ABSTRACT
When still inside of their mother’s womb, as-yet-unborn babies have their first encounter with statistics, at least in the industrial countries. During ultrasound examinations, anthropometric measurements are taken and compared to the characteristics of children in a reference population. For a given gestational age one can directly compare, say, the femur length of the examined fetus with the femur lengths of all fetuses in the reference population. Too small or too large values may indicate development problems and require an intervention. From a statistical point of view, the question what too small or too large actually means, in precise numbers preferably, arises. Starting in 1955, four large cross-sectional studies on the growth of children
and juveniles were performed in The Netherlands. The fourth study, comprising 7018 girls and 7482 boys up to 21 years old, took place between 1996 and 1997 (Fredriks et al., 2000). One of the aims of this study was the calculation of age-specific reference data, for example for weight, height, or head circumference. In this chapter, we focus on head circumference for boys older than 24 months, the age (in years), and the head circumference (in cm) for five of the 5101 are given in Table 12.1. Our aim here is to construct a so-called growth chart, i.e., the head circumference for age distribution, or, in more technical words, the conditional distribution of head circumference given age. Age-specific quantiles from this distribution tell us how many boys in the reference population have a smaller head circumference compared to the single boy a physician is looking at. One method to estimate conditional quantiles is called Quantile Regression.
