A self-consistent estimator of marginal survival functions based on dependent competing risk data and an assumed copula

When the time to death, X, and the time to censoring, Y, are associated some additional information is need to identify the marginal survival functions. A natural function which provides this additional information is the copula of X and Y. Assuming that the copula is known, we use the notion of self consistency to construct an estimator of the marginal survival functions based on dependent competing risk data. Results of a small simulation study are shown to compare this estimator to other estimators of the marginal survival function based on an assumed copula.