Frailty models allow us to take into account the non-observable inhomogeneity of individual hazard functions. Although models with time-independent frailty have been intensively studied over the last decades and a wide range of applications in survival analysis have been found, the studies based on the models with time-dependent frailty are relatively rare. In this paper, we formulate and prove two propositions related to the identifiability of the bivariate survival models with frailty given by a nonnegative bivariate Lévy process. We discuss parametric and semiparametric procedures for estimating unknown parameters and baseline hazard functions. Numerical experiments with simulated and real data illustrate these procedures. The statements of the propositions can be easily extended to the multivariate case.

中文翻译：

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使用基于Lévy过程的脆弱模型研究双变量生存数据

脆弱模型使我们能够考虑到单个危险函数的不可观察的不均匀性。尽管在过去的几十年中对具有时间依赖性的脆弱性的模型进行了深入研究，并且发现了其在生存分析中的广泛应用，但是基于具有时间依赖性的脆弱性的模型的研究相对较少。在本文中，我们提出并证明了与非负二元Lévy过程给出的具有脆弱性的二元生存模型的可识别性有关的两个命题。我们讨论用于估计未知参数和基线危害函数的参数和半参数过程。带有模拟和真实数据的数值实验说明了这些过程。这些命题的陈述可以很容易地扩展到多元情况。