On the lower predictive bound approach for noninferiority clinical trials with binary data

Clinical trials are mostly designed to provide data that allow direct inference of the underlying hypotheses. This, however, is not the case for noninferiority trials where placebo controls are absent due to ethical considerations, resulting in the need for indirect inference about the underlying hypotheses of the treatment effect of a new drug against a putative placebo control. In particular, the European Committee for Medicinal Products for Human Use (CHMP) guideline for noninferiority trials requires indirect confidence bounds for the "putative" effect of the new drug. To meet this requirement, we develop a new approach by which the lower predictive bound of a given confidence level is used to determine the noninferiority margin. For this approach, we provide methods for calculating the sample size and for making indirect statistical inference (i.e., p-values, confidence intervals, and point estimates) on the putative effect of the new test drug. For an actual trial example, we assess designs by the lower predictive bound approach as well as other approaches for determining noninferiority margins.