Mathematical modelling of human growth: A comparative study

Kernel regression is a nonparametric procedure that provides good approximations to individual serial data. The method is useful and flexible when a parametric method is inappropriate due to restricted assumptions on the shape of the curve. In the present study, we compared kernel regression in fitting human stature growth with two models, one of which incorporates the possible existence of the midgrowth spurt while the other does not. Two families of mathematical functions and a nonparametric kernel regression were fitted to serial measures of stature on 227 participants enrolled in the Fels Longitudinal Study. The growth parameters that describe the timing, magnitude, and duration of the growth spurt, such as midgrowth spurt and pubertal spurts, were derived from the fitted models and kernel regression for each participant. The two parametric models and kernel regression were compared in regard to their overall goodness of fit and their capabilities to quantify the timing, rate of increase, and duration of the growth events. The Preece-Baines model does not describe the midgrowth spurt. The dervied growth parameters from the Preece-Baines model show an earlier onset and a longer duration of the pubertal spurt, and a slower increase in velocity. The kernel regression with bandwidth 2 years and a second-order polynomial kernel function yields relatively good fits compared with the triple logistic model. The derived biological parameters for the pubertal spurt are similar between the kernel regression and the triple logistic model. Kernel regression estimates an earlier onset and a more rapid increase of velocity for the midgrowth spurt.