Sample Size Considerations in Clinical Trials When Comparing Two Interventions Using Multiple Co-Primary Binary Relative Risk Contrasts

The effects of interventions are multidimensional. Use of more than one primary endpoint offers an attractive design feature in clinical trials as they capture more complete characterization of the effects of an intervention and provide more informative intervention comparisons. For these reasons, multiple primary endpoints have become a common design feature in many disease areas such as oncology, infectious disease, and cardiovascular disease. More specifically in medical product development, multiple endpoints are used as co-primary to evaluate the effect of the new interventions. Although methodologies to address continuous co-primary endpoints are well-developed, methodologies for binary endpoints are limited. In this article, we describe power and sample size determination for clinical trials with multiple correlated binary endpoints, when relative risks are evaluated as co-primary. We consider a scenario where the objective is to evaluate evidence for superiority of a test intervention compared with a control intervention, for all of the relative risks. We discuss the normal approximation methods for power and sample size calculations and evaluate how the required sample size, power, and Type I error vary as a function of the correlations among the endpoints. Also we discuss a simple, but conservative procedure for appropriate sample size calculation. We then extend the methods allowing for interim monitoring using group-sequential methods. Supplementary materials for this article are available online.