Imprecision issues of two conditional powers and six predictive powers when the sample size of the interim data is fixed

Imprecisions are often encountered for powers and predictive powers in clinical trials. The imprecision issues of two conditional powers (classical conditional power (CCP) and bayesian conditional power (BCP)) and six predictive powers with interim data are investigated in this article. At the beginning, we have evaluated the limits of the probabilities of control superior (CS), treatment superior (TS), and equivocal (E) of the two conditional powers and the six predictive powers at point 0 when the sample size of the interim data is fixed. Moreover, we have conducted extensive numerical experiments to exemplify the imprecision issues of the two conditional powers and the six predictive powers. First, we have computed the probabilities of CS, TS, and E for the two conditional powers when the true treatment effect favors control, treatment, and equivocal, respectively. Second, we have computed the probabilities of CS, TS, and E for the six predictive powers under the sceptical prior and the optimistic prior, respectively. We find that the two conditional powers and the six predictive powers will encounter the imprecision issues as long as the parameter values are properly chosen. Finally, a real data example is given to illustrate the imprecision issues.