suggest that combined nomogram offers robust potential for predicting post-treatment OGE in clear aligner therapy. In this study, a strong correlation was shown between ClinCheck OGE-area and actual clinical outcomes. This relationship can be attributed to manufacturing protocols and biomechanical mechanisms underlying clear aligners. Through digital intraoral scanning, ClinCheck obtains precise 3D modeling that eliminates soft tissue displacement caused by traditional impression material compression, enabling more accurate simulation of soft tissue remodeling [ 17 ]. Furthermore, the encroachment of aligners into interdental embrasures mechanically restricted gingival papilla adaptation, thereby predicted and actual OGE sharing the similar incidence and morphology [ 4 ]. Clinically, improvement of clear aligners with simulated fulfilling gingival papilla covering might be helpful in decreasing the incidence of OGE. The GPA was firstly employed to quantify the joint effects of papilla height and adjacent crown morphology on OGE formation. Authors of a previous study have confirmed the association between gingival angle and papilla fill [ 18 ]. However, the assessment of gingival angle in their study, which was defined as the angle at the gingival margin formed by two adjacent gingival papillae, exhibited limitations due to discrepancies in both the gingival margin and crown contours of adjacent teeth. Previous studies have independently examined crown contours or papilla heights, which respectively determined the scalloping pattern of gingival margins and the degree of interproximal tissue fill [ 5 , 6 , 18 ]. While adjacent crowns and gingival papillae formed an inseparable functional community that shaped interdental three-dimensional unit and related to gingival thickness [ 19 ]. An evidence-based review indicated that “thick-flat” gingiva correlates with better periodontal health and lower risks of papilla height loss versus “thin-scalloped” biotypes [ 20 ]. In contrast, thick gingival biotypes are fibrotic and resilient, demonstrating a tendency for pocket formation over OGE [ 21 ]. In our clinical model, the GPA showed significant correlation with OGE (OR, 1.07; 95% CI, 1.04–1.10), indicating that this parameter might be a key indicator for future studies. Among the patient factors, crown morphology demonstrated a significant association with the occurrence of OGE in both the clinical model and the comprehensive model. This result was consistent with previous studies on the risk factors of OGE [ 6 , 22 ]. In the comprehensive predictive model of this study, a greater crown ratio was associated with a lower probability of OGE. This phenomenon may be related to the apical position of proximal contacts. Long and narrow crowns were often accompanied by proximal contact points closer to the incisal edge, and as the distance between the contact point and the alveolar crest increased, the height of the gingival papilla correspondingly decreased [ 23 ]. Furthermore, studies have shown that regardless of the amount of plaque accumulation, long and narrow teeth are at a higher risk of developing periodontal inflammation compared to short and wide teeth, suggesting that periodontal health might be more easily maintained around square-shaped crowns [ 24 ]. In clinical practice, appropriate modification of tooth morphology would be helpful to prevent or reduce OGE. Additionally, the results of the clinical model indicated that for every one-year increase in age, the risk of OGE increased by 8%. For older patients, providing a thorough preoperative risk consent might of great importance. Compared with previous studies utilizing cephalometry or study models [ 25 , 26 ], this study assessed the impact of treatment factors on OGE through the ClinCheck tooth movement metrics. With the aid of ClinCheck metrics, dental crowding was indirectly measured by calculating the movement differences of adjacent teeth in the same direction. Previous work by An SS et al. evaluated crowding between central incisors through incisal edge angulation and the sagittal and transverse distances of mesial contact points [ 25 ]. However, potential errors from reference line placement in mandibular crowded cases exited. The metrics enhanced accuracy and repeatability while simplifying the evaluation process. In this study, the differential movement of rotation, which indirectly represented the crowding, was determined to be associated with OGE. This outcome likely resulted from gingival fiber stretching and decreased gingival thickness during the alignment of crowded teeth [ 27 ]. Preoperative assessment through CBCT or evaluation of gingival biotype could improve the predictive accuracy of OGE after alignment of crowded dentition. To minimize the occurrence of OGE, a "staged alignment" strategy would be recommended to prioritize the correction of tooth rotations and reduce back-and-forth movements [ 28 ]. Limitation Several limitations should be acknowledged in this study. Due to the retrospective nature, this study might introduce selection bias and failed to incorporate important clinical indicators such as periodontal biotype and gingival index. Although ICC analysis confirmed measurement reliability, future researches need to explore automated procedure with artificial intelligence to enhance result robustness. As discrepancies may exist between ClinCheck-predicted tooth movement and actual outcomes due to overcorrection design and clinical efficacy in CAT, digital model or radiomics-based superimposition could be employed to further investigate the correlation between tooth movement and OGE. Additionally, participants in our study originated from specific Invisalign cases, which may limit the nomogram's predictive capability in other clear aligner systems. Due to the limited sample size, external validation of the nomogram was not conducted in this study. Therefore, the generalizability of our combined nomogram necessitates further external validation in larger and more diverse populations. Conclusion A comprehensive nomogram was developed and validated for predicting OGE between lower central incisors after CAT. The model integrated predicted OGE-area with 6 clinical features (including IPR, crown morphology, inclination, GPA, D-rotation and age), demonstrating superior predictive performance. Accurate prediction of OGE can be achieved by this combined nomogram, thereby improving clinical decision-making. Declarations Ethics approval and consent to participate This study has been approved by the Ethics Committee of XX Hospital (Approval Number: XXX), and followed the contents in the Declaration of Helsinki concerning human subjects. Consent for publication The undersigned author(s) of the manuscript titled “A novel machine-learning-based model for prediction of open gingival embrasures between mandibular central incisors after clear aligners treatment: A retrospective cohort study” hereby grant “Progress in Orthodontics” the right to publish the aforementioned work, including any supplementary material that may be associated with it. We confirm that this work is original, has not been published elsewhere, and does not infringe upon any copyright or any other rights of any third party. We also affirm that all contributing authors have agreed to the submission of this work for publication in “Progress in Orthodontics.” In the event that this work includes any data or images from individuals, we confirm that we have obtained the necessary consents from the individuals involved. Funding This work was funded by XXX (XXXX). Author Contribution L.L. was the supervisor and designed the study. G.L. and F.G. drafted the manuscript and writing the manuscript. G.L. and F.G. performed the statistical analysis and data analysis. J.C. and H.L assisted with data curation. All authors read and approved the final manuscript. Acknowledgement The authors would like to express their gratitude to all individuals who have contributed to this study. We appreciate the support from the National Natural Science Foundation. References Singh VP, Uppoor AS, Nayak DG, Shah D. Black triangle dilemma and its management in esthetic dentistry. Dent Res J (Isfahan). 2013;10:296–301. Tanaka OM, Furquim BD, Pascotto RC, Ribeiro GL, Bósio JA, Maruo H. The dilemma of the open gingival embrasure between maxillary central incisors. J Contemp Dent Pract. 2008;9:92–8. Sriphadungporn C, Chamnannidiadha N. Perception of smile esthetics by laypeople of different ages. Prog Orthod. 2017;18:8. Yang T, Jiang L, Sun W, et al. The incidence and severity of open gingival embrasures in adults treated with clear aligners and fixed appliances: a retrospective cohort study. Head Face Med. 2023;19:30. Cui W, Liu Y, Zhao Y, Lei L, Li H. Risk factors for open gingival embrasures after clear aligners treatment: a retrospective study. BMC Oral Health. 