Journal of Data Science

Abstract: Testosterone levels decline as men age. There is little consensus on what testosterone levels are normal for aging men. In this paper, we estimate age-specific prevalence of testosterone deficiency in men using nor mal mixture models when no generally agreed on cut-off value for defining testosterone deficiency is available. The Box-Cox power transformation is used to determine which transformation is most appropriate for correcting skewness in data and best suits normal mixture distributions. Parametric bootstrap tests are used to determine the number of components in a normal mixture.

Abstract: Two-part random effects models have been used to fit semi-continuous longitudinal data where the response variable has a point mass at 0 and a con tinuous right-skewed distribution for positive values. We review methods pro posed in the literature for analyzing data with excess zeros. A two-part logit-log normal random effects model, a two-part logit-truncated normal random effects model, a two-part logit-gamma random effects model, and a two-part logit-skew normal random effects model were used to examine effects of a bottle-weaning intervention on reducing bottle use and daily milk intake from bottles in toddlers aged 11 to 13 months in a randomized controlled trial. We show in all four two-part models that the intervention promoted bottle-weaning and reduced daily milk intake from bottles in toddlers drinking from a bottle. We also show that there are no differences in model fit using either the logit link function or the probit link function for modeling the probability of bottle-weaning in all four models. Furthermore, prediction accuracy of the logit or probit link function is not sensitive to the distribution assumption on daily milk intake from bottles in toddlers not off bottles.