A Curve Similarity Index for Testing Parallelism 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 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. A simple and intuitive curve similarity approach is proposed that tests the hypothesis that the sample material is a dilution or concentration of the reference standard. The test is achieved by quantifying the total area between the two curves and provides a single composite measure of parallelism that ranges from 0 to 1. Both a frequentist and a Bayesian approach to the test are provided. A simulation study shows that the curve similarity approach overcomes the drawbacks of the typical methods and is effective at detecting parallelism and non-parallelism for bioassays.