2025;25:547. Guo F, Wang C, Han L, Li H, Lei L, Mei L. Invisalign ClinCheck can predict open gingival embrasures in adult extraction cases: a pilot study. Angle Orthod. 2025. Zhang Y, Wang X, Wang J, et al. IPR treatment and attachments design in clear aligner therapy and risk of open gingival embrasures in adults. Prog Orthod. 2023;24:1. Sharma AA, Park JH. Esthetic considerations in interdental papilla: remediation and regeneration. J Esthet Restor Dent. 2010;22:18–28. Prato GP, Rotundo R, Cortellini P, Tinti C, Azzi R. Interdental papilla management: a review and classification of the therapeutic approaches. Int J Periodontics Restor Dent. 2004;24:246–55. Tian E, Luo K, Zhou Y, et al. Factors influencing open gingival embrasures in orthodontic treatment: a retrospective clinical study. Prog Orthod. 2025;26:6. Mahasneh SA, Goodwin M, Pretty I, Cunliffe J. The use of radiographs to assess the impact of the distance between the contact area and the crest of the bone to predict the presence or absence of interdental papilla: an in vivo study. Br Dent J. 2023. Wang X, Lu J, Song Z, Zhou Y, Liu T, Zhang D. From past to future: Bibliometric analysis of global research productivity on nomogram (2000–2021). Front Public Health. 2022;10:997713. Grobman WA, Stamilio DM. Methods of clinical prediction. Am J Obstet Gynecol. 2006;194:888–94. Fang X, Xiong X, Lin J, Wu Y, Xiang J, Wang J. Machine-learning-based detection of degenerative temporomandibular joint diseases using lateral cephalograms. Am J Orthod Dentofac Orthop. 2023;163:260–e271265. Shi X, Wu B, Cao D, et al. Effect of socioeconomic and malocclusion-related factors on duration of orthodontic treatment by fixed appliance: A retrospective study. Orthod Craniofac Res. 2023;26:650–9. Leavitt L, Volovic J, Steinhauer L, et al. Can we predict orthodontic extraction patterns by using machine learning? Orthod Craniofac Res. 2023;26:552–9. Kihara H, Hatakeyama W, Komine F, et al. Accuracy and practicality of intraoral scanner in dentistry: A literature review. J Prosthodont Res. 2020;64:109–13. Joshi K, Baiju CS, Khashu H, Bansal S, Maheswari IB. Clinical assessment of interdental papilla competency parameters in the esthetic zone. J Esthet Restor Dent. 2017;29:270–5. Chow YC, Eber RM, Tsao YP, Shotwell JL, Wang HL. Factors associated with the appearance of gingival papillae. J Clin Periodontol. 2010;37:719–27. Kim DM, Bassir SH, Nguyen TT. Effect of gingival phenotype on the maintenance of periodontal health: An American Academy of Periodontology best evidence review. J Periodontol. 2020;91:311–38. Ahmad I. Anterior dental aesthetics: gingival perspective. Br Dent J. 2005;199:195–202. Kolte AP, Kolte RA, Bawankar P. Proximal contact areas of maxillary anterior teeth and their influence on interdental papilla. Saudi Dent J. 2018;30:324–9. Tarnow DP, Magner AW, Fletcher P. The effect of the distance from the contact point to the crest of bone on the presence or absence of the interproximal dental papilla. J Periodontol. 1992;63:995–6. Trombelli L, Farina R, Manfrini R, Tatakis DN. Modulation of clinical expression of plaque-induced gingivitis: effect of incisor crown form. J Dent Res. 2004;83:728–31. An SS, Choi YJ, Kim JY, Chung CJ, Kim KH. Risk factors associated with open gingival embrasures after orthodontic treatment. Angle Orthod. 2018;88:267–74. Kurth JR, Kokich VG. Open gingival embrasures after orthodontic treatment in adults: prevalence and etiology. Am J Orthod Dentofac Orthop. 2001;120:116–23. Burke S, Burch JG, Tetz JA. Incidence and size of pretreatment overlap and posttreatment gingival embrasure space between maxillary central incisors. Am J Orthod Dentofac Orthop. 1994;105:506–11. Liu Y, Li CX, Nie J, Mi CB, Li YM. Interactions between Orthodontic Treatment and Gingival Tissue. Chin J Dent Res. 2023;26:11–8. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 15 Oct, 2025 Read the published version in Progress in Orthodontics → Version 1 posted Editorial decision: Revision requested 27 Aug, 2025 Reviews received at journal 27 Aug, 2025 Reviewers agreed at journal 14 Aug, 2025 Reviews received at journal 01 Jul, 2025 Reviewers agreed at journal 27 Jun, 2025 Reviewers invited by journal 13 Jun, 2025 Submission checks completed at journal 04 Jun, 2025 First submitted to journal 27 May, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6663025","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":471065456,"identity":"618e2869-4131-40eb-902b-b9b9a8a89d60","order_by":0,"name":"Guifeng Li","email":"","orcid":"","institution":"Department of Orthodontics, Nanjing Stomatological Hospital, Affiliated Hospital of Medical School, Institute of Stomatology, Nanjing University","correspondingAuthor":false,"prefix":"","firstName":"Guifeng","middleName":"","lastName":"Li","suffix":""},{"id":471065458,"identity":"27502e2e-f81a-4ec8-bd36-bbe5e9f0edaa","order_by":1,"name":"Feng Guo","email":"","orcid":"","institution":"Department of Orthodontics, Nanjing Stomatological Hospital, Affiliated Hospital of Medical School, Institute of Stomatology, Nanjing University","correspondingAuthor":false,"prefix":"","firstName":"Feng","middleName":"","lastName":"Guo","suffix":""},{"id":471065459,"identity":"de3c6067-7206-4665-8969-201861268132","order_by":2,"name":"Jun Chen","email":"","orcid":"","institution":"Department of Orthodontics, Nanjing Stomatological Hospital, Affiliated Hospital of Medical School, Institute of Stomatology, Nanjing University","correspondingAuthor":false,"prefix":"","firstName":"Jun","middleName":"","lastName":"Chen","suffix":""},{"id":471065461,"identity":"45623aaf-02c5-4c99-9ae5-d842515f5d93","order_by":3,"name":"Houxuan Li","email":"","orcid":"","institution":"Department of Periodontics, Nanjing Stomatological Hospital, Affiliated Hospital of Medical School, Institute of Stomatology, Nanjing University","correspondingAuthor":false,"prefix":"","firstName":"Houxuan","middleName":"","lastName":"Li","suffix":""},{"id":471065462,"identity":"9ef6af01-d59b-4bf5-857e-9b2ae1e9015b","order_by":4,"name":"Lang Lei","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABDElEQVRIiWNgGAWjYBACPgbGxgNAmrEBxHtQwcAMoiXwaWEDKoZqASpOOEOUFgYGhJbENogofi3szQ0Hfu6ole2X7j/4IXHeHXaDA8wHb/Mw2OXh1MJzsOFg75njxjPnHGaWSNz2jNngAFuyNQ9DcjFOLRKJDQd4244lbriRzADUchiohcdMmofhQGIDLi3yDxsO/gVq2X8jmflH4hyQFv5v+LVIMDYc5m2rSdwgkQyyEWwLG34tPEBlsm0HjGfcSDazSDh2mFnyMJux5RyDZJxa+NmPP3z4tq1Otn9G4uMbH2oOJ/Mdb354402FHU4tUHAYzkqGRKYBfvVAUAdn2RFUOwpGwSgYBSMOAABb0l0F2khiqQAAAABJRU5ErkJggg==","orcid":"","institution":"Department of Orthodontics, Nanjing Stomatological Hospital, Affiliated Hospital of Medical School, Institute of Stomatology, Nanjing University","correspondingAuthor":true,"prefix":"","firstName":"Lang","middleName":"","lastName":"Lei","suffix":""}],"badges":[],"createdAt":"2025-05-14 10:08:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6663025/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6663025/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s40510-025-00584-0","type":"published","date":"2025-10-15T15:57:59+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":84857791,"identity":"a511fc15-1013-45d1-8632-eae62ce6013b","added_by":"auto","created_at":"2025-06-18 06:26:59","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":6000999,"visible":true,"origin":"","legend":"\u003cp\u003eWorkflow of the study.\u003c/p\u003e","description":"","filename":"Fig.1Workflowofthestudy..jpg","url":"https://assets-eu.researchsquare.com/files/rs-6663025/v1/788b83524d345db6b1c8f1c9.jpg"},{"id":84857790,"identity":"83c76e09-a2da-4d9d-b4fc-c1537cc28257","added_by":"auto","created_at":"2025-06-18 06:26:59","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":3206164,"visible":true,"origin":"","legend":"\u003cp\u003eMeasurement of clinical features. \u003cstrong\u003eA\u003c/strong\u003e The OGE-area was derived as (base × height)/2. \u003cstrong\u003eB\u003c/strong\u003e Lines a, b, and c composed a triangle formed by the most apical points of adjacent gingival margins and the coronal peak of the gingival papilla. The gingival papilla angle (α) was calculated based on the cosine and arccosine formulas. \u003cstrong\u003eC\u003c/strong\u003e Measurement of crown morphology. Crown length (CL) and was defined as the distance between the gingival curvature and the midpoint of the incisal edge. Crown width (CW) refers to the measurement of the width at the interface between the cervical third and the middle third of the crown. \u003cstrong\u003eD\u003c/strong\u003e An example of ClinCheck tooth movement metrics.\u003c/p\u003e","description":"","filename":"Fig.2Measurementofclinicalfeatures..jpg","url":"https://assets-eu.researchsquare.com/files/rs-6663025/v1/1df292423bc3d194d6581018.jpg"},{"id":84857789,"identity":"96ff0a95-2ea6-4b5e-9aed-345442190d55","added_by":"auto","created_at":"2025-06-18 06:26:59","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1164024,"visible":true,"origin":"","legend":"\u003cp\u003eClinical feature selection with LASSO logistic regression. \u003cstrong\u003eA\u003c/strong\u003e The tuning parameter lambda (λ) was selected through 10-fold cross-validation using the 1se criteria. The optimal λ value was 0.051, corresponding to a log(λ) value of -2.976. \u003cstrong\u003eB\u003c/strong\u003e Coefficient profiles of the 23 clinical features. A total of 6 features with nonzero coefficients were selected. \u003cstrong\u003eC\u003c/strong\u003e Coefficients of the 6 selected clinical features.