Longitudinal assessment of hormonal and physical alterations during normal puberty in boys. VI. Modeling of growth velocity, mean growth hormone (GH mean), and serum testosterone (T) concentrations.

The growth and hormonal status of 23 prepubertal and early pubertal normally growing boys were evaluated for at least 6 years as they entered and progressed through puberty. Each subject was observed during a 24-hr hospital admission approximately every 4 months. Standing height was measured upon arising. At the same time an early morning (0600hr) serum level of testosterone was obtained. A mean growth hormone level was determined from a pool of equal quantities of serum from 72 samples obtained every 20 min for 24 hr. The early morning testosterone level was used as an index of pubertal status. The effect of the chronological age, mean growth hormone, and testosterone levels on the growth velocity was investigated. In addition to age, the interaction between the mean growth hormone level and testosterone concentration has a significant effect on the velocity of growth. Several nonlinear models were explored to describe growth velocity, mean growth hormone level, and testosterone concentration in terms of chronological age of each subject. Models used were chosen for simplicity, interpretability of the model itself and its parameters, and the ability to estimate (and then test) the parameters. Unknown parameters of the model were estimated using ordinary least squares (OLS), which minimizes the L(2) norm of the observed and the predicted values. The L(2) norm may be unduly influenced by outlying observations which commonly occur in many biological data sets. Hence, in addition to the OLS estimators, the least absolute deviation (LAD) estimator which minimizes the L(1) norm of the observed and the predicted values was also considered. Typically, the LAD estimators are more robust than OLS estimators. From a clinical point of view it may be important to know the "normal" values of growth velocity, mean growth hormone level, and testosterone at a given age during puberty. For this reason population models for each of these variables along with their 90% confidence regions were developed. These will permit identification of those children who are outside the boundaries of normal growth for the purpose of evaluation for the etiology of the deviation. Am. J. Hum. Biol. 12:814-824, 2000. Copyright 2000 Wiley-Liss, Inc.