Asymptotical tests on the equivalence, substantial difference and non-inferiority problems with two proportions

Let d = p(2) - p(1) be the difference between two binomial proportions obtained from two independent trials. For parameter d, three pairs of hypothesis may be of interest: HI: d less than or equal to delta vs. K-1: d > delta; H-2: d is not an element of (delta(1); delta(2)) vs. K-2: d is an element of (delta(1), delta(2)); and H-3: d is an element of [delta(1), delta(2)] vs. K-3: d is not an element of [delta(1),delta(2)], where H-i is the null hypothesis and K-i is the alternative hypothesis. These tests are useful in clinical trials, pharmacological and vaccine studies and in statistics generally. The three problems may be investigated by exact unconditional tests when the sample sizes are moderate. Otherwise, one should use approximate (or asymptotical) tests generally based on a Z-statistics like those suggested in the paper. The article defines a new procedure for testing H-2 or H-3, demonstrates that this is more powerful than tests based on confidence intervals (the classic TOST - two one sided tests - test), defines two corrections for continuity which reduce the liberality of the three tests, and selects the one that behaves better. The programs for executing the unconditional exact and asymptotic tests described in the paper can be loaded at http:H www.ugr.es/similar tobioest/software.htm.