Bayesian Decision Theory and the Design and Analysis of Randomized Clinical Trials

Traditional approaches to the analyses and sample size determinations for randomized clinical trials are based on tests of hypotheses and rely on arbitrarily set error probabilities and smallest clinically important differences. Recently Bayesian methods have been proposed as an alternative. In particular, many authors have argued that Bayesian decision theory and associated value of information methods can be used to the determine if current evidence in support of a new health care intervention is sufficient for adoption and, if not, the optimal sample size for a future trial. Value of information methods incorporate current knowledge, the value of health outcome, the incidence and accrual rates, time horizon and trial costs, while maximizing the expected net benefit of future patients and providing an operational definition of equipoise. In this chapter value of information methods are developed in detail and illustrated using a recent example from the literature.