• Correlated observations;
  • Dose-finding studies;
  • Heteroscedastic regression;
  • Locally optimal design;
  • Multiplicative algorithms;
  • Population pharmacokinetics;
  • Random effects

Summary Random effects models are widely used in population pharmacokinetics and dose-finding studies. However, when more than one observation is taken per patient, the presence of correlated observations (due to shared random effects and possibly residual serial correlation) usually makes the explicit determination of optimal designs difficult. In this article, we introduce a class of multiplicative algorithms to be able to handle correlated data and thus allow numerical calculation of optimal experimental designs in such situations. In particular, we demonstrate its application in a concrete example of a crossover dose-finding trial, as well as in a typical population pharmacokinetics example. Additionally, we derive a lower bound for the efficiency of any given design in this context, which allows us on the one hand to monitor the progress of the algorithm, and on the other hand to investigate the efficiency of a given design without knowing the optimal one. Finally, we extend the methodology such that it can be used to determine optimal designs if there exist some requirements regarding the minimal number of treatments for several (in some cases all) experimental conditions.