Monitoring clinical trials: Conditional or predictive power?

At an interim point in a clinical trial, trial organisers may wish to use the data on the initial series of patients to judge the likely consequences of further patient accrual. Halperin and colleagues (Controlled Clin Trials 3:311-323, 1982) have suggested calculating the power of a continued trial, conditional on the data observed so far and the null and alternative hypothesis specified at the start of the trial. Here we argue that this idea should be extended to obtain the predictive power of the trial, derived by averaging the conditional power with respect to the current belief about the unknown parameters. Although numerical methods are generally required for evaluating the necessary integrals, the results may be presented graphically and enable the statistician to answer the question: "With the data so far, what is the chance that the trial will end up showing a conclusive result?".