A methodology to [formula omitted]-augment experimental designs

Abstract

One of the main criticisms of optimal experimental designs is that they tend not to adequately meet the practical needs of the experimenter. For example, optimal designs for estimation of the parameters in a model frequently have too few designs points to check the model adequacy, to discriminate between rival models or to estimate a particular function of the parameters. Further, some experimenters like toxicologists have been schooled to using many doses in an animal experiment and there is great resistance to using a design with just a few doses. This paper uses the General Equivalence Theorem to define regions where the practitioner may select points flexibly to augment a design that meets the practical needs more adequately and has a user-specified minimum efficiency requirement. As examples, we demonstrate the usefulness of our theory-based method in various setups using statistical models, such as Antoine’s Equation, the Michaelis–Menten model and a quadratic heteroscedastic model. We also explore the power of the lack-of-fit test for several D-augmented designs in a simulation study. We provide user-friendly codes, either through the R package optedr or through a graphical user interface in Shiny, to facilitate practitioners implement our methodology to find an improved D-augmented designs for their problems.