A Bayesian Approach to Show Assay Equivalence with Replicate Measurements Over a Specified Response Range

Abstract

Drug discovery scientists routinely develop and use in-vitro assays; for example, to identify “hits,” or to quantify the efficacious concentrations of compounds in a lead series. New and improved assays are developed to replace existing ones as the new assays may be cheaper, faster, or easier to use. An existing assay typically cannot be replaced until the new format is determined to produce equivalent measurements to the original on a test set of compounds with a diverse range of activity. In this article we propose two definitions for assessing assay equivalence across a range of responses, and apply Bayesian methods to estimate the probability of assay equivalence. Data are modeled via orthogonal regression for the case where the relative variability of the two assays is unknown a priori, and replicate measurements for each assay and compound are sufficient to identify the full set of model parameters in a likelihood model. The article reports results of a simulation experiment to explore the performance of the two metrics for testing assay equivalence under a variety of experimental designs and model parameter settings. These metrics measure similarity over a predefined assay range. This range provides a practical and focused measure of similarity which also has the effect of rendering the resulting measures robust to various distribution forms over the range of interest. The two metrics are also applied to a real data example to test equivalence between two in-vitro assays.

Keywords:

• Equivalence test
• Gibbs sampling
• Measurement error
• Orthogonal regression

Acknowledgments

Thanks to Daniel Gillie (GlaxoSmithKline) for generously donating his dataset. Thanks also to the reviewers whose helpful comments helped to clarify key points in this article.