Selecting among treatments with two Bernoulli endpoints

In this article we propose a procedure for selecting a random size subset that contains all experimental treatments that are better than the standard. The comparison is made with regard to two binary endpoints. An experimental treatment is considered to be better than the standard if its two endpoints have successful rates higher than standard rates. We assume responses from different treatments are independent, however, responses from each treatment may be associated. We use the odds ratio as the association parameter and describe the bivariate binomial distribution involved in the computation of the probability of a correct selection for our procedure. We derive the design parameters for three different cases: independent endpoints, dependent endpoints with known association and dependent endpoints with unknown association, and provide tables including the minimum sample size needed for the probability requirements to be satisfied.