Strength of evidence of noninferiority trials with the two confidence interval method with random margin

This article deals with the dependency(ies) of noninferiority test(s) when the two confidence interval method is employed. There are two different definitions of the two confidence interval method. One of the objectives of this article is to sort out some of the confusion in these two different definitions. In the first definition the two confidence interval method is considered as the fixed margin method that treats a noninferiority margin as a fixed constant after it is determined based on historical data. In this article the method is called the two confidence interval method with fixed margin. The issue of the dependency(ies) of noninferiority test(s) does not occur in this case. In the second definition the two confidence interval method incorporates the uncertainty associated with the estimation for the noninferiority margin. In this article the method is called the two confidence interval method with random margin. The dependency(ies) occurs, because the two confidence interval method(s) with random margin shares the same historical data. In this article we investigate how the dependency(ies) affects the unconditional and conditional across-trial type I error rates.