\u003c/p\u003e","description":"","filename":"Fig.3ClinicalfeatureselectionwithLASSOlogisticregression..jpg","url":"https://assets-eu.researchsquare.com/files/rs-6663025/v1/1d18566fd60c47c9ace41550.jpg"},{"id":84859881,"identity":"9cf02514-ea68-47f0-a928-521e638c57c4","added_by":"auto","created_at":"2025-06-18 06:42:59","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":579241,"visible":true,"origin":"","legend":"\u003cp\u003eNomogram of the combined model for predicting OGE between mandibular central incisors.\u003c/p\u003e","description":"","filename":"Fig.4Nomogramofthecombinedmodel.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6663025/v1/8974bb5878e560d4333b251d.jpg"},{"id":84857795,"identity":"308e0a2b-e1c6-48f9-acd2-2f0836211f3a","added_by":"auto","created_at":"2025-06-18 06:26:59","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":414427,"visible":true,"origin":"","legend":"\u003cp\u003eCalibration curves of the combined nomogram constructed by bootstrap (1000 bootstrap resamples).\u003c/p\u003e","description":"","filename":"Fig.5Calibrationcurvesofthecombinednomogram..jpg","url":"https://assets-eu.researchsquare.com/files/rs-6663025/v1/670a99e7295b4794b99dee23.jpg"},{"id":84857799,"identity":"f7af2831-f498-4da1-834f-9ea7178e644c","added_by":"auto","created_at":"2025-06-18 06:26:59","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":674626,"visible":true,"origin":"","legend":"\u003cp\u003ePerformances of three predictive models. \u003cstrong\u003eA\u003c/strong\u003e ROC curves for the ClinCheck model, Clinical model, and combined model.\u003cstrong\u003e B \u003c/strong\u003eDCA curves of three models. The \"all\" line and \"none\" line indicate the assumption that no participants or all participants have OGE, respectively. The net benefit of decision-making using the nomogram at various threshold probabilities was presented with the orange (clinical model), blue (ClinCheck model), and red (combined model) lines.\u003c/p\u003e","description":"","filename":"Fig.6Performancesofthreepredictivemodels..jpg","url":"https://assets-eu.researchsquare.com/files/rs-6663025/v1/0db1f6f36bab34ab7b144074.jpg"},{"id":93956217,"identity":"1c9831c6-551d-422d-8b9c-2c0d7c8e4e60","added_by":"auto","created_at":"2025-10-20 16:11:34","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":12904524,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6663025/v1/5c15b61e-3723-406b-8cf1-f43a92e47855.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A novel machine-learning-based model for prediction of open gingival embrasures between mandibular central incisors after clear aligners treatment: A retrospective cohort study","fulltext":[{"header":"Introduction","content":"\u003cp\u003eOpen gingival embrasures (OGE), often defined by a significant reduction in the height of the gingival papillae, are a common complication of orthodontic therapy [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Clinically, OGE compromise both function and aesthetics by promoting food impaction, plaque accumulation, and oral hygiene difficulties, and may simultaneously induce smile anxiety and aesthetic insecurity [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Clear aligner treatment (CAT), while known for its aesthetic superiority, has demonstrated a higher incidence of post-treatment OGE compared to conventional fixed appliances [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. The literature revealed a pronounced disparity in non-extraction CAT cases, with mandibular anterior OGE occurring at 2.3 times the rate of maxillary OGE [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Notably, extraction cases exhibited even greater prevalence, with mandibular incidence rates approaching 52.3% [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eGiven the high prevalence of OGE, their management remains one of the most challenging and unpredictable procedures and accurate preoperative prediction is of great clinical importance. The clinical utility of OGE prediction during treatment planning is twofold. First, it aids patients in better understanding the expected treatment outcomes, thereby managing expectations and reducing post-treatment dissatisfaction [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Second, targeted interventions such as controlled interproximal enamel reduction and axis-adjusted tooth repositioning can be guided to minimize complications related to gingival discrepancies [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Furthermore, early prediction facilitates preoperatively interdisciplinary collaboration, where combined periodontal and prosthetic approaches (such as microsurgical papilla reconstruction and restorative procedures) can effectively address both aesthetic and functional concerns [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAlthough clinical risk factors for OGE (e.g., age, crowding, tooth movement) have been extensively investigated [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], predictive approaches for this condition have received little attention in the literature. Researchers of a recent in vivo study have explored the prediction of OGE through alveolar bone height assessment; however, pre-treatment crowding complicates bone height evaluation, and treatment-associated bone recession introduced additional complexity [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Although a previous study confirmed ClinCheck's high OGE prediction accuracy (94% in maxilla, 86% in mandible) in adult extraction CAT cases, its generalizability to non-extraction and adolescent patients remains unclear, and clinical risk factors failed to be incorporated [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Considering the high prevalence of OGE and the absence of simple yet sensitive predictive features, a reliable tool for precise prediction is critically needed in dental practice.\u003c/p\u003e \u003cp\u003eAs existing prediction methods rely on subjective clinician expertise, recent research has shifted toward data-driven prediction models [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Nowadays, nomograms serve as visual prediction tools that integrate multiple clinical parameters, including general information, treatment procedures and radiomics features, into a scoring system, enabling clinicians to calculate the risk of outcomes for patients [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Some researchers have developed machine-learning-based models for detection of degenerative temporomandibular joint diseases [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], prediction of fixed appliances treatment duration [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], potential design of orthodontic extraction patterns [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], etc. The user-friendly interface of nomograms offers broad clinical utility in assessing disease onset and progression; however, their clinical values in predicting OGE have never been reported.\u003c/p\u003e \u003cp\u003eTherefore, the purposes of this study were to: (1) develop a machine-learning-based model that integrated ClinCheck features and clinical risk factors to predict OGE between mandibular central incisors after CAT; (2) validate the combined model and determine its comparative performance against simple clinical and ClinCheck model.\u003c/p\u003e"},{"header":"Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eParticipants\u003c/h2\u003e \u003cp\u003e This retrospective cohort study received approval from the Ethics Committee (Approval Number: XXXX). All data were screened from the Orthodontic Department of XXX Hospital, during the period from July 2015 to July 2022. Informed consent was obtained from all participants.\u003c/p\u003e \u003cp\u003eThe inclusion criteria were (1) full permanent dentition with no missing teeth (excluding third molars); (2) absence of OGE or mandibular midline diastema at initial examination; (3) complete clinical records available; (4) completion of dual arch Invisalign\u0026reg; treatment (Align Technology, California, USA) with 22-hour daily wear and aligner changes every 7\u0026ndash;10 days; (5) clear and high quality of intraoral photographs at pre- and post-treatment stages. The exclusion criteria were (1) concurrent use of fixed orthodontic appliances; (2) periodontitis cases with radiographic bone loss\u0026thinsp;\u0026gt;\u0026thinsp;25% of root length and/or clinical attachment loss\u0026thinsp;\u0026ge;\u0026thinsp;2 mm; (3) planned surgical interventions (periodontal, orthognathic, or periodontally accelerated osteogenic orthodontics); (4) tooth defects of lower central incisors; (5) history of orthodontic therapy. The workflow of this study was presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eAssessment of post-treatment OGE and predicted OGE-area\u003c/h3\u003e\n\u003cp\u003eTwo orthodontists and one periodontist independently assessed OGE between mandibular central incisors using post-aligner-removal intraoral photos. Non-consensus assessment was excluded after discussion.