Resistant cross‐ age smoothing of age‐specific percentiles for growth reference data

Resistant delineation, a technique adapted from exploratory data analysis (Tukey, Exploratory Data Analysis, 1977), was applied to smooth age-specific percentiles for triceps skinfold thickness across ages from 1 to 20 years. Row percentiles were transformed to logarithms to promote symmetry and to render variability more nearly homogeneous across ages. The delineation involved smoothing resistantly the sequences of age-specific log medians and the sequence of age-specific positive differences between the "4253H, twice" (Velleman, J. Am. Statist. Assoc., 75:609-615, 1980). The delineation concluded by recombining these smoothed sequences to obtain smoothed percentiles in the log scale. Finally, the logarithmic transformation was reversed, yielding the smoothed age-specific percentiles. Comparisons of smoothed results from resistant, delineation with the original data indicated a satisfactory fit. Comparisons with published smoothed percentiles, obtained from the same data by a cubic-spline procedure, showed that the resistant delineation captured the structure of the raw data better than the cubic-spline procedure. The resistant delineation procedure makes few assumptions of the underlying data, it ensures a proper order relationship among the smoothed percentiles, it is relatively insensitive to isolated unusual data, and it is available in a common software package.