One of the commonly used approaches to capture dependence in multivariate survival data is through the frailty variables. The identifiability issues should be carefully investigated while modeling multivariate survival with or without competing risks. The use of non-parametric frailty distribution(s) is sometimes preferred for its robustness and flexibility properties. In this paper, we consider modeling of bivariate survival data with competing risks through four different kinds of non-parametric frailty and parametric baseline cause-specific hazard functions to investigate the corresponding model identifiability. We make the common assumption of the frailty mean being equal to unity.

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