\u003c/p\u003e \u003cp\u003eThe predicted area of OGE was measured from the frontal view in the final step of initial ClinCheck treatment plan. In the post-treatment digital models, the height of the OGE was defined as the distance between the interproximal papilla's uppermost margin and the lowest point of central incisors' contact area, while the base was the width of the upper margin of the interproximal papilla [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Therefore, the predicted OGE-area was derived as (base \u0026times; height)/2 (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eA).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003eMeasurement of clinical features\u003c/h3\u003e\n\u003cp\u003eThe clinical features for OGE prediction included: age, gender, extraction patterns, attachment placement, interproximal reduction (IPR) design, crown morphology, gingival papilla angle (GPA) and three-dimensional predicted tooth movement. General clinical data, including age, gender and extraction patterns (non-extraction or two premolars extraction pattern), were extracted from institutional medical records, while attachment placement and IPR design were obtained from ClinCheck plans.\u003c/p\u003e \u003cp\u003eThrough linear measurements of the triangle formed by the most apical points of adjacent gingival margins and the coronal peak of the gingival papilla, the GPA was calculated based on the cosine and arccosine formula (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eB). The crown morphology was assessed using the ratio of crown width (CW) to crown length (CL) on post-treatment digital models (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eC).\u003c/p\u003e \u003cp\u003ePredicted tooth movement was extracted from simulated ClinCheck metrics (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eD). Extrusion, buccal and mesial movement were recorded as positive values. A total of 16 parameters were quantified, encompassing both absolute and differential displacement magnitudes between central incisors across eight movement categories: (1) crown extrusion/ intrusion, (2) buccolingual crown translation, (3) mesial-distal crown translation, (4) rotation, (5) angulation, (6) inclination, (7) buccolingual root translation, (8) mesial-distal root translation. The absolute magnitude was recorded as zero if incisors move in opposite direction.\u003c/p\u003e\n\u003ch3\u003eInterrater and Intrarater Reliability\u003c/h3\u003e\n\u003cp\u003eTo evaluate the reproducibility of all parameters, two orthodontists traced 50 randomly selected participants, repeating the measurement after a 15-day interval. With interclass and intraclass correlation coefficients of 0.85 and 0.92, the measurements demonstrated excellent reliability.\u003c/p\u003e\n\u003ch3\u003eDevelopment of ClinCheck, clinical and combined model\u003c/h3\u003e\n\u003cp\u003eIncorporating the predicted OGE-area as input, the ClinCheck model was constructed with univariate logistic regression. Subsequently, the Least Absolute Shrinkage and Selection Operator (LASSO) logistic regression was employed to identify the most relevant predictors from the recorded 23 clinical features. A penalty coefficient (λ) was applied in the a ten-fold cross-validated LASSO analysis to obtain features with non-zero coefficients, which were selected to develop the clinical model using multiple logistic regression. Then, the selected clinical features and OGE-area were integrated to develop a combined model for OGE prediction. This combined model was presented as a nomogram to serve as personalized and user-friendly tool for predicting the occurrence of OGE.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003ePerformance and assessments of nomograms\u003c/h2\u003e \u003cp\u003ePerformance assessments were conducted for the ClinCheck, clinical, and combined models separately. Receiver operating characteristic (ROC) curves were used as evaluation metrics, with area under the curve (AUC) values exceeding 0.75 indicating favorable predictability. The differences of these models\u0026rsquo; performance were compared using the DeLong's test. Model calibration was evaluated through calibration curves. The model\u0026rsquo;s performance was internally validated using the corrected C-statistic, derived from the bootstrapping method with 1000 replications. Additionally, potential clinical utility was further quantified via decision curves to compare the net benefit among the three models.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eStatistical Analysis\u003c/h2\u003e \u003cp\u003eStatistical analysis was performed using SPSS software (version 23; IBM, Armonk, NY) and R (version 4.4.1; R Core Team). Multiple relevant packages, including rms, readxl, rmda, ResourceSelection, ggplot2, glmnet, caret, boot, DynNom, rsconnect and pROC were utilized in the R analysis. Continuous variables were compared using t-tests or Wilcoxon tests, whereas categorical variables were assessed via chi-square tests. All tests were two-tailed, with \u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05 considered statistically significant.\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eParticipant characteristics\u003c/h2\u003e \u003cp\u003eA total of 297 participants (63 males, 234 females, mean age of 23.12\u0026thinsp;\u0026plusmn;\u0026thinsp;6.68 years) were eventually included to develop and validate the predictive model. The incidence of OGE was 45.12% in this study. The clinical characteristics of the OGE group (n\u0026thinsp;=\u0026thinsp;134) and the Normal group (n\u0026thinsp;=\u0026thinsp;163) were analyzed and compared, and the results showed that significant differences were observed in age, extraction pattern, IPR, GPA, crown morphology, D-rotation, D-angulation and inclination between patients with and without OGE (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eClinical characteristics of participants and comparison of characteristics between patients with and without OGE.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCharacteristics\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOverall (n\u0026thinsp;=\u0026thinsp;297)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOGE (n\u0026thinsp;=\u0026thinsp;134)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNormal (n\u0026thinsp;=\u0026thinsp;163)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGender (male/female)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e63/234\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e23/111\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e40/123\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.122\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e23.12\u0026thinsp;\u0026plusmn;\u0026thinsp;6.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e25.04\u0026thinsp;\u0026plusmn;\u0026thinsp;6.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e21.54\u0026thinsp;\u0026plusmn;\u0026thinsp;6.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e\u0026lt;0.001**\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExtraction pattern (Y/N)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e117/180\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e64/70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e53/110\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.007**\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAttachment design\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0 (0, 0)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0 (0, 0)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0 (0, 0)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.334\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIPR (Y/N)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e51/246\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e13/121\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e38/125\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.002**\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGPA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e77.04\u0026thinsp;\u0026plusmn;\u0026thinsp;10.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e79.20\u0026thinsp;\u0026plusmn;\u0026thinsp;10.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e75.27\u0026thinsp;\u0026plusmn;\u0026thinsp;10.