Choice of lambda-margin and dependency of non-inferiority trials

For a two-arm active control clinical trial designed to test for non-inferiority of the test treatment compared with the active control standard treatment, data of historical studies are often utilized. 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 the ratio of the active control and placebo obtained in the historical data when the positive response indicates treatment effectiveness. The regulatory agency usually requires that the clinical trials of two different test treatments are independent in most regular cases. It also requires, in general, two independent trials of the same test treatment in order to provide confirmatory evidence of the efficacy of the test product. In this article, we derived the relationship between the correlation of the test statistics of two trials with the choice of lambda (the percentage to preserve), the sample sizes and variances under the normality assumption. We showed that the smaller a lambda, the higher the correlation between the two non-inferiority tests. It is further shown that when an 80 per cent or larger lambda is used, the correlation can be controlled to be less than 10 per cent if the variances of the response variables in the current trial are not much smaller than those of the historical studies.