Design of experiments for the Monod model : robust and efficient designs

In this paper the problem of designing experiments for a model which is called Monod model and is frequently used in microbiology is studied. The model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, environmental research, pharmacokinetics, and plant physiology. The designs presented so far in the literature are locally optimal designs, which depend sensitively on a preliminary guess of the unknown parameters, and are for this reason in many cases not robust with respect to their misspecification. Uniform designs and maximin optimal designs are considered as a strategy to obtain robust and efficient designs for parameter estimation. In particular standardized maximin D- and E- optimal designs are determined and compared with uniform designs, which are usually applied in these microbiological models. It is shown that standardized maximin optimal designs are always supported on a finite number of points and it is demonstrated that maximin optimal designs are substantially more efficient than uniform designs. Parameter variances can be decreased by a factor two by simply sampling at optimal times during the experiment. Moreover, the maximin optimal designs usually provide the possibility for the experimenter to check the model assumptions, because they have more support points than parameters in the Monod model.