We propose a variable ranking procedure based on copula bivariate time- to-event margins under a general censoring scheme. The procedure is able to identify the important variables influencing the two time-to-events in a high dimensional set- ting introducing a proper metric able to take into account the probabilistic copula structure. The proposal is the first attempt to apply a variable selection method to a copula bivariate time-to-event domain. The advantages of the proposed approach are illustrated in a case study based on AREDS dataset.