In time-to-event randomized clinical trials, it is common to use composite endpoints as the main endpoint when comparing two treatment groups. A new statistical methodology has been recently developed in order to derives guidelines for deciding whether to expand the use a single or composite endpoint. This methodology, developed by Gómez and Lagakos, is based on the asymptotic relative efficiency (ARE) of a logrank test for comparing two treatment groups with respect to a relevant endpoint versus the composite endpoint. In order to compute the ARE, it is necessary to have the joint law of the time to the relevant and additional endpoints and it is obtained using Frank copula. The main aim of this master thesis is to develop this methodology using Gumbel copula and to compare it with the results obtained using Frank copula. This project shows that the results obtained using Gumbel copula are similar to the ones obtained using Frank copula and, therefore, we conclude that the ARE method is robust for the choice of the copula when restricted to Frank and Gumbel copulas.

Gómez i Lagakos calculen l'eficiència relativa (ARE) del logrank per comparar dos tractaments A i B usant el temps T1 fins E1 o T* fins E*= E1 U E2. L'ARE s'obté fixant la llei de (T1, T2) i es modela via la còpula de Frank. L'objectiu és modelar la llei amb altres còpulas i estudiar les repercussions que aquest canvi té en el càlcul del ARE. L'estudiant haurà d'estudiar la metodologia de GL; estudiar les propietats de les còpules; escollir una còpula diferent de la de Frank i programar l'ARE; i discutir quan robust és l'ARE en front d'un canvi de còpula.