Machine learning models for improving the diagnosing efficiency of skeletal class I and III in German orthodontic patients

The precise and efficient diagnosis of an individual's skeletal class is necessary in orthodontics to ensure correct and stable treatment planning. However, it is difficult to efficiently determine the true skeletal class due to several correlations between various anatomic structures. The primary outcome of this prospective cross-sectional study was developing a machine learning model for classifying patients as skeletal class I and III. Furthermore, the investigation intended to compare cephalometric variables between skeletal class I and III as well as between age and sex-specific subgroups to analyse correlations between cephalometric parameters and to perform Principal Component Analysis (PCA) to identify the most important variables contributing to skeletal class I and III variances. This study was based on the pre-treatment lateral cephalograms of 509 German orthodontic patients diagnosed as skeletal class I (n = 341) or III (n = 168) according to the individualised ANB of Panagiotidis and Witt, following descriptive analyses of cephalometric parameters, correlation analyses followed by Principal Component Analysis (PCA) to identify key cephalometric variables. Machine learning models, including Random Forest (RF), Classification and Regression Trees (CART), k-nearest Neighbors (KNN), Linear Discriminant Analysis (LDA), Support Vector Machines (SVM), and Generalized Linear Model (GLM), were evaluated for accuracy. Within the same skeletal class, age influenced cephalometric parameters: in skeletal class I, adolescents presented a more horizontal pattern (PFH/AFH, Gonial angle, NL-ML) and prominent mandible (SNB, SN-Pg) than children. In skeletal class III, the degree of sagittal discrepancy between jaw bases was most notable in adults (ANB: III_Age > 21-III _14 < Age < 20 - 1.78°). Comparing skeletal class I and III, the latter had more prognathic mandibles (SNB) and compensated incisors' inclination (proclination of the upper (+ 1/NA: 9.01°), retroinclination of the lower incisors (- 1/ML: 8.99°). Among others, a correlation was found between the sagittal (degree of prognathism, SNB) and vertical (inclination, ML-NSL) orientation of the mandible (skeletal class I: p < 0.001, ρ = - 0.742; skeletal class III: p < 0.001, ρ = - 0.665). PCA revealed that the first four principal components explain 93% of the variance in skeletal class I/III diagnosis and that these parameters had the most influence loading score on the first component-PFH/AFH ratio (0.35), SNB angle (0.35), SN-Pg (0.37), and ML-NSL (- 0.35). Evaluating machine learning models, the general model, including all cephalometric parameters, age, and sex, resulted in perfect (1.00) accuracy and kappa scores compared to the gold standard Calculated_ANB with the model's RF and CART. In model 2 the amount of input variables was reduced (Wits, SNB only), but the accuracy (0.88), and kappa (0.73) were still good in the KNN model. In the last section of this study, we applied different machine learning classification models. We examined the ability of the parameters-SNA, SNB, and ML-NSL angles to predict the classification as skeletal class I or III. The results demonstrated that the GLM model gained an accuracy of 0.99 (Accuracy = 0.99, Kappa = 0.97). The precise diagnosis of skeletal class I/III can be simplified by applying the machine learning model GLM with the input variables SNA, SNB, and ML-NSL only. This stresses the importance of their correct identification. However, considering all skeletal classes, a larger population is needed to validate and generalize this approach.