Testing for parallelism in the heteroscedastic four-parameter logistic model

For bioassay data in drug discovery and development, it is often important to test for parallelism of the mean response curves for two preparations, such as a test sample and a reference sample in determining the potency of the test preparation relative to the reference standard. For assessing parallelism under a four-parameter logistic model, tests of the parallelism hypothesis may be conducted based on the equivalence t-test or the traditional F-test. However, bioassay data often have heterogeneous variance across dose levels. Specifically, the variance of the response may be a function of the mean, frequently modeled as a power of the mean. Therefore, in this article we discuss estimation and tests for parallelism under the power variance function. Two examples are considered to illustrate the estimation and testing approaches described. A simulation study is also presented to compare the empirical properties of the tests under the power variance function in comparison to the results from ordinary least squares fits, which ignore the non-constant variance pattern.