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

This paper proposes a closed adaptive sequential procedure for selecting a random-sized subset of size $t(>0)$among $k (\ge t)$ experimental treatments so that the selected subset contains all treatments superior to the control treatment. 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 its both 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 show that for any sample size n and any parameter configuration, the sequential procedure maintains the same probability of correct selection as the corresponding fixed-sample-size procedure. 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.