Bayesian estimation of the binomial parameter in sequential experiments.

This article presents an objective Bayesian approach to estimating the binomial parameter in group sequential experiments with a binary endpoint. The idea of deriving design-dependent priors was first introduced using Jeffreys criterion. Another class of priors was developed based on the reference prior theory. A theoretical framework was established showing that explicit reference to the experimental design in the prior is fully Bayesian justified. Using a design-dependent prior which generalizes the reference prior, I propose a comprehensive and unified approach to the point and the interval estimations in group sequential experiments, and I evidence the good frequentist properties of the posterior estimators through comparative studies with the existing methods. The effect of the prior correction on the posterior estimates is studied in three classical designs of clinical trials. Finally, I discuss the idea of using this approach as a default choice for estimation upon sequential experiment termination.