In survival analysis, frailty variables are often used to model the association in multivariate survival data. Identifiability is an important issue while working with such multivariate survival data with or without competing risks. In this work, we consider bivariate survival data with competing risks and investigate identifiability results with non-parametric baseline cause-specific hazards and different types of Gamma frailty. Prior to that, we prove that, when both baseline cause-specific hazards and frailty distributions are non-parametric, the model is not identifiable. We also construct a non-identifiable model when baseline cause-specific hazards are non-parametric but frailty distribution may be parametric. Thereafter, we consider four different Gamma frailty distributions, and the corresponding models are shown to be identifiable under fairly general assumptions.

翻译：在生存分析中，脆弱变量常用于建模多元生存数据中的关联性。无论是否存在竞争风险，可识别性都是处理此类多元生存数据时的重要问题。本文研究具有竞争风险的二元生存数据，探讨在非参数基线病因别风险与不同类型伽马脆弱性条件下的可识别性结果。首先，我们证明当基线病因别风险与脆弱性分布均为非参数时，模型不可识别。随后构建了当基线病因别风险为非参数而脆弱性分布可能为参数时的不可识别模型。在此基础上，我们考虑四种不同的伽马脆弱性分布，并证明在相当一般的假设条件下，相应模型均具有可识别性。