Mixed noninferiority margin and statistical tests in active controlled trials

In an active controlled noninferiority trial without a placebo arm, one of the major considerations is the selection of the noninferiority margin. Although the ICH E10 guideline provides general principles for the selection of appropriate noninferiority margins, there are no established rules or gold standards for the selection of noninferiority margins in active control trials. Hung et al. (2003) proposed a margin selection based on relative risk. However, with relative risk, it is difficult to adjust for covariates. On the other hand, Chow and Shao (2006) proposed a method for selecting noninferiority margins based on treatment difference. The determination of noninferiority margin based on either a test for treatment difference or a test for relative risk would be critical. In this paper, we propose a method for noninferiority testing with the use of a mixed null hypothesis. The mixed null hypothesis consists of a margin based on treatment difference and a margin based on relative risk. Both noninferiority margins will simultaneously satisfy the principles as described in the ICH E10 guideline. Statistical tests for mixed noninferiority margin are also derived. An example concerning the efficacy of a test therapy to an active control on a clinical adverse event in the target patient population with cardiovascular disease is presented to illustrate the proposed method. Simulation studies were also conducted to assess the type I error rate and the power.