Using ROC Curve for the Quality of Designing a Clinical Trial with Multiple Treatments

Abstract

In pharmaceutical manufacturing, developing a new drug that ensures the post-marketing safety and efficacy is costly and time-consuming, most spent on the process of clinical trials. In clinical trials, one of the objective goals is to identify the valuable treatments among several treatments and to compare the efficacy of them with that of a standard control therapy. To reduce the cost and shorten the duration of the trials, several two-stage designs with interim and final stages have been proposed. After observing the results of interim analysis, it is undesirable to recruit patients to the treatments with little therapeutic effect due to ethical and cost imperative. Thus, conditional power, based on the interim results, has been a feasible method to determine whether these lower efficacious treatments can go to next stage. However, there is a lack of discussions about that the timing of observing result at first stage impacts the conditional power in the literature. In this article, we provide the optimal conditional power (OCP) by using the receiver operating characteristic (ROC) curve to show the quality of a two-stage design with multiple treatments. Also, based on the constraint of the OCP, the optimal design, minimizing the expected sample size, for selecting the promising treatment(s) from multiple treatments is proposed. Tables and an example of the two- stage design subject to OCP for different combinations of parameters are provided.