  Bayesian inference and the use of posterior or posterior predictive
probabilities for decision making have become increasingly popular in clinical
trials. The current practice in Bayesian clinical trials relies on a hybrid
Bayesian-frequentist approach where the design and decision criteria are
assessed with respect to frequentist operating characteristics such as power
and type I error rate conditioning on a given set of parameters. These
operating characteristics are commonly obtained via simulation studies. The
utility of Bayesian measures, such as ``assurance", that incorporate
uncertainty about model parameters in estimating the probabilities of various
decisions in trials has been demonstrated recently. However, the computational
burden remains an obstacle toward wider use of such criteria. In this article,
we propose methodology which utilizes large sample theory of the posterior
distribution to define parametric models for the sampling distribution of the
posterior summaries used for decision making. The parameters of these models
are estimated using a small number of simulation scenarios, thereby refining
these models to capture the sampling distribution for small to moderate sample
size. The proposed approach toward the assessment of conditional and marginal
operating characteristics and sample size determination can be considered as
simulation-assisted rather than simulation-based. It enables formal
incorporation of uncertainty about the trial assumptions via a design prior and
significantly reduces the computational burden for the design of Bayesian
trials in general.
