A New Method for the Comparison of Powers of Noninferiority Exact Tests for the Difference of Proportions

Noninferiority tests for comparing 2 proportions are frequently used in clinical trials to prove that a new drug with few side effects or low cost is not significantly inferior in efficacy to the standard drug. In the literature, the reported comparisons of powers of noninferiority tests are based on simulations or gross approximations. By using the concept of “mean power,” Martín-Andrés and Silva-Mato developed a new method to compare the powers of superiority tests for the difference of proportions. In the present article, this method is extended to the comparison of powers of noninferiority exact tests for trials with equal sample sizes. To illustrate this new method, we have compared 2 popular noninferiority exact tests for the difference of proportions: the likelihood ratio test and the Farrington-Manning test. The conclusion is that the likelihood ratio test has greater mean power than the Farrington-Manning test.