Analyzing longitudinal growth data in orthodontics

Longitudinal growth data with repeated measurements of distances and angles on radiographs are usually collected to study skeletal and dental changes throughout childhood and adolescence. The analysis of longitudinal data usually requires sophisticated statistical methods and modeling techniques because repeated measurements made on the same subject violate the assumption of independence underlying classical statistical tests. Advanced methods, such as multilevel modeling, must be used to account for the correlations between repeated measurements. In this article, we describe four statistical models for the analysis of growth data: linear multilevel model, curvilinear multilevel model, multilevel Preece-Baines model, and super imposition by translation and rotation (SITAR) model. We use data of 42 children on the mandibular length obtained from the archives at the AAOF Craniofacial Growth Legacy Collection for demonstration. Our analyses showed that although the multilevel curvilinear model appears to fit the data well from a statistical perspective, the Preece-Baines model and the SITAR model provide additional insights into mandibular growth. The SITAR model suggests two growth peaks which is consistent with the current understanding of mandibular growth and deserves more attention from orthodontic researchers.