Equivalence Testing for Parallelism in the Four-Parameter Logistic Model

Abstract

For assay or dose-response data in drug discovery, it is often important to test for parallelism of the response curves for two preparations, such as a test drug and a standard drug, in order to determine the potency of the test preparation relative to the standard preparation. A typical approach is to perform a three-degree of freedom approximate F test of the null hypothesis that the relevant parameters are equal for the two preparations. We argue that this problem may be more appropriately viewed as a practical equivalence testing problem, and present an alternative method for testing parallelism in the four-parameter logistic response curve, based on the theory of intersection–union tests. The approach is intuitively appealing and simple to implement using commonly available software, and may provide more appropriate inference for the problem of interest. Two examples are discussed to illustrate the testing approach outlined in this article, and to compare it with the typical approach to testing parallelism. A simulation study is also presented to compare the empirical properties of the two different testing approaches for a set of cases based approximately on one of the examples.

Key Words:

• Calibration
• Dilutional similarity
• Dose-response curve
• Intersection-union test
• Nonlinear model
• Parallel assay

ACKNOWLEDGMENTS

The authors are grateful to the editor and to two anonymous referees for comments that helped greatly improve a previous version of the article.