Optimal designs for the Michaelis–Menten model with correlated observations

Abstract

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.

Keywords:

• autoregressive errors
• Michaelis–Menten model
• exact designs
• locally D-optimal designs
• standardized maximin optimal design

AMS Subject Classification:

• 62K05

Acknowledgements

Support by the Collaborative Research Center ‘Statistical modelling of nonlinear dynamic processes’ (SFB 823, Teilprojekt C2) of the German Research Foundation (DFG) is gratefully acknowledged. The authors thank Martina Stein, who typed parts of this manuscript with considerable technical expertise. This paper was written while both authors were at the Isaac Newton Institute, Cambridge, UK during the 2011 programme Design and Analysis of Experiments. The authors are also grateful to two unknown referees for their constructive comments on an earlier version of this paper.