Inferiority Index, Margin Functions, and Hybrid Designs for Noninferiority Trials with Binary Outcomes

Abstract

In the design of noninferiority (NI) trials with binary outcomes, two basic problems are invariably present. The first problem pertains to the appropriateness of a fixed margin. The two-step fixed margin approach recommended in the Food and Drug Administration (FDA) guidance to industry on NI trials (US FDA, Guidance to industry: non-inferiority clinical trials, 2010) relies on the availability of relevant historical data and expert clinical knowledge and experience to provide the assurance that the derived fixed margin is appropriate. Nonetheless, it still needs an objective measure for assessing its stringency. The FDA approach has its merit in that the fixed margin is determined empirically using the best control response rate and control effect estimates and the best clinical judgment. This feature should be retained in a new design. However, once this fixed margin has been determined, one is faced with the second problem of what appropriate margin to use when the control rate from the NI trial differs from the estimated control response rate. This question was raised by the FDA Anti-infective Division at the November 2011 Anti-infective Advisory Committee meeting. A hybrid design for NI trials with binary outcomes is proposed here that integrates the FDA’s fixed margin approach with a variable margin by applying the theory of inferiority index developed for Bernoulli distributions. The inferiority index is an objective measure of the relative stringency of a margin, and it can be used to define a special margin function that retains the empirical nature of the fixed margin but also allows the margin to vary.