Pre-Posterior Distributions in Drug Development and Their Properties

The topic of this article is pre-posterior distributions of success or failure. These distributions, determined before a study is run and based on all our assumptions, are what we should believe about the treatment effect if we are told only that the study has been successful, or unsuccessful. I show how the pre-posterior distributions of success and failure can be used during the planning phase of a study to investigate whether the study is able to discriminate between effective and ineffective treatments. I show how these distributions are linked to the probability of success (PoS), or failure, and how they can be determined from simulations if standard asymptotic normality assumptions are inappropriate. I show the link to the concept of the conditional $PoS$ introduced by Temple and Robertson in the context of the planning of multiple studies. Finally, I show that they can also be constructed regardless of whether the analysis of the study is frequentist or fully Bayesian.