A modified Wald test for reference scaled assessment of analytical equivalence.

For the reference scaled equivalence hypothesis to reduce the deficiency of the current practice in analytical equivalence assessment, the Wald test with Constrained Maximum Likelihood Estimate (CMLE) of the standard error was proposed to improve the efficiency when the sample sizes of test and reference product lots are small, and variances are unequal. However, by using the Wald test with CMLE standard error, simulations show that the type I error rate is below the nominal significance level. We proposed the Modified Wald test with CMLE standard error by replacing the maximum likelihood estimate of reference standard deviation with the sample estimate (MWCMLE), resulting in further improvement of type I error rate and power over the Wald test with CMLE standard error. In this paper, we further compare the proposed MWCMLE method to the Exact-test-Based (EB) method and the Generalized Pivotal Quantity (GPQ) method with equal or unequal variances, or equal or unequal sample sizes of both product lots. The simulations show that the proposed MWCMLE method outperforms the other two methods in type I error rate control and power improvement.