A Reference Scaled Difference in Means Approach to Equivalence Test for Binary Clinical Outcomes

Abstract

A proposed generic drug product needs to be compared with some reference product through equivalence test to support marketing approval. One important type of treatment outcome is the binary response indicating whether a favorable outcome is achieved. The binary response rates of the test and reference treatments are often compared via their difference with some margin. While the difference can usually be estimated in a clinical study, it is frequently difficult to determine a proper margin. Existing approaches suggest a fixed margin or a margin as a function of the reference response rate, such as step-wise constant margin, piece-wise smooth margin, etc. The issues with existing margin choices were discussed recently and a variable margin was proposed for non-inferiority test, which is a constant multiple of the standard deviation of reference response rate. In this paper, we extended the discussion to equivalence test, which can be formulated as two one-sided tests. Our discussion revealed some unique features of the equivalence test for binary responses with a variable margin. For instance, this approach may improve power control when the reference product has a high response rate. On the other hand, when both sample size and margin multiplier is small, the rejection rate of the equivalence test is nearly zero.