Estimating age-related trends in cross-sectional studies using S-distributions

Growth trends in children are often based on cross-sectional studies, in wh ich a sample of the population is investigated at one given point in time. Estimating age-related percentiles in such studies involves fitting data di stributions, each of which is specific for one age group, and a subsequent smoothing of the percentile curves. The first requirement for this process is the selection of a distributional form that is expected to be consistent with the observed data. If a goodness-of-fit test reveals significant disc repancies between the data and the best-fitting member of this distribution al form, an alternative distribution must be found. In practice, there is s eldom an objective argument for selecting any particular distribution. Also , different distributions can yield very similar fits, so that any selectio n is somewhat arbitrary. Finally, the shapes of the observed distributions may change throughout the age range so drastically that no single tradition al distribution can fit them all in a satisfactory manner. To overcome thes e difficulties in population studies, non-parametric smoothing techniques a nd normalizing transformations have been used to derive percentile curves. In this paper we present an alternative strategy in the form of a flexible parametric family of statistical distributions: the S-distribution. We sugg est a method that guides the search for well-fitting S-distributions for gr oups of observed distributions. The method is first tested with simulated d ata sets and subsequently applied to actual weight distributions of girls o f different ages. As far as the results can be tested, they are consistent with observations and with results from other methods. Copyright (C) 2000 J ohn Wiley & Sons, Ltd.