A geometric characterization of optimal designs for regression models with correlated observations


Holger Dette, Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany.
Email: holger.dette@rub.de


Summary.  We consider the problem of optimal design of experiments for random-effects models, especially population models, where a small number of correlated observations can be taken on each individual, whereas the observations corresponding to different individuals are assumed to be uncorrelated. We focus on c-optimal design problems and show that the classical equivalence theorem and the famous geometric characterization of Elfving from the case of uncorrelated data can be adapted to the problem of selecting optimal sets of observations for the n individual patients. The theory is demonstrated by finding optimal designs for a linear model with correlated observations and a non-linear random-effects population model, which is commonly used in pharmaco-kinetics.