Summary: 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. D. A. Berry
and C.-H. Ho
[Biometrics 44, No. 1, 219-227 (1988; Zbl 0707.62263
)] 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 how it is also possible to optimize further, with respect to the sample-size rule. This last 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).