Absolute Power Corrupts Absolutely: A Review of the Use of Unconditional Probabilities in the Planning of Clinical Trials

For the most part the planning of a clinical trial involves consideration of the power of a test of a given alternative hypothesis, generally about the relative efficacy of a new treatment compared to a control, based on ideas introduced by Neyman and Pearson in 1933. Shortly thereafter testing they introduced the idea of “resultant power.” The “resultant power” is a weighted average of the powers associate with a finite set of values for the treatment effect. In 1939, Jeffreys pointed out that if the true value of the relative efficacy were unknown, so was the power of the test. Jeffreys suggested that to understand the true power of a study the conditional power values should be averaged with respect to their prior probabilities which gives rise to an unconditional, or absolute, power. The idea was taken up in the 1980’s by Spiegelhalter and colleagues and in the early 2000’s by O’Hagan and Stevens who introduced the concept of assurance which extends the definition of success for an individual study as well as for multiple studies. All of this work uses unconditional as opposed to conditional probabilities. In this chapter I review the concepts that underlie these absolute approaches.