Phase variation in child and adolescent growth.

Child growth is characterised by increases in height, and increases in maturational status. Functional data analysis provides a tool to separate these two sources of variation (registration) and differentiates between the variation in maturational tempo (temporal, or “phase” variation) and the variation in height (amplitude variation). We extended this concept by combining Principal Component Analysis (PCA) and the Maximum Likelihood Principle. Longitudinal data on height were obtained from two large growth studies from Lublin, Poland, and Zurich, Switzerland, with altogether 361 children. Variation in amplitude monotonically rises with age; variation in phase peaks during puberty. During mid-puberty, phase variation is large and explains up to 40 percent of total height variance in girls, and up to 50 percent in boys. Eight amplitude and 4 phase components appeared biologically significant. The largest amplitude component explained 91% of the amplitude variance and is characterised by an almost horizontal pattern. The largest phase component explained 66% (boys) and 63% (girls) of phase variance, rises throughout childhood and reaches up to 0.85 years in adolescent boys, and up to 0.75 years in adolescent girls. Phase components significantly correlated with the clinical signs of puberty. The combination of PCA and the Maximum Likelihood Principle provides a new, powerful and automatic tool for growth modelling that includes estimates of future growth, adult stature and developmental tempo. Preliminary results indicate that this approach can be used for automatised screening purposes.