When we design a Phase III trial, sample size is determined by the values of α, power = 1-β, and the anticipated treatment effect D. Traditionally, we treat D as a fixed constant. Is it more realistic to treat D as random? In general, the choice of the distribution for D is pretty subjective. In this lecture, we will consider the distribution being determined by the results of a Phase II study with the same endpoint. Under normality, there exists a simple formula for the evaluation of sample size for the Phase III study. We will use numerical examples to explore the limit of this approach, as well as the Bayesian explanation for the corresponding prior belief.
The same idea applies to the evaluation of conditional power, and its extension to the concept of average conditional power.