Optimal designs for the Michaelis-Menten model with correlated observations

摘要

In this paper we investigate the problem of designing experiments for generalized least-squares analysis in the Michaelis-Menten model. We study the structure of exact D-optimal designs in a model with an autoregressive error structure. Explicit results for locally D-optimal designs are derived for the case where two observations can be taken per subject. Additionally standardized maximin D-optimal designs are obtained in this case. The results illustrate the enormous difficulties to find exact optimal designs explicitly for nonlinear regression models with correlated observations.