Generalised Binomial Models to Examine the Historical Control Assumption in Active Control Equivalence Studies

Active control equivalence studies, with the goal of demonstrating therapeutic equivalence between a new and an active control treatment, are becoming more widespread due to current therapies that reflect previous successes in the development of new treatments. An important feature of such studies is the reliance on an implicit 'historical control assumption'; that is, whether the active control would have performed significantly better than a placebo, had a placebo been used in the trial. A quantitative approach to examine this assumption is described in our paper. Generalised binomial models are proposed to model overdispersed and underdispersed binomial data. Goodness-of-fit tests are described to test whether the binomial distribution is sufficient or whether a more general model is needed to evaluate the historical control assumption. These methods are illustrated using one-week mortality data following myocardial infarction. The steps we describe to establish the superiority of an active control relative to placebo are recommended in the design and interpretation of active equivalence control studies.