A mathematical model in the analysis of the response to growth hormone treatment in pediatric patients with diagnosis of growth hormone deficiency

In the literature, few studies analyze the effect of GH therapy on height, preferring a more indirect approach, where factors influencing the total pubertal and pre-pubertal growth in GH-deficient patients are evaluated and subsequently used to estimate the overall effect at the end of the therapy; unfortunately, this approach does not quantify the real growth gain in treated patients. Using a non-parametric Empirical Bayes approach, our study analyzes the growth response to GH treatment in a homogeneous cohort of 317 patients with pituitary GH deficiency who were enrolled during their pre-pubertal stage in the GH Piedmont Registry (Italy), between January 2000-October 2008, and have at least 2 yr of follow-up. To estimate the growth curve for males and females, a non-parametric regression model was fitted, applying Empirical Bayes techniques. A validation of the model was also performed. Improvement was evident in both genders, since both males and females mean growth curve, which started below the 3^rd percentile at the beginning of the therapy, reached the 10 ^th percentile of the Tanner curve at the end of observation (17 yr old for males and 14 yr old for females); the estimation procedure achieved a good precision. The methodological approach allows for fitting a model able to evaluate longitudinally the response to GH treatment, by means of estimating the overall growth curve, even in presence of sparse information about children heights.