Interim evaluation of efficacy or futility in group-sequential trials with multiple co-primary endpoints

We discuss group-sequential designs in superiority clinical trials with multiple co-primary endpoints, that is, when trials are designed to evaluate if the test intervention is superior to the control on all primary endpoints. We consider several decision-making frameworks for evaluating efficacy or futility, based on boundaries using group-sequential methodology. We incorporate the correlations among the endpoints into the calculations for futility boundaries and sample sizes as a function of other design parameters, including mean differences, the number of analyses, and efficacy boundaries. We investigate the operating characteristics of the proposed decision-making frameworks in terms of efficacy/futility boundaries, power, the Type I error rate, and sample sizes, while varying the number of analyses, the correlations among the endpoints, and the mean differences. We provide an example to illustrate the methods and discuss practical considerations when designing efficient group-sequential designs in clinical trials with co-primary endpoints.