Non-inferiority tests for binary endpoints with variable margins

Non-inferiority comparison between binary response rates of test and reference treatments is often performed in clinical studies. The most common approach to assess non-inferiority is to compare the difference between the estimated response rates with some margin. Previous methods use a variety of margins, including fixed margin, step-wise constant margin, and piece-wise smooth margin, where the latter two are functions of the reference response rate. The fixed margin approach assumes that the margin can be determined from historical trials with the consistent difference between the reference treatment and placebo, which may not be available. The step-wise constant margin approach suffers discontinuity in the power function which can cause trouble in sample size determination. Furthermore, many methods ignore the variability in margins dependent on the estimated reference response rate, leading to poor type I error control and power function approximation. In this study, we propose a variable margin approach to overcome the difficulties in fixed and step-wise constant margin approaches. We discuss several test statistics and evaluate their performance through simulation studies.