Optimal designs for asymmetric sigmoidal response curves in bioassays and immunoassays

The 5-parameter logistic (5PL) model is frequently used to model and analyze responses from bioassays and immunoassays which can be skewed. Various types of optimal experimental designs for 2, 3 and 4-parameter logistic models have been reported but not for the more complicated 5PL model. We construct different types of optimal designs for studying various features of the 5PL model and show that commonly used designs in bioassays and immunoassays are generally inefficient for statistical inference. To facilitate use of such designs in practice, we create a user-friendly software package to generate various tailor-made optimal designs for the 5PL model and evaluate robustness properties of a design under a variation of criteria, model forms and misspecification in the nominal values of the model parameters.