Parallelism of four-parameter logistic bioassay models: equivalence testing for parameter differences*

Parallelism is a prerequisite assumption that the test product behaves like dilution or concentration of the reference product since this biological similarity is the basis for defining the relative potency of the test product to the reference standard. Once the parallelism between test and reference dose-response curves is established, the relative potency remains constant across any effective response levels. Traditionally, parallelism in four-parameter logistic models is assessed using equivalence testing approach based on fixed margins (0.8 to 1.25) for ratios of parameters. However, due to fixed margins, the statistical power of this approach decreases significantly as the coefficient of variation in response data increases. An equivalence test with the equivalence margin determined by the tolerance interval for the ratio of slopes derived from historical data was proposed for the parallelism testing of two straight lines in the literature. However, under the normality assumption for the estimate of each parameter, the ratio of estimates for two parameters is not normally distributed. To determine the tolerance limits for the ratio of slopes, one needs to rely on a complicated procedure with modern technology. As an alternative, we propose the use of parameter difference-based equivalence tests with margins determined from historical data analyzed with the four-parameter logistic model. Simulation studies are conducted to evaluate the proposed method's ability to identify parallelism and non-parallelism across various scenarios.