Tests for equivalence or noninferiority between two proportions

Bioequivalence between two treatments or two drugs is often assessed by comparing the two proportions (success rate or eradication rate) of binomial outcomes when the conventional pharmacokinetic parameters are inadequate for the assessment. Setting the equivalence limits can be based on one of the three measures: difference, ratio, or odds ratio between the two binomial probabilities. This paper reviews the existing asymptotic test statistics for comparing two independent binomial probabilities in terms of the three measures in the context of equivalence or noninferiority testing. The actual type I error and power of the asymptotic tests are evaluated by enumerating the exact probabilities in the rejection region. The results show that to establish an equivalence between two treatments with an equivalence limit of 20% in difference, a sample size of at least 50 per treatment is needed. When the sample size is sufficient, the actual type I error rate is close to the nominal level (slightly above the nominal level in several cases) for a test in terms of difference for equivalence limits, and it tends to exceed the nominal level for tests in terms of ratio or odds ratio.