Abstract
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.
Keywords
Direct Coverage Control - Generalized Estimation Equations - Incomplete Beta Integral
- Nonlinear Mixed Model - Repeated Measurements - Sequential Diagnostic Process
