Testing a noninferiority hypothesis: what to anticipate when the adverse event is rare

While randomized controlled trials may not be considered efficient for investigating rare adverse events based on their size, biases associated with other epidemiological designs may justify the additional resources. In certain contexts it may be appropriate, for example, to inflate the noninferiority (NI) margin to decrease the sample size, provided the excess risk that will be ruled out remains clinically relevant. The implication of a reduced sample size on the number of events anticipated from the trial is often not considered at the study design phase but may have important ramifications. To assess the implications of modifying study design parameters, approximations are presented for (a) how likely it is that no events will be observed, (b) how many events should be anticipated, and (c) how likely it is that v or more events will be observed. The approximations presented are intended to serve as tangible a priori expectations from the study. This work is motivated from an FDA Advisory Committee meeting regarding a discussion at the association between long-acting beta-agonists and asthma-related deaths.