Standardized maximim D-optimal designs for enzyme kinetic inhibition models

Abstract

Locally optimal designs for nonlinear models require a single set of nominal values for the unknown parameters. An alternative is the maximin approach that allows the user to specify a range of values for each parameter of interest. However, the maximin approach is difficult because we first have to determine the locally optimal design for each set of nominal values before maximin types of optimal designs can be found via a nested optimization process. We show that particle swarm optimization (PSO) techniques can solve such complex optimization problems effectively. We demonstrate numerical results from PSO can help find, for the first time, formulae for standardized maximin D-optimal designs for nonlinear model with 3 or 4 parameters on the compact and nonnegative design space. Additionally, we show locally and standardized maximin D-optimal designs for inhibition models are not necessarily supported at a minimum number of points. To facilitate use of such designs, we create a web-based tool for practitioners to find tailor-made locally and standardized maximin optimal designs.