Optimal designs for asymmetric sigmoidal response curves in bioassays and immunoassays

Recent studies show that asymmetric sigmoidal response curves are not uncommonin biomedical studies. For example, the 5-parameter logistic (5PL) model isfrequently used to model and analyze responses from bioassays and immunoassayswhich can be skewed. Various types of optimal experimental designs for 2, 3 and4-parameter logistic models have been reported but not for the more complicated5-parameter logistic (5PL) model. Designs currently used for the 5PL model seemad-hoc with no formal quantitative assessment of their efficiencies. We constructdifferent types of optimal designs for studying various features of the 5PL modeland use them to evaluate efficiencies of commonly used designs in bioassays andimmunoassays. We also create a user-friendly software package to search for optimaldesigns tailor-made to user-specified problems for the 5PL model and evaluaterobustness properties of the design under a variation of criteria, model formsand mis-specification in the nominal values of the model parameters. Our designstrategies can also account for several objectives with varying degrees of importance.As an application, we generate optimal designs for the 5PL model for real studiesin immunoassays and bioassays, and show currently used designs are generallyinefficient for statistical inference