Abstract: To apply group sequential methods in interim analyses for early stopping in clinical trials, the joint distribution of sequentially computed test statistics has to be established for repeated significance testing. Often the joint distribution is multivariate normal or at least asymptotically so, and the group sequential methods require multivariate numerical integration. However, if the increments between successive test statistics are independent, the multivariate numerical integration reduces to univariate numerical integration involving simple recursion. This allows the use of standard group sequential methods for early stopping to become practical. In this presentation I will provide review of historical developments that established independent increments in successive test statistics for clinical trials in which trial participants enter over time.
