Large sample tests for simultaneous comparison to multiple controls in terms of binomial proportions

A problem of illustrating simultaneous superiority of a certain treatment over three (or more) controls in terms of binomial proportions is considered. Applications of nine large sample intersection-union tests are discussed. The tests include the Min tests based on Wald, pooled, and Falk and Koch (1998) tests for the differences between two proportions, and their adjustments via Berger and Boos (1994) and Röhmel and Mansmann (1999) methods. Results of a large simulation study conducted to compare the proposed tests in terms of their Type I error rate and power and investigate proximity of the proposed approximate power and alternative approaches to estimate the minimum required sample size for balanced designs are discussed.