How to avoid concerns with the interpretation of two primary endpoints if significant superiority in one is sufficient for formal proof of efficacy

Formal proof of efficacy of a drug requires that in a prospective experiment, superiority over placebo, or either superiority or at least non-inferiority to an established standard, is demonstrated. Traditionally one primary endpoint is specified, but various diseases exist where treatment success needs to be based on the assessment of two primary endpoints. With co-primary endpoints, both need to be “significant” as a prerequisite to claim study success. Here, no adjustment of the study-wise type-1-error is needed, but sample size is often increased to maintain the pre-defined power. Studies that use an at-least-one concept have been proposed where study success is claimed if superiority for at least one of the endpoints is demonstrated. This is sometimes also called the dual primary endpoint concept, and an appropriate adjustment of the study-wise type-1-error is required. This concept is not covered in the European Guideline on multiplicity because study success can be claimed if one endpoint shows significant superiority, despite a possible deterioration in the other. In line with Röhmel's strategy, we discuss an alternative approach including non-inferiority hypotheses testing that avoids obvious contradictions to proper decision-making. This approach leads back to the co-primary endpoint assessment, and has the advantage that minimum requirements for endpoints can be modeled flexibly for several practical needs. Our simulations show that, if planning assumptions are correct, the proposed additional requirements improve interpretation with only a limited impact on power, that is, on sample size.