Conditional type I error rate for superiority test conditioned on establishment of noninferiority in clinical trials

In clinical trials, it is often desirable to test for superiority conditioned on establishment of noninferiority based on the same primary endpoint. According to a guidance document issued by the European regulatory agency Committee for Proprietary Medicinal Products in 2001, no type I error rate adjustment is necessary for switching between superiority and noninferiority because the family-wise type I error rate is controlled at the same nominal level. However, Ng raised the issues of switching between superiority and noninferiority even though there is no inflation of the family-wise type I error rate and showed that the false discovery rate could be increased. To alleviate these concerns, we propose to control the conditional type I error rate of the second-step superiority test at the nominal significance level, which leads to a lower (unconditional) significance level of the secondstep superiority test. The suggested adjustment posts a more rigorous condition to claim superiority, which is an effort to decrease the number of erroneous claims of superiority.