Longitudinal assessment of hormonal and physical alterations during normalpuberty 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 normall y growing boys were evaluated for at least 6 years as they entered and prog ressed through puberty. Each subject was observed during a 24-hr hospital a dmission approximately every 4 months. Standing height was measured upon ar ising. At the same time an early morning (0600hr) serum level of testostero ne 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 statu s. The effect of the chronological age, mean growth hormone, and testostero ne levels on the growth velocity was investigated. In addition to age, the interaction between the mean growth hormone level and testosterone concentr ation has a significant effect on the velocity of growth. Several nonlinear models were explored to describe growth velocity, mean growth hormone leve l, and testosterone concentration in terms of chronological age of each sub ject. 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 p redicted values. The L-2 norm may be unduly influenced by outlying observat ions which commonly occur in many biological data sets. Hence, in addition to the OLS estimators, the least absolute deviation (LAD) estimator which m inimizes the L-2 norm of the observed and the predicted values was also con sidered. Typically, the LAD estimators are more robust than OLS estimators. From a clinical point of view it may be important to know the "normal" val ues of growth velocity, mean growth hormone level, and testosterone at a gi ven age during puberty. For this reason population models for each of these variables along with their 90% confidence regions were developed. These wi ll permit identification of those children who are outside the boundaries o f normal growth for the purpose of evaluation for the etiology of the devia tion. (C) 2000 Wiley-Liss, Inc.