Noninferiority trials without a placebo arm often require an indirect statistical inference for assessing the effect of a test treatment relative to the placebo effect or relative to the effect of the selected active control treatment. The indirect inference involves the direct comparison of the test treatment with the active control from the noninferiority trial and the assessment, via some type of meta-analyses, of the effect of the active control relative to a placebo from historical studies. The traditional within-noninferiority-trial Type I error rate cannot ascertain the statistical risks associated with the indirect inference, though this error rate is of the primary consideration under the frequentist statistical framework. Another kind of Type I error rate, known as across-trial Type I error rate, needs to be considered in order that the statistical risks associated with the indirect inference can be controlled at a small level. Consideration of the two kinds of Type I error rates is also important for defining a noninferiority margin. For the indirect statistical inference, the practical utility of any method that controls only the across-trial Type I error rate at a fixed small level is limited.

For two-period crossover trials where the residual carryover can only exist in the presence of treatment effect, Willan (1988, Biometrics 44, 211-218) recommended use of the maximum test statistic that chooses the analysis with the larger test statistic corresponding to the parallel analysis and the crossover analysis. We construct two alternative two-stage test procedures, based on Grizzle's approach, that maintain the actual type I error rate at the desirable level. The power, accuracy, and precision of the analysis based on the modified two-stage procedures are compared to those based on the parallel analysis, crossover analysis, and the maximum test statistic.