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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).

This study takes a statistical-modeling point of view to the assessment of health care services and procedures. The emphasis is on small-area prediction of incidence rates from spatially contiguous regions, although suitable modifications can also give doctor-level predictions. The main idea is to recognize the individuality of each region through a spatial Bayesian model for incidence rates. A noise component, because of location error and measurement error, is filtered out using empirical Bayes methods. The resulting smoothed predictors of incidence rates provide an accurate picture of the health care service or procedure under investigation.