  Bayesian predictive probabilities are commonly used for interim monitoring of
clinical trials through efficacy and futility stopping rules. Despite their
usefulness, calculation of predictive probabilities, particularly in
pre-experiment trial simulation, can be a significant challenge. We introduce
an approximation for computing predictive probabilities using either a p-value
or a posterior probability that significantly reduces this burden. We show the
approximation has a high degree of concordance with standard Monte Carlo
imputation methods for computing predictive probabilities, and present five
simulation studies comparing the approximation to the full predictive
probability for a range of primary analysis strategies: dichotomous,
time-to-event, and ordinal endpoints, as well as historical borrowing and
longitudinal modeling. We find that this faster method of predictive
probability approximation works well in all five applications, thus
significantly reducing the computational burden of trial simulation, allowing
more virtual trials to be simulated to achieve greater precision in estimating
trial operating characteristics.