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.001**\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCrown morphology\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.60\u0026thinsp;\u0026plusmn;\u0026thinsp;0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.57\u0026thinsp;\u0026plusmn;\u0026thinsp;0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.62\u0026thinsp;\u0026plusmn;\u0026thinsp;0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e\u0026lt;0.001**\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePredicted tooth movement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExtrusion/intrusion\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-2.00 (-3.30, -1.05)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-2.10 (-3.33, -1.08)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-2.00 (-3.10, -1.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.665\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD-extrusion/intrusion\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.20 (0.10, 0.45)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.30 (0.10, 0.50)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.20 (0.10, 0.40)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.110\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eB/L crown translation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00 (-1.50, 0.80)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00 (-1.83, 0.80)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.00 (-1.20, 1.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.178\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD-B/L crown translation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.50 (0.30, 1.10)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.50 (0.30, 1.30)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.60 (0.20, 1.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.282\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM/D-crown translation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00 (-0.10, 0.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00 (-0.13, 0.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.00 (-0.10, 0.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.082\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD-M/D crown translation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.90 (0.40, 2.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.90 (0.40, 2.40)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.80 (0.40, 1.60)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.262\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRotation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-1.60 (-9.40, 0.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00 (-8.63, 0.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-2.80 (-9.80, 0.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.237\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD-rotation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9.90 (4.55, 17.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e13.00 (7.08, 21.90)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7.40 (4.10, 12.80)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e\u0026lt;0.001**\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAngulation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00 (0.00, 0.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00 (0.00, 0.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.00 (0.00, 0.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.107\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD-angulation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.10 (1.90, 7.75)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.65 (2.00, 9.70)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.50 (1.80, 6.90)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.011*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInclination\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.30 (0.00, 5.80)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.30 (0.00, 4.68)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.20 (0.00, 7.80)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.014*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD-inclination\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.60 (1.80, 6.85)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.00 (2.00, 7.05)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.30 (1.60, 6.80)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.209\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eB/L root translation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.70 (-2.80, 0.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.60 (-2.33, 0.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.80 (-3.00, 0.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.456\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD-B/L root translation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.70 (0.30, 1.20)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.70 (0.30, 1.20)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.70 (0.30, 1.10)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.915\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM/D root translation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00 (-0.40, 0.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00 (-0.33, 0.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.00 (-0.40, 0.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.382\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD-M/D root translation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.00 (0.50, 1.90)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.00 (0.50, 1.90)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.10 (0.50, 1.90)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.782\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003eData with a normal distribution were presented as mean\u0026thinsp;\u0026plusmn;\u0026thinsp;SD, while data with a non-normal distribution were presented as median (25%, 75%).\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003eIPR, interproximal reduction; GPA, gingival papilla angle; D-Extrusion/intrusion, differential movement of extrusion/intrusion; B/L crown translation, buccolingual crown translation; D-B/L crown translation, differential movement of buccolingual crown translation; M/D-crown translation, mesial-distal crown translation; D-M/D crown translation, differential movement of mesial-distal crown translation; D-rotation, differential movement of rotation; D-angulation, differential movement of angulation; D-inclination, differential movement of inclination; B/L root translation, buccolingual root translation; D-B/L root translation, differential movement of buccolingual root translation; M/D root translation, mesial-distal root translation; D-M/D root translation, differential movement of mesial-distal root translation.\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003e\u003cem\u003eP\u003c/em\u003e value\u0026thinsp;\u0026lt;\u0026thinsp;0.05 was considered significant given in bold. *\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05, **\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.01.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eDevelopment and nomogram of OGE prediction models\u003c/h2\u003e \u003cp\u003eA ClinCheck model was constructed using the virtual OGE-area. Twenty-three clinical features were standardized (z-score) and included in the LASSO regression analysis for predictor selection. Through ten-fold cross-validation, the optimal regularization parameter (λ) was determined to be 0.051 with one standard error (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA). Following this criterion, six clinical features with nonzero coefficients were selected (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB), including crown morphology, IPR, inclination, age, D-rotation, and GPA (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eC). Subsequently, the six features were included as predictors to construct a clinical model by multivariable logistic regression (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). In this clinical model, all features except inclination were significantly associated with the occurrence of OGE (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDescription of predictors in the clinical and combined models.