Sample size determination and treatment screening in two-stage phase II clinical trials via ROC curve

In pharmaceutical-related research, we usually use clinical trials methods to identify valuable treatments and compare their efficacy with that of a standard control therapy. Although clinical trials are essential for ensuring the efficacy and postmarketing safety of a drug, conducting clinical trials is usually costly and time-consuming. Moreover, to allocate patients to the little therapeutic effect treatments is inappropriate due to the ethical and cost imperative. Hence, there are several 2-stage designs in the literature where, for reducing cost and shortening duration of trials, they use the conditional power obtained from interim analysis results to appraise whether we should continue the lower efficacious treatments in the next stage. However, there is a lack of discussion about the influential impacts on the conditional power of a trial at the design stage in the literature. In this article, we calculate the optimal conditional power via the receiver operating characteristic curve method to assess the impacts on the quality of a 2-stage design with multiple treatments and propose an optimal design using the minimum expected sample size for choosing the best or promising treatment(s) among several treatments under an optimal conditional power constraint. In this paper, we provide tables of the 2-stage design subject to optimal conditional power for various combinations of design parameters and use an example to illustrate our methods.