Subset Selection with Curtailment Among Treatments with Two Binary Endpoints in Comparison with a Control

We propose a sequential procedure with a closed and adaptive structure. It selects a subset of size t ( > 0 ) from k ( ≥ t ) treatments in such a way that any treatment superior to the control is guaranteed to be included. All the experimental treatments and the control are assumed to produce two binary endpoints, and the procedure is based on those two binary endpoints. A treatment is considered superior if both its endpoints are larger than those of the control. While responses across treatments are assumed to be independent, dependence between endpoints within each treatment is allowed and modeled via an odds ratio. The proposed procedure comprises explicit sampling, stopping, and decision rules. We demonstrate that, for any sample size n and parameter configuration, the probability of correct selection remains unchanged when switching from the fixed-sample-size procedure to the sequential one. We use the bivariate binomial and multinomial distributions in the computation and derive design parameters under three scenarios: (i) independent endpoints, (ii) dependent endpoints with known association, and (iii) dependent endpoints with unknown association. We provide tables with the sample size savings achieved by the proposed procedure compared to its fixed-sample-size counterpart. Examples are given to illustrate the procedure.