  This paper explores an approach to Bayesian sample size determination in
clinical trials. The approach falls into the category of what is often called
"proper Bayesian", in that it does not mix frequentist concepts with Bayesian
ones. A criterion for a "successful trial" is defined in terms of a posterior
probability, its probability is assessed using the marginal distribution of the
data, and this probability forms the basis for choosing sample sizes. We
illustrate with a standard problem in clinical trials, that of establishing
superiority of a new drug over a control.
