Some properties of non inferiority tests for two independent probabilities

For exact tests of non inferiority for two independent binomial probabilities, in 1999 Röhmel and Mansmann proved that if a rejection region from an exact test fulfills the Barnard convexity condition, then the corresponding significance level can be computed as the maximum in a subset of the null space boundary. This is particularly important because computing time of significance levels is greatly reduced. Later, in 2000, Frick extended the Röhmel and Mansmann theorem to more general critical regions also corresponding to exact tests. In this article, we generalize Frick's theorem to both exact and asymptotic tests. Like the two theorems mentioned, in this article the resulting theorem also includes, as particular cases, non inferiority hypotheses for parameters such as difference between proportions, proportions ratio, and odds ratio for two independent binomial probabilities. Moreover, proof of this result follows a different line of reasoning than that followed by Frick and is much simpler. In addition, some applications of the main result are provided.