Multiple comparisons procedures for comparing several treatments with a control based on binary data

In this paper, we examine three approaches for comparing several treatments with a control with use of binary response data. The first approach relies on asymptotic theory applied to the Freeman-Tukey transformation of the observed proportions. The second finds an acceptance region based on the binomial distributions estimated under the joint null hypotheses. The third approach applies Dunnett's procedure to the binary data. We evaluated the actual overall type I error rates of the Freeman-Tukey test and Dunnett's procedure using both simulation and binomial calculations while we assessed those of the binomial approach using simulation. Based upon their capability to preserve the desirable overall type I error rate, we provide recommendations regarding the choices among the three approaches for various occasions. In addition, we provide comments on the power of these three approaches.