ABSTRACT
In this chapter, we introduce the idea of unconditional, as opposed to conditional power in clinical trials. Unconditional power averages conditional power with respect to the prior distribution of the treatment effect. After the introduction, we provide four different approaches to calculating it: analytic, predictive, numerical integration and simulation. We then review a number of important issues related to average power. The first issue is the boundedness of the average power in which the upper bound is the prior probability that the treatment effect is positive, a probability of interest to drug regulators. The second issue concerns the average power in cases in which a robust mixture prior is used. The third issue is that the average power includes a contribution from values of the treatment effect which correspond to type I errors and more generally includes regions of the treatment effect space which may be regarded as irrelevant since they are less than the minimally clinically important difference. These considerations lead to a decomposition of the average power. Finally, we consider the case when the variance is estimated and the decision rule is based on the t-distribution and develop a numerical method for calculating the average power.
