Projection from previous studies: a Bayesian and frequentist compromise

We present methods that use the results of a previous study to predict the outcome of a specified comparative trial in which each subject's outcome is categorized dichotomously (e.g., response or no response). The methods can be generalized to other two-sample cases for which power can be calculated (e.g., exponential survival), and to one-sample cases such as demonstrating a minimal response rate or demonstrating superiority to a historic control. Bayesian methods are used on the results of the preliminary study to obtain a posterior distribution representing the state of knowledge of the parameters of interest. This distribution provides the probability that the experimental regimen is superior to the standard by any particular amount. The probability that a future study will demonstrate the superiority of the experimental treatment is obtained by using the posterior distribution to average the power of the test over the parameter space.