Construction of Reference Centiles Using Mean and Dispersion Additive Models

Abstract

Summary. A procedure for constructing 'age'-related reference centiles by flexible modelling of the mean and variance of a dependent variable, assuming normal errors, is described. Both the mean and the variance of the dependent variable are modelled by using either parametric or smooth nonparametric functions of age. This model is a submodel of the more general mean and dispersion additive model (MADAM). Maximum (penalized) likelihood estimation is used for fitting the (non)parametric model. The problem of skewness in the data is dealt with by using a Box-Cox transformation. Flexible and interactive model fitting is provided by a menu-driven GLIM4 library macro called MADAM. A method of model selection is provided which uses the deviance as a measure of the goodness of fit to the data. The method is demonstrated by an example.