Explainable Machine-Learning Classification of Vertical Skeletal Patterns in a German Orthodontic Cohort: A Nested Cross-Validation Study

Background: Vertical craniofacial morphology represents a continuous spectrum from hypodivergent to hyperdivergent skeletal patterns. Although the intermaxillary angle between the palatal and mandibular planes is commonly used to categorize these patterns, vertical morphology reflects a broader combination of facial height, mandibular, cranial base, and dentoalveolar characteristics. Machine-learning approaches may capture complex and potentially nonlinear relationships among these features; however, their validity and clinical interpretability require rigorous prevention of target leakage and transparent interpretation of model predictions. Objectives: Here, we aimed to develop and internally validate an explainable multiclass machine-learning model for distinguishing deep-bite, healthy, and open-bite skeletal patterns in a German orthodontic cohort. A secondary objective was to identify the cephalometric features contributing to each class-specific prediction using the SHapley Additive exPlanations (SHAP). Materials and Methods: We analyzed pretreatment cephalometric records from 1,524 unique patients. We categorized the vertical skeletal pattern according to the NL/ML angle as deep bite (<18.0°), healthy (18.0°–28.0°), or open bite (>28.0°). Because NL/ML can be mathematically reconstructed from ML–NSL and NL/NSL, the outcome-defining angle and its direct components were excluded from the primary model to prevent target leakage. A leakage-resistant XGBoost model was developed using 19 demographic and cephalometric predictors. Performance was estimated using nested stratified cross-validation with five outer folds and five inner folds. Fifty randomly sampled hyperparameter combinations were evaluated within each outer training fold. Class-balanced observation weights were calculated exclusively from the training data. Confidence intervals were estimated from 2,000 bootstrap samples of the out-of-fold predictions. SHAP values were calculated only for observations held out from model training. Results: The cohort included 236 patients with a deep-bite pattern, 976 with a healthy pattern, and 312 with an open-bite pattern. The XGBoost model achieved an out-of-fold accuracy of 0.778 (95% CI, 0.758–0.798), balanced accuracy of 0.749 (95% CI, 0.722–0.774), macro-F1 score of 0.740 (95% CI, 0.715–0.763), and macro one-versus-rest area under the receiver operating characteristic curve of 0.893 (95% CI, 0.879–0.907). Sensitivity was 0.695 for the deep-bite pattern, 0.810 for the healthy pattern, and 0.740 for the open-bite pattern. The corresponding class-specific AUC values were 0.927, 0.827, and 0.926 for deep-bite, healthy, and open-bite patterns, respectively. No patient with a deep-bite pattern was directly classified as having an open-bite pattern, and no patient with an open-bite pattern was directly classified as having a deep-bite pattern. PFH/AFH was the most influential predictor for all three classes. Gonial angle and facial axis were the next most influential variables for the deep-bite and open-bite classes. A sensitivity model containing predictors that mathematically reconstructed NL/ML achieved an accuracy of 0.957, demonstrating the substantial inflation in apparent performance caused by target leakage. Conclusions: A leakage-resistant XGBoost model demonstrated moderate-to-good ability to distinguish three NL/ML-defined vertical skeletal patterns. PFH/AFH, gonial angle, and facial axis were the principal contributors to class-specific predictions. The findings also demonstrate that including mathematical components of the reference standard can produce misleadingly high estimates of model performance.