Abstract

Mixed models play an important role in describing observations in healthcare. To keep things simple we only consider linear mixed models, and we are only interested in the typical response, i.e. in the population location parameters. When discussing the corresponding design issues one is often faced with the widespread belief that standard designs which are optimal, when the random effects are neglected, retain their optimality in the mixed model. This seems to be obviously true, if there are only random block effects related to a unit specific level (e.g. random intercept). However, if there are also random effect sizes which vary substantially between units, then these standard designs may lose their optimality property. This phenomenon occurs in the situation of a cross-sectional design, where the experimental setting is fixed for each unit and varies between units, as well as in the situation of a longitudinal design, where the experimental setting varies within units and coincides across units. We will compare the resulting optimal solutions and check their relative efficiencies.