Bioassay case study applying the maximin D‐optimal design algorithm to the four‐parameter logistic model

Abstract

Cell-based potency assays play an important role in the characterization of biopharmaceuticals but they can be challenging to develop in part because of greater inherent variability than other analytical methods. Our objective is to select concentrations on a dose-response curve that will enhance assay robustness. We apply the maximin D-optimal design concept to the four-parameter logistic (4 PL) model and then derive and compute the maximin D-optimal design for a challenging bioassay using curves representative of assay variation. The selected concentration points from this 'best worst case' design adequately fit a variety of 4 PL shapes and demonstrate improved robustness.

Optimal designs for asymmetric sigmoidal response curves in bioassays and immunoassays

“…Chen et al 20 provide examples of minimax and standardized minimax optimal designs, including showing how locally optimal designs are first determined before a standardized minimax optimal design is found. Recent work on maximin optimal designs, which are equivalent to minimax optimal designs, and Bayesian optimal designs are Coffey 21 and McCallum and Bornkamp, 22 respectively, among others. For space consideration, these two approaches will not be further discussed here.…”

Standardized maximim D -optimal designs for enzyme kinetic inhibition models

“…Ref. [15] constructed maximin D -optimal designs for a bioassay study using the four-parameter logistic model. However, his approach was not based on theory and the optimal designs were found under a restrictive setting so that the resulting designs are not truly maximin optimal.…”