In this paper, we provide a nonparametric estimator of the distribution of bivariate censored lifetimes, in a model where the two censoring variables differ only through an additional observed variable. This situation is motivated by a particular application to insurance, where the supplementary variable corresponds to the age difference between two individuals. Asymptotic results for our estimator are provided. The new tools that we develop are used to perform goodness-of-fit tests for survival copula models. The practical performance is illustrated through simulations and a real data analysis.
