Age-related reference ranges for growth parameters

We propose an approach to the computation of age-related reference ranges which guarantees that the proportion of sampled data points covered by the reference band has an arbitrarily specified value. Unlike other approaches in the literature, this method does not have to rely on parametric distributional assumptions. The boundaries of the bands are given by smooth curves, and for modeling the mean as a function of age, a sufficiently flexible class of monotonically increasing functions is used, since in the applications all measured variables are biological growth parameters. The width of the reference band is allowed to be proportional to any suitably fixed function of age which we propose in practice to be taken linear. The approach is illustrated by examples from a large-scale study of the distribution of fetal size measurements obtained by routine prenatal sonography.