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.