Some Frequentist Properties of a Bayesian Method in Clinical Trials

Abstract Interim analysis in clinical trials involving two treatments are commonplace nowadays. Concerns from different points of view are widely seen in the literature. With a Bayesian approach there is no consideration of type I error and no power calculation. In contrast, there is no difficulty or arbitrariness in picking a prior distribution with a classical approach. In this paper, however, a stopping rule based on the Bayesian approach is discussed from a classical point of view. In specific, we consider application to normal sampling analyzed in stages and demonstrate the role of the prior distributions. In the first part of the paper, we define the stopping rules based on the posterior probabilities. We then develop the stopping boundaries in explicit forms, which can be easily computed with a hand calculator and a standard normal probability distribution table. We also summarize the frequency characteristics of this stopping rule into several results. The major question that is addressed in the second part of the paper is: how will a prior affect the results of a clinical trial study based on the posterior probabilities? The criteria for assessment will be strictly of a Neyman‐Pearson kind. We use N ( v , τ 2 ) as the prior distribution for the difference between treatments, δ. We show that the test is unbiased if v = 0 or τ = ∞. In addition, some rather obvious facts are again summarized into a couple of results. We also discuss, with a table and a figure, the power functions of non‐trivial cases with extreme v and τ using a numerical example.