Testing for consistency in a single multicenter trial

One of the criteria for demonstrating efficacy in a single multicenter trial is that the centers are consistent with respect to the direction and significance of results. The purpose of this research is to discuss the use of the noncentrality parameter delta of an F distribution as a means of testing for the consistency of treatment effects across centers. We state the testing problem as H0: (delta > delta 0) versus H1: (delta < or = delta 0), where delta 0 is prespecified, so that H0 represents inconsistency and H1 consistency. Thus, strong evidence from the sample data is required in order to conclude that the treatment effects are consistent across centers. We discuss reasonable choices for delta 0 and develop the alpha-level, uniformly most powerful and unbiased test, which is equivalent to rejecting H0 if the 100(1 - alpha)% uniformly most accurate and unbiased upper confidence limit for delta is less than or equal to delta 0. We examine other tests based on upper confidence limits, such as those calculated from linear estimators of delta and those calculated from a likelihood approach. We investigate the performance of the tests in a small simulation study and present an example from a four-center clinical trial.