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003ePredictors\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eClinical model\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003eCombined model\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOR (95%CI)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eOR (95%CI)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIPR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.20 (0.09, 0.45)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e\u0026lt;\u0026thinsp;0.001**\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.58 (0.22, 1.47)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.261\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCrown morphology\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00 (0.00, 0.00)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e\u0026lt;\u0026thinsp;0.001**\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.00 (0.00, 0.01)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e\u0026lt;\u0026thinsp;0.001**\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInclination\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.96 (0.92, 1.01)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.121\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.98 (0.92, 1.03)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.428\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGPA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.07 (1.04, 1.10)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e\u0026lt;\u0026thinsp;0.001**\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.03 (0.99, 1.06)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.126\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD-rotation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.06 (1.03, 1.09)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e\u0026lt;\u0026thinsp;0.001**\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.04 (1.01, 1.08)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.024*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.08 (1.03, 1.13)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.001**\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.06 (1.00, 1.11)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.036*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOGE-area\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.78 (3.00, 8.14)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e\u0026lt;\u0026thinsp;0.001**\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003eNA, not available.\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003eIPR, interproximal reduction; GPA, gingival papilla angle; D-rotation, differential movement of rotation; D-B/L root translation, differential movement of buccolingual root translation; OR, odds ratio; CI, confidence interval.\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u003cem\u003eP\u003c/em\u003e value\u0026thinsp;\u0026lt;\u0026thinsp;0.05 was considered significant given in bold. *\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05, **\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.01.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eA combined model incorporating OGE-area and clinical predictors was developed with multivariable logistic regression analysis. Four indicators, including OGE-area, crown morphology, age and differential movement of rotation, were all significantly correlated with OGE (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The combined model was visualized in a nomogram for individual risk estimation (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Each factor was assigned a score based on a point scale axis. The total score was calculated by summing the individual scores. By projecting this total score onto the bottom risk scale axis, the probability of OGE could be estimated. To facilitate implementation of the model in clinical settings, a user-friendly R-Shiny web application was developed and shared at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://fenguo4863364.shinyapps.io/DynNomapp/\u003c/span\u003e\u003cspan address=\"https://fenguo4863364.shinyapps.io/DynNomapp/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eValidation and performances of the models\u003c/h2\u003e \u003cp\u003eThrough 1000 bootstrap resamples, the corrected C-statistic of the combined nomogram was 0.889, demonstrating favorable internal validation performance. The calibration curve showed strong concordance between predicted and observed values, with a mean absolute error of 0.015 (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Additionally, the Hosmer-Lemeshow test confirmed the acceptable fit of this combined model (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.737).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn this study, the combined nomogram demonstrated superior predictive performance with an AUC of 0.891 (95% CI: 0.850\u0026ndash;0.927), significantly outperforming both the ClinCheck model (AUC\u0026thinsp;=\u0026thinsp;0.860; 95% CI: 0.817\u0026ndash;0.900; \u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05) and the clinical model (AUC\u0026thinsp;=\u0026thinsp;0.820; 95% CI: 0.774\u0026ndash;0.867; \u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.01) (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eA). However, according to DeLong's test, no significant difference was observed between the ClinCheck and clinical models. The DCA curves exhibited clinical utility in all three prediction models. In the DCA curve, the combined model showed higher net benefit than the clinical model when the threshold probability exceeded 0.13, and higher than the ClinCheck model between 0.13 and 0.62 (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eB).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eA novel nomogram, integrating ClinCheck OGE-area with clinical predictors, was firstly developed and validated in this study to quantify the risk of OGE between mandibular incisors. The combined nomogram demonstrated superior predictive performance (AUC: 0.891), significantly outperforming both the independent ClinCheck model and conventional clinical models. Decision curve analysis further confirmed the enhanced clinical utility of the integrated model. These findings suggest that combined nomogram offers robust potential for predicting post-treatment OGE in clear aligner therapy.\u003c/p\u003e \u003cp\u003eIn this study, a strong correlation was shown between ClinCheck OGE-area and actual clinical outcomes. This relationship can be attributed to manufacturing protocols and biomechanical mechanisms underlying clear aligners. Through digital intraoral scanning, ClinCheck obtains precise 3D modeling that eliminates soft tissue displacement caused by traditional impression material compression, enabling more accurate simulation of soft tissue remodeling [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Furthermore, the encroachment of aligners into interdental embrasures mechanically restricted gingival papilla adaptation, thereby predicted and actual OGE sharing the similar incidence and morphology [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Clinically, improvement of clear aligners with simulated fulfilling gingival papilla covering might be helpful in decreasing the incidence of OGE.\u003c/p\u003e \u003cp\u003eThe GPA was firstly employed to quantify the joint effects of papilla height and adjacent crown morphology on OGE formation. Authors of a previous study have confirmed the association between gingival angle and papilla fill [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. However, the assessment of gingival angle in their study, which was defined as the angle at the gingival margin formed by two adjacent gingival papillae, exhibited limitations due to discrepancies in both the gingival margin and crown contours of adjacent teeth. Previous studies have independently examined crown contours or papilla heights, which respectively determined the scalloping pattern of gingival margins and the degree of interproximal tissue fill [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. While adjacent crowns and gingival papillae formed an inseparable functional community that shaped interdental three-dimensional unit and related to gingival thickness [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. An evidence-based review indicated that \u0026ldquo;thick-flat\u0026rdquo; gingiva correlates with better periodontal health and lower risks of papilla height loss versus \u0026ldquo;thin-scalloped\u0026rdquo; biotypes [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. In contrast, thick gingival biotypes are fibrotic and resilient, demonstrating a tendency for pocket formation over OGE [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. In our clinical model, the GPA showed significant correlation with OGE (OR, 1.07; 95% CI, 1.04\u0026ndash;1.10), indicating that this parameter might be a key indicator for future studies.