Locally D-optimal designs based on a class of composed models resulted from blending Emax and one-compartment models

TL;DR

This paper develops locally D-optimal designs for nonlinear pharmacokinetic-pharmacodynamic models, identifying specific design structures and conditions for minimal sampling, and explores robustness and parameter nuisance effects.

Contribution

It introduces a class of composed models combining Emax and one-compartment models and derives explicit LD design strategies, including conditions for minimal sampling and robustness considerations.

Findings

LD design for four-parameter model is a four-point uniform design with boundary points

For five-parameter models, minimal sampling conditions are established

LD designs with k parameters are equivalent to those with k-1 parameters when a linear parameter is nuisance

Abstract

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 four-parameter composed model is found to be a saturated four-point uniform LD design with the two boundary points of the design space in the LD design support. For a five-parameter composed model, a sufficient 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 $k-1$ parameters if the linear parameter in the two composed models is a nuisance parameter. Assorted examples of LD designs are presented.