A curve similarity approach to parallelism testing in bioassay

Potency determination via bioassay is a relative measure that requires an evaluation of parallelism between the dose–response relationships of a reference standard and a sample material. Typical approaches for assessing parallelism include difference (p-value) and equivalence tests. These traditional methods rely on a statistical assessment of model parameters as opposed to direct evaluation of the similarity of the dose–response curves. We propose a simple curve similarity approach that tests the hypothesis that the sample material is a dilution or concentration of the reference standard. The test is achieved by quantifying and normalizing the total area between the two curves and provides a single composite measure of parallelism. Both a frequentist and a Bayesian approach to the test are provided. We show through a simulation study that the curve similarity approach overcomes the drawbacks of the traditional methods and is effective at detecting parallelism and non-parallelism for bioassays.