We extend the ARE method proposed in Gómez and Lagakos (2013) devised to decide which primary endpoint to choose when comparing two treatments in a randomized clinical trial. The ARE method is based on the Asymptotic Relative Efficiency (ARE) between two logrank tests to compare two treatments: one is based on a relevant endpoint E1 while the other is based on a composite endpoint E* = E1 ¿ E2, where E2 is an additional endpoint. The ARE depends, besides some intuitive parameters, on the joint law of the times T1 and T2 from randomization to E1 and E2, respectively. Gómez and Lagakos (2013) characterize this joint law by means of Frank’s copula. In our work, several families of copulas can be chosen for the bivariate survival function of (T1, T2) so that different dependence struc- tures between T1 and T2 are feasible. We motivate the problem and show how to apply the method through a real cardiovascular clinical trial. We explore the influence of the copula chosen into the ARE value by means of a simulation study. We conclude that the recommendation on whether or not to use the composite endpoint as the primary endpoint for the investigation is, almost always, independent of the copula chosen.