Optimal design in random-effects regression models

An approach is proposed to optimal design of experiments for estimating random-effects regression models. The population designs are defined by the number of subjects and the individual designs to be performed. Cost functions associated with individual designs are incorporated. For a given maximal cost, an algorithm is proposed for finding the statistical population design that maximises the determinant of the Fisher information matrix of the population parameters. The Fisher information matrix is formulated for linear models and normal distributions. The approach is applied to the design of an optimal experiment in toxicokinetics using a first-order linearisation of the model. Several cost functions and designs of various orders are studied. An example illustrates the optimal population designs and the increased efficiency of some optimal designs over more standard designs.