Superiority of ROC curves among four powers and eight predictive powers with historical and interim data

The Receiver Operating Characteristic (ROC) analyses of powers and predictive powers play a crucial role in clinical trials, providing valuable insights. We derive analytical expressions for the ROC curves of four powers (Classical Power (CP), Classical Conditional Power (CCP), Bayesian Power (BP), and Bayesian Conditional Power (BCP)) as well as their associated eight predictive powers for both hypotheses and reversed hypotheses. Furthermore, we thoroughly investigate the comparative superiority of these ROC curves across the four powers and eight predictive powers in five distinct aspects. Our findings reveal that among all the considered powers, the second and eighth predictive powers exhibit exceptional performance. Finally, extensive numerical experiments are conducted along with a real data example to comprehensively evaluate the relative merits of these ROC curves.