A Note on repeated p-values for group sequential designs

One-sided confidence intervals and overall p-values for group-sequential designs are typically based on a sample space ordering which determines both the overall p-value and the corresponding confidence bound. Accordingly, the strength of evidence against the null hypothesis is consistently measured by both quantities such that the order of the p-values of two distinct sample points is consistent with the order of the respective confidence bounds. An exception is the commonly used repeated p-values and repeated confidence intervals. We show that they are not ordering-consistent in the above sense and propose an alternative repeated p-value which is ordering-consistent and has the monitoring property of the classical repeated p-value in being valid even when deviating from the prefixed stopping rule. Copyright 2008, Oxford University Press.