A Global Evaluation of the Probability of Success of an Experiment

PoS, the acronym of Probability of Success, is the expected value of the power function of a test with respect to a design prior distribution, often used in clinical trials for sample size determina- tion. It is easy to check that PoS is the weighted average of an expected probability of a wrong action (rejecting the null hypothesis when true) and of an expected probability of a correct decision (rejecting the null hypothesis when false). This mix may determine underestimation of the chances of success of a trial and unnecessary large sample sizes. Given these drawbacks, we propose a simple modification of PoS that yields a global hybrid Bayesian-frequentist evaluation of success and we explore its impact in terms of sample size.