An objective Bayesian approach to estimation in multistage experiments

Abstract

This article presents a Bayesian approach to estimation in multistage experiments based on the reference prior theory. The idea of deriving design-dependent priors was first introduced using Jeffreys’ criterion. A theoretical framework was then established by showing that explicit reference to the design is fully Bayesian justified and Bayesian objectivity cannot ignore such information. Extending the work to multi-parameter problems, a general form of priors was derived from the reference prior theory. In this article, I evidence the good frequentist properties of the reference posterior estimators with normally distributed data. As a notable advance, I address the issue of the point and the interval estimations upon experiment termination. The approach is applied to a data set collected in a clinical trial in schizophrenia with the possibility to stop the trial early if interim results provide sufficient evidence of efficacy or futility. Finally, I discuss the idea of using the reference posterior estimators as a default choice for objective estimation in multistage experiment.