Choice of δ noninferiority margin and dependency of the noninferiority trials

For a two-arm active control clinical trial designed to test for noninferiority of the test treatment to the active control standard treatment, data of historical studies were often used. For example, with a cross-trial comparison approach (also called synthetic approach or lambda-margin approach), the trial is conducted to test the hypothesis that the mean difference or the ratio between the current test product and the active control is no larger than a certain portion of the mean difference or no smaller that a certain portion of the ratio of the active control and placebo obtained in the historical data when the positive response indicates treatment effective. For a generalized historical control approach (also known as confidence interval approach or delta-margin approach), the historical data is often used to determine a fixed value noninferiority margin delta for all trials involving the active control treatment. The regulatory agency usually requires that the clinical trials of two different test treatments need to be independent and in most regular cases, it also requires to have two independent positive trials of the same test treatment in order to provide confirmatory evidence of the efficacy of the test product. Because of the nature of information (historical data) shared in active-controlled trials, the independency assumption of the trials is not satisfied in general. The correlation between two noninferiority tests has been examined which showed that it is an increasing function of (1-lambda) when the response variable is normally distributed. In this article, we examine the relationship between the correlation of the two test statistics and the choice of the noninferiority margin, delta as well as the sample sizes and variances under the normality assumption. We showed that when delta is determined by the lower limit of the confidence interval of the adjusted effect size of the active control treatment (mu(C) - mu(P)) using data from historical studies, dependency of the two noninferiority tests can be very high. In order to control the correlation under 15%, the overall sample