Evaluation of Autoregressive Models for Predicting Two-Dimensional Mandibular Landmark Displacement During Pubertal Growth.

Abstract

Objectives: To predict mandibular landmark displacement during pubertal growth using autoregressive models.

Materials and methods: The study included 225 subjects with complete cephalometric radiographs from ages 10 to 18. Data were split by subject into training (180; 83 males, 97 females) and test sets (45; 21 males, 24 females). Mandibular landmarks analysed were Condylion, Gonion, Menton, Pogonion, and Point B. Radiographs were aligned using the Sella-Nasion line with Sella as the origin, and 2D coordinates for each landmark were recorded over time. An autoregressive model predicted future landmark positions. Accuracy was measured using mean absolute error and the percentage of predictions within 2 mm of true values. Logistic regression with generalised estimating equations evaluated the effects of coordinate dimension, landmark type, prediction interval (1-4 years), prediction age (11-18), and sex.

Results: Females demonstrated higher predictive accuracy than males (65% vs. 49%), by using the percentage of predictions within 2 mm of the true coordinates. Accuracy declined with longer prediction intervals: 66% (1-year), 58% (2-year), and 46% (4-year). Condylion was the most predictable landmark (71%), followed by Point B (63%) and Gonion (61%), whereas Menton was least predictable (40%). Accuracy was similar between x- and y-dimensions (58% vs. 56%). Overall predictive accuracy decreased substantially when Euclidean distance was used instead of separate coordinate-based assessments, ranging from 39% for Condylion to 18% for Menton.

Conclusions: Autoregressive models can generate clinically meaningful short-term predictions of mandibular growth, particularly for selected landmarks and among female subjects. However, predictive performance declines over longer time intervals and varies substantially across anatomical sites, with Condylion demonstrating the highest accuracy and Menton showing the greatest variability.