Group sequential tests for bivariate response: Interim analyses of clinical trials with both efficacy and safety endpoints

We describe group sequential tests for a bivariate response. The tests are defined in terms of the two response components jointly, rather than through a single summary statistic. Such methods are appropriate when the two responses concern different aspects of a treatment; for example, one might wish to show that a new treatment is both as effective and as safe as the current standard. We present a formulation of the bivariate testing problem, introduce group sequential tests that satisfy Type I error conditions, and show how to find the sample size guaranteeing a specified power. We describe how properties of group sequential tests for bivariate normal observations can be computed by numerical integration.