A sample-size-optimal Bayesian procedure for sequential pharmaceutical trials.

Consider a pharmaceutical trial where the consequences of different decisions are expressed on a financial scale. The efficacy of the new drug under consideration has a prior distribution obtained from the underlying biological process, animal experiments, clinical experience, and so forth. Berry and Ho (Biometrics 44, 219-227) show how these components are used to establish an optimal (Bayes) sequential testing procedure, assuming a known constant sample size at each decision point. We show in this article how it is also possible to optimize further, with respect to the sample-size rule. This component of the design, which is missing from most sequential procedures, has the potential to yield considerably larger expected net gains (equivalently, considerably smaller Bayes risks).