The Imprecision Issues of Four Powers and Eight Predictive Powers with Historical and Interim Data

Imprecision is commonly encountered with respect to powers and predictive powers in clinical trials. In this article, we investigate the imprecision issues of four powers (Classical Power, Classical Conditional Power, Bayesian Power, and Bayesian Conditional Power) and eight predictive powers. To begin with, we derive the probabilities of Control Superior (CS), Treatment Superior (TS), and Equivocal (E) of the four powers and the eight predictive powers, and evaluate the limits of the probabilities at point 0. Moreover, we conduct extensive numerical experiments to exemplify the imprecision issues of the four powers and the eight predictive powers. In the numerical experiments, first, we compute the probabilities of CS, TS, and E for the four powers as functions of the sample size of the future data when the true treatment effect favors control, treatment, and equivocal, respectively. Second, we compute the probabilities of CS, TS, and E for the eight predictive powers as functions of the sample size of the future data under the sceptical prior and the optimistic prior, respectively. Finally, we carry out a real data example to show the prominence of the methods.