Age-related reference regions for longitudinal measurements of growth characteristics

Most studies on age-related reference centiles published up to now have adopted a strictly cross-sectional perspective. Clearly, the results of studies of that type do not provide a tool for the diagnostic assessment of whole series of measurements taken sequentially over time in the same individual. In this paper, the approach of Wellek & Merz (1995) to the construction of age-dependent reference ranges for cross-sectional measurements is generalized in such a way that data sets containing time series of arbitrary length varying between subjects can be accommodated. Since repeated measurements on the same subject are typically correlated, the regression function to be used as the central line for the reference band eventually obtained is determined by fitting a nonlinear mixed model describing the dependence of conditional means on age by growth functions of the same class we proposed in the case of cross-sectional data. Estimation of the parameters of this mixed model is done in a way closely related to the population-averaged GEE approach by Zeger et al. (1988). Given the regression line, the reference band is constructed by means of an iterative procedure guaranteeing that the proportion of observed profiles which nowhere leave the band, has some prespecified value (frequently set equal to 90% in practice). The approach is illustrated with two examples taken from child psychiatry and prenatal sonography.