Development and testing of multilevel models for longitudinal craniofacial growth prediction

The aims of this study were to (1) develop longitudinal growth curves that would allow individual variations to be accurately modeled and (2) use these models to predict craniofacial growth changes in children with varying amounts of longitudinal data available.

Based on a sample of 159 girls (994 cephalograms) and 128 boys (947 cephalograms), multilevel population models were derived. Polynomial models of the population's growth curve were derived for the measurements MPA, Me-X, Me-theta, Me-Y, and Me-R. Angular and horizontal measures (MPA, Me-X, and Me-theta) were described by simpler, second-order models, and vertical measures (Me-Y and Me-R) were described by more complex, fifth-order models.

Decreases in MPA during childhood and increases in Me-theta during adolescence could be explained by the relative contributions of the horizontal (Me-X) and vertical (Me-Y) movements of menton. There was greater anterior movement of menton during childhood and greater inferior movement during the adolescent growth spurt. By using varying numbers of longitudinal cephalograms between 6 and 10 years of age, the models were used to predict subjects' craniofacial growth changes from ages 10 to 15. Based on correlations, root mean squared error, and percent accuracy, individual growth predictions for the various measures were found to be highly accurate on an independent subsample drawn from the larger sample and on an independent validation sample. Correlations between predicted and actual values on the sample used to develop the models ranged from 0.81 to 0.95. Accuracy was best for the measurements that changed the most during the prediction period (Me-Y and Me-R), with accuracies between 83% and 90%. More longitudinal data did not increase the predictive accuracy for all measurements. The models that were least accurate (Me-X, MPA, and Me-theta) showed the greatest improvement in prediction accuracy with more longitudinal data. These improvements ranged from 1.6% to 15%.

Longitudinal growth curves based on multilevel procedures can accurately describe population and individual growth curves, and 5-year predictions with this method are highly accurate and externally valid.