LOCALLY D-OPTIMAL DESIGNS BASED ON A CLASS OF COMPOSED MODELS RESULTED FROM BLENDING EMAX AND ONE-COMPARTMENT MODELS ⁄

A class of nonlinear models combining a pharmacokinetic compartmental model and a pharmacodynamic Emax model is introduced. The locally D-optimal (LD) design for a 4-parameter composed model is found to be a saturated 4-point uniform LD design with the two boundary points of the design space in the LD design support. For a 5-parameter composed model, a su‐cient condition for the LD design to require the minimum number of sampling time points is derived. Robust LD designs are also investigated for both models. It is found that an LD design with k parameters is equivalent to an LD design with k i1 parameters if the linear parameter in the two composed models is a nuisance parameter. Assorted examples of LD designs are presented. ⁄ Research supported by National Science Foundation (NSF) Grants DMS-0103727, DMS-0603761 and National Institutes of Health (NIH) Grant P50-AT00155 (jointly supported by National Center for Complementary and Alternative Medicine, the O‐ce of Dietary Supplements, the O‐ce of Research on Women’s Health, and National Institute of General Medicine). Any opinions, flndings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily re∞ect the views of the NSF and the NIH.

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