The choice of the primary endpoint is an important issue when designing a clinical trial. The motivation of this Master thesis is to develop a methodology based on the Asymptotic Relative Efficiency (ARE) that discerns between a compound of binary variables or one of its elements as the primary response of the trial. The decision turns into a quantified comparison that captures which variable is more efficient for the clinical trial. In this work, we explore four different definitions of ARE measure. Further, we study the behavior of binary endpoints and its use for comparing two groups. Following the ARE method developed by Gómez and Lagakos (2013), the extension of the method for binary endpoints and its applicability for fixed alternatives are presented.