Development and validation of a predictive nomogram for bilateral posterior condylar displacement using cone-beam computed tomography and machine-learning algorithms: a retrospective observational study

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BACKGROUND: Temporomandibular disorders (TMDs) are frequently associated with posterior condylar displacement; however, early prediction of this displacement remains a significant challenge. Therefore, in this study, we aimed to develop and evaluate a predictive model for bilateral posterior condylar displacement. METHODS: In this retrospective observational study, 166 cone-beam computed tomography images were examined and categorized into two groups based on condyle positions as observed in the sagittal images of the joint space: those with bilateral posterior condylar displacement and those without. Three machine-learning algorithms-Random Forest, Least Absolute Shrinkage and Selection Operator (LASSO) regression, and Extreme Gradient Boosting (XGBoost)-were used to identify risk factors and establish a risk assessment model. Calibration curves, receiver operating characteristic curves, and decision curve analyses were employed to evaluate the accuracy of the predictions, differentiation, and clinical usefulness of the models, respectively. RESULTS: Articular eminence inclination (AEI) and age were identified as significant risk factors for bilateral posterior condylar displacement. The area under the curve values for the LASSO and Random Forest models were both > 0.7, indicating satisfactory discriminative ability of the nomogram. No significant differences were observed in the differentiation and calibration performance of the three models. Clinical utility analysis revealed that the LASSO regression model, which incorporated age, AEI, A point-nasion-B point (ANB) angle, and facial height ratio (S-Go/N-Me), demonstrated superior net benefit compared to the other models when the probability threshold exceeded 45%. CONCLUSION: Patients with a steeper AEI, insufficient posterior vertical distance (S-Go/N-Me), an ANB angle ≥ 4.7°, and older age are more likely to experience bilateral posterior condylar displacement. The prognostic nomogram developed and validated in this study may assist clinicians in assessing the risk of bilateral posterior condylar displacement.

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