Classical and Bayesian power functions; their use in clinical trials.

The most widely used method for sample size determination in clinical trials is based on the power function. This function expresses the probability of rejecting a statistical null hypothesis on the quantity of interest, typically the unknown difference between the effects of two alternative treatments. The standard classical power function, which we will refer to hereafter as the Conditional Frequentist Power function, does not take into account the following: (a) uncertainty on the design value used for the unknown parameter to compute the power; (b) pre-experimental information on the difference of unknown effects, provided, for instance, by previous clinical studies. By taking into account (a) and (b), several extensions of the power function have been proposed: the Predictive Frequentist Power function, the Conditional and Predictive Bayesian Power functions. We review these methods, their relationships with the standard approach and implications on sample size determination.