\u003c/p\u003e \u003cp\u003eAmong the patient factors, crown morphology demonstrated a significant association with the occurrence of OGE in both the clinical model and the comprehensive model. This result was consistent with previous studies on the risk factors of OGE [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. In the comprehensive predictive model of this study, a greater crown ratio was associated with a lower probability of OGE. This phenomenon may be related to the apical position of proximal contacts. Long and narrow crowns were often accompanied by proximal contact points closer to the incisal edge, and as the distance between the contact point and the alveolar crest increased, the height of the gingival papilla correspondingly decreased [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Furthermore, studies have shown that regardless of the amount of plaque accumulation, long and narrow teeth are at a higher risk of developing periodontal inflammation compared to short and wide teeth, suggesting that periodontal health might be more easily maintained around square-shaped crowns [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. In clinical practice, appropriate modification of tooth morphology would be helpful to prevent or reduce OGE. Additionally, the results of the clinical model indicated that for every one-year increase in age, the risk of OGE increased by 8%. For older patients, providing a thorough preoperative risk consent might of great importance.\u003c/p\u003e \u003cp\u003eCompared with previous studies utilizing cephalometry or study models [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], this study assessed the impact of treatment factors on OGE through the ClinCheck tooth movement metrics. With the aid of ClinCheck metrics, dental crowding was indirectly measured by calculating the movement differences of adjacent teeth in the same direction. Previous work by An SS et al. evaluated crowding between central incisors through incisal edge angulation and the sagittal and transverse distances of mesial contact points [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. However, potential errors from reference line placement in mandibular crowded cases exited. The metrics enhanced accuracy and repeatability while simplifying the evaluation process. In this study, the differential movement of rotation, which indirectly represented the crowding, was determined to be associated with OGE. This outcome likely resulted from gingival fiber stretching and decreased gingival thickness during the alignment of crowded teeth [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Preoperative assessment through CBCT or evaluation of gingival biotype could improve the predictive accuracy of OGE after alignment of crowded dentition. To minimize the occurrence of OGE, a \"staged alignment\" strategy would be recommended to prioritize the correction of tooth rotations and reduce back-and-forth movements [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e].\u003c/p\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eLimitation\u003c/h2\u003e \u003cp\u003eSeveral limitations should be acknowledged in this study. Due to the retrospective nature, this study might introduce selection bias and failed to incorporate important clinical indicators such as periodontal biotype and gingival index. Although ICC analysis confirmed measurement reliability, future researches need to explore automated procedure with artificial intelligence to enhance result robustness. As discrepancies may exist between ClinCheck-predicted tooth movement and actual outcomes due to overcorrection design and clinical efficacy in CAT, digital model or radiomics-based superimposition could be employed to further investigate the correlation between tooth movement and OGE. Additionally, participants in our study originated from specific Invisalign cases, which may limit the nomogram's predictive capability in other clear aligner systems. Due to the limited sample size, external validation of the nomogram was not conducted in this study. Therefore, the generalizability of our combined nomogram necessitates further external validation in larger and more diverse populations.\u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eA comprehensive nomogram was developed and validated for predicting OGE between lower central incisors after CAT. The model integrated predicted OGE-area with 6 clinical features (including IPR, crown morphology, inclination, GPA, D-rotation and age), demonstrating superior predictive performance. Accurate prediction of OGE can be achieved by this combined nomogram, thereby improving clinical decision-making.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study has been approved by the Ethics Committee of XX Hospital (Approval Number: XXX), and followed the contents in the Declaration of Helsinki concerning human subjects.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe undersigned author(s) of the manuscript titled \u0026ldquo;A novel machine-learning-based model for prediction of open gingival embrasures between mandibular central incisors after clear aligners treatment: A retrospective cohort study\u0026rdquo; hereby grant \u0026ldquo;Progress in Orthodontics\u0026rdquo; the right to publish the aforementioned work, including any supplementary material that may be associated with it. We confirm that this work is original, has not been published elsewhere, and does not infringe upon any copyright or any other rights of any third party. We also affirm that all contributing authors have agreed to the submission of this work for publication in \u0026ldquo;Progress in Orthodontics.\u0026rdquo; In the event that this work includes any data or images from individuals, we confirm that we have obtained the necessary consents from the individuals involved.\u003c/p\u003e\n\u003ch2\u003eFunding\u003c/h2\u003e\n\u003cp\u003eThis work was funded by XXX (XXXX).\u003c/p\u003e\n\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\n\u003cp\u003eL.L. was the supervisor and designed the study. G.L. and F.G. drafted the manuscript and writing the manuscript. G.L. and F.G. performed the statistical analysis and data analysis. J.C. and H.L assisted with data curation. All authors read and approved the final manuscript.\u003c/p\u003e\n\u003ch2\u003eAcknowledgement\u003c/h2\u003e\n\u003cp\u003eThe authors would like to express their gratitude to all individuals who have contributed to this study. We appreciate the support from the National Natural Science Foundation.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eSingh VP, Uppoor AS, Nayak DG, Shah D. Black triangle dilemma and its management in esthetic dentistry. Dent Res J (Isfahan). 2013;10:296\u0026ndash;301.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTanaka OM, Furquim BD, Pascotto RC, Ribeiro GL, B\u0026oacute;sio JA, Maruo H. The dilemma of the open gingival embrasure between maxillary central incisors. J Contemp Dent Pract. 2008;9:92\u0026ndash;8.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSriphadungporn C, Chamnannidiadha N. Perception of smile esthetics by laypeople of different ages. Prog Orthod. 2017;18:8.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYang T, Jiang L, Sun W, et al. The incidence and severity of open gingival embrasures in adults treated with clear aligners and fixed appliances: a retrospective cohort study. Head Face Med. 2023;19:30.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCui W, Liu Y, Zhao Y, Lei L, Li H. Risk factors for open gingival embrasures after clear aligners treatment: a retrospective study. BMC Oral Health. 2025;25:547.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGuo F, Wang C, Han L, Li H, Lei L, Mei L. Invisalign ClinCheck can predict open gingival embrasures in adult extraction cases: a pilot study. Angle Orthod. 2025.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang Y, Wang X, Wang J, et al. IPR treatment and attachments design in clear aligner therapy and risk of open gingival embrasures in adults. Prog Orthod. 2023;24:1.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSharma AA, Park JH. Esthetic considerations in interdental papilla: remediation and regeneration. J Esthet Restor Dent. 2010;22:18\u0026ndash;28.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePrato GP, Rotundo R, Cortellini P, Tinti C, Azzi R. Interdental papilla management: a review and classification of the therapeutic approaches. Int J Periodontics Restor Dent. 2004;24:246\u0026ndash;55.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTian E, Luo K, Zhou Y, et al. Factors influencing open gingival embrasures in orthodontic treatment: a retrospective clinical study. Prog Orthod. 2025;26:6.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMahasneh SA, Goodwin M, Pretty I, Cunliffe J. The use of radiographs to assess the impact of the distance between the contact area and the crest of the bone to predict the presence or absence of interdental papilla: an in vivo study. Br Dent J. 2023.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang X, Lu J, Song Z, Zhou Y, Liu T, Zhang D. From past to future: Bibliometric analysis of global research productivity on nomogram (2000\u0026ndash;2021). Front Public Health. 2022;10:997713.