Analytical calculations of various powers assuming normality

Abstract

Assuming normality for the prior and the likelihood, we calculate the rejection region, the power or the conditional power, and the predictive power or the conditional predictive power of one-sided hypotheses with a nonzero threshold that corresponds to a noninferiority test for two-arm trials for five different scenarios, which are nonsequential trials with classical power and Bayesian power and sequential trials with hybrid predictions, Bayesian predictions, and classical predictions. The rejection regions and the powers of one-sided hypotheses with a zero threshold that corresponds to a superiority test for two-arm trials are also obtained. Then the calculations of the various powers are illustrated through two examples. The article can be regarded as a reference manual for researchers interested in power calculations of one-sided hypotheses with a nonzero or zero threshold for the five different scenarios assuming normality for the prior and the likelihood.