Modelling the predicted patterns of growth in the craniofacial skeleton allows estimation of peak growth velocity (PGV) and age at peak growth velocity (aPGV) as well as other clinically relevant values such as age at growth cessation and size at cessation. The study used dense, longitudinal craniometric data in the Craniofacial Growth Consortium Study (CGCS), selecting individuals with nine or more serial radiographs. The sample included 5,692 to 6,177 observations from 497 to 548 individuals, depending on sex and trait. The study focused initially on four craniometric traits that define anterior and posterior facial heights as well as palatal and mandibular lengths. Multilevel Bayesian double-logistic growth models were fit separately by sex, allowing all six parameters to vary by individual. This method produces a unique growth curve for each individual, which is simultaneously informed by the population pattern.
Fully parameterized models were fit successfully to four traits in both sexes, and population parameter estimates for these models closely approximated less complex models. The observed growth pattern for each individual was fit much better in the complex model. Across all traits and both sexes, we found a consistent negative correlation between PGV and aPGV ranging from -0.06 to -0.28.
The results show that growth modelling at the individual level is both possible and beneficial, providing insights into the association between determinants of adult morphology. Bayesian approaches are more successful than polynomial- or spline-based models largely due to the parameter constraints imposed by priors. As predicted, a negative correlation was found between PGV and aPGV, indicating that individuals with chronologically early growth spurts have higher PGV.
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