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGrobman WA, Stamilio DM. Methods of clinical prediction. Am J Obstet Gynecol. 2006;194:888\u0026ndash;94.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFang X, Xiong X, Lin J, Wu Y, Xiang J, Wang J. Machine-learning-based detection of degenerative temporomandibular joint diseases using lateral cephalograms. Am J Orthod Dentofac Orthop. 2023;163:260\u0026ndash;e271265.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShi X, Wu B, Cao D, et al. Effect of socioeconomic and malocclusion-related factors on duration of orthodontic treatment by fixed appliance: A retrospective study. Orthod Craniofac Res. 2023;26:650\u0026ndash;9.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLeavitt L, Volovic J, Steinhauer L, et al. Can we predict orthodontic extraction patterns by using machine learning? Orthod Craniofac Res. 2023;26:552\u0026ndash;9.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKihara H, Hatakeyama W, Komine F, et al. Accuracy and practicality of intraoral scanner in dentistry: A literature review. J Prosthodont Res. 2020;64:109\u0026ndash;13.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJoshi K, Baiju CS, Khashu H, Bansal S, Maheswari IB. Clinical assessment of interdental papilla competency parameters in the esthetic zone. J Esthet Restor Dent. 2017;29:270\u0026ndash;5.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChow YC, Eber RM, Tsao YP, Shotwell JL, Wang HL. Factors associated with the appearance of gingival papillae. J Clin Periodontol. 2010;37:719\u0026ndash;27.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKim DM, Bassir SH, Nguyen TT. Effect of gingival phenotype on the maintenance of periodontal health: An American Academy of Periodontology best evidence review. J Periodontol. 2020;91:311\u0026ndash;38.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAhmad I. Anterior dental aesthetics: gingival perspective. Br Dent J. 2005;199:195\u0026ndash;202.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKolte AP, Kolte RA, Bawankar P. Proximal contact areas of maxillary anterior teeth and their influence on interdental papilla. Saudi Dent J. 2018;30:324\u0026ndash;9.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTarnow DP, Magner AW, Fletcher P. The effect of the distance from the contact point to the crest of bone on the presence or absence of the interproximal dental papilla. J Periodontol. 1992;63:995\u0026ndash;6.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTrombelli L, Farina R, Manfrini R, Tatakis DN. Modulation of clinical expression of plaque-induced gingivitis: effect of incisor crown form. J Dent Res. 2004;83:728\u0026ndash;31.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAn SS, Choi YJ, Kim JY, Chung CJ, Kim KH. Risk factors associated with open gingival embrasures after orthodontic treatment. Angle Orthod. 2018;88:267\u0026ndash;74.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKurth JR, Kokich VG. Open gingival embrasures after orthodontic treatment in adults: prevalence and etiology. Am J Orthod Dentofac Orthop. 2001;120:116\u0026ndash;23.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBurke S, Burch JG, Tetz JA. Incidence and size of pretreatment overlap and posttreatment gingival embrasure space between maxillary central incisors. Am J Orthod Dentofac Orthop. 1994;105:506\u0026ndash;11.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu Y, Li CX, Nie J, Mi CB, Li YM. Interactions between Orthodontic Treatment and Gingival Tissue. Chin J Dent Res. 2023;26:11\u0026ndash;8.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"progress-in-orthodontics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"pior","sideBox":"Learn more about [Progress in Orthodontics](http://progressinorthodontics.springeropen.com)","snPcode":"40510","submissionUrl":"https://submission.nature.com/new-submission/40510/3","title":"Progress in Orthodontics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Machine-learning-based model, Prediction, Open gingival embrasures, Clear aligner treatment","lastPublishedDoi":"10.21203/rs.3.rs-6663025/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6663025/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eObjective\u003c/h2\u003e \u003cp\u003eTo develop a machine-learning-based model and construct a nomogram that integrates ClinCheck features and clinical risk factors for accurately predicting open gingival embrasures (OGE) between mandibular central incisors after clear aligner treatment (CAT).\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e \u003cp\u003eA total of 297 patients (163 normal and 134 with OGE) who underwent Invisalign\u0026reg; treatment were enrolled. A ClinCheck model was developed based on predicted OGE-area in the final step from initial ClinCheck treatment plan. Twenty-three clinical features were extracted from electronic medical records and ClinCheck tooth movement metrics. Predictors were selected through Least Absolute Shrinkage and Selection Operator (LASSO) regression to establish a clinical model. Additionally, a nomogram incorporating ClinCheck features and clinical predictors was constructed via logistic regression and validated with bootstrap resampling. The performances of these models were evaluated through receiver operating characteristic (ROC) curves, area under curves (AUC), and decision curve analyses (DCA).\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eSix clinical features, including age, gingival papilla angle, interproximal reduction, crown morphology and two types of tooth movement, were selected through LASSO regression. The integrated model that consisted of OGE-area and clinical features demonstrated superior predictive capacity (AUC: 0.891; 95% \u003cem\u003eCI\u003c/em\u003e: 0.850\u0026ndash;0.927), outperforming both clinical model (AUC: 0.820; 95% \u003cem\u003eCI\u003c/em\u003e: 0.774\u0026ndash;0.867; \u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001) and ClinCheck model (AUC: 0.860; 95% \u003cem\u003eCI\u003c/em\u003e: 0.817-0.900; \u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05). The corrected C-statistic of the combined nomogram was 0.889, and the calibration curve exhibited great performance with a mean absolute error of 0.015. In the DCA curve, the combined model showed higher net benefit than the clinical model when the threshold probability exceeded 0.13, and higher than the ClinCheck model between 0.13 and 0.62.\u003c/p\u003e\u003ch2\u003eConclusion\u003c/h2\u003e \u003cp\u003eThe integration of clinical features and ClinCheck in the machine-learning-based model demonstrated favorable predictive capabilities for OGE between lower central incisors. This comprehensive nomogram may contribute to precisely prediction and prevention of OGE in clinical practice.\u003c/p\u003e","manuscriptTitle":"A novel machine-learning-based model for prediction of open gingival embrasures between mandibular central incisors after clear aligners treatment: A retrospective cohort study","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-18 06:26:54","doi":"10.21203/rs.3.rs-6663025/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-08-27T20:12:53+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-27T17:53:00+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"76470075120288597711047954869075053969","date":"2025-08-14T06:47:22+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-01T09:18:34+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"105928174035116965493611284317822341982","date":"2025-06-27T15:59:28+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-06-13T11:42:34+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-06-04T23:34:52+00:00","index":"","fulltext":""},{"type":"submitted","content":"Progress in Orthodontics","date":"2025-05-27T12:17:07+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"progress-in-orthodontics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"pior","sideBox":"Learn more about [Progress in Orthodontics](http://progressinorthodontics.springeropen.com)","snPcode":"40510","submissionUrl":"https://submission.nature.com/new-submission/40510/3","title":"Progress in Orthodontics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"b7c92fcb-90e4-46de-a8ca-031400e889a1","owner":[],"postedDate":"June 18th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-10-20T16:07:08+00:00","versionOfRecord":{"articleIdentity":"rs-6663025","link":"https://doi.org/10.1186/s40510-025-00584-0","journal":{"identity":"progress-in-orthodontics","isVorOnly":false,"title":"Progress in Orthodontics"},"publishedOn":"2025-10-15 15:57:59","publishedOnDateReadable":"October 15th, 2025"},"versionCreatedAt":"2025-06-18 06:26:54","video":"","vorDoi":"10.1186/s40510-025-00584-0","vorDoiUrl":"https://doi.org/10.1186/s40510-025-00584-0","workflowStages":[]},"version":"v1","identity":"rs-6663025","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6663025","identity":"rs-6663025","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}