In the theory of competing risks, the nonparametric Kaplan-Meier estimator plays an important role. In this paper, a bivariate nonparametric estimator for the competing risk problem is given, which for the special case of independent causes gives the Kaplan-Meier estimator. This paper also introduces a matrix $w$, through which dependent models for the competing problem can be studied. These results also indicate the special case on the matrix $w$ for which the bounds to the survival function given by Peterson  can be obtained.
"A Generalized Kaplan-Meier Estimator." Ann. Statist. 12 (1) 366 - 371, March, 1984. https://doi.org/10.1214/aos/1176346414