A fast and reliable test for parallelism in bioassay

Parallelism in bioassay is a synonym of similarity between two concentration–response curves. Before the determination of relative potency in bioassays, it is necessary to test for and claim parallelism between the pair of concentration–response curves of reference standard and test sample. Methods for parallelism testing include p-value-based significance tests and interval-based equivalence tests. Most of the latter approaches make statistical inference about the equivalence of parameters of the concentration–response curve models. An apparent drawback of such methods is that equivalence in model parameters does not guarantee similarity between the reference and test sample. In contrast, a Bayesian method was recently proposed that directly tests the parallelism hypothesis that the concentration–response curve of the test sample is a horizontal shift of that of the reference. In other words, the testing sample is a dilution or concentration of the reference standard. The Bayesian approach is shown to protect against type I error and provides sufficient statistical power for parallelism testing. In practice, however, it is challenging to implement the method as it requires both specialized Bayesian software and a relatively long run time. In this paper, we propose a frequentist version of the test with split-second run time. The empirical properties of the frequentist parallelism test method are evaluated and compared with the original Bayesian method. It is demonstrated that the frequentist method is both fast and reliable for parallelism testing for a variety of concentration–response models.