Sample size determination for equivalence trials

In clinical practice we are usually interested in showing that an innovative therapy is more effective than a standard one. However, in some cases we have to respond to the different purpose of proving equivalence of two competing treatments (equivalence trials). For example, when a pharmaceutical company is aware that there is not evidence enough for proving superiority of a new treatment, it can decide to go for equivalence. The idea is that the new drug has chances to be approved and put on the market if it guarantees at the same time other advantages, for instance in terms of safety or costs. In this paper we refer to the setting of equivalence trials, with specific regard to the issue of sample size determination (SSD). First step is to define the so called equivalence interval I, that is a set of values of the parameter of interest indicating a negligible difference between the treatments effects. Hence, we declare success if an interval estimate of θ is entirely included in I. By adapting the metodology presented in Brutti and De Santis (2008) to equivalence trials, we derive two alternative SSD criteria based on Bayesian credible intervals. In particular we consider the so-called two priors approach (see Wang and Gelfand, 2002): on the one hand pre-experimental information is represented by the analysis prior, on the other hand uncertainty on the target value θ D – that is chosen in the range of equivalence – is modeled by the design prior. Finally, we also consider a robust version of the above criteria in which the single analysis prior is replaced by a suitable class of prior distribution. In this work we derive results for the normal model with conjugate priors, illustrating an application, based on a real example by Spiegelhalter et al. (2004).