Worm Plot: a Simple Diagnostic Device for Modelling Growth Reference Curves

The worm plot visualizes differences between two distributions, conditional on the values of a covariate. Though the worm plot is a general diagnostic tool for the analysis of residuals, this paper focuses on an application in constructing growth reference curves, where the covariate of interest is age. The LMS model of Cole and Green is used to construct reference curves in the Fourth Dutch Growth Study 1997. If the model fits, the measurements in the reference sample follow a standard normal distribution on all ages after a suitably chosen Box-Cox transformation. The coefficients of this transformation are modelled as smooth age-dependent parameter curves for the median, variation and skewness, respectively. The major modelling task is to choose the appropriate amount of smoothness of each parameter curve. The worm plot assesses the age-conditional normality of the transformed data under a variety of LMS models. The fit of each parameter curve is closely related to particular features in the worm plot, namely its offset, slope and curvature. Application of the worm plot to the Dutch growth data resulted in satisfactory reference curves for a variety of anthropometric measures. It was found that the LMS method generally models the age-conditional mean and skewness better than the age-related deviation and kurtosis.