We show that in a large class of proportional hazard competing risks models, the distribution of the bivariate frailty among survivors converges to a limiting distribution. This generalizes the result of Abbring and van den Berg (Biometrika 94(1):87–99, 2007 ), who show that in a single spell duration model, the frailty distribution converges to the gamma distribution. The resulting limiting distribution has an interpretation in terms of partition of a gamma distribution, and allows for both positive and negative correlation between the survival variables. This result provides a natural and flexible specification for the frailty in competing risks models.

中文翻译：

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竞争风险模型中未观察到的异质性分布

我们表明，在一大类比例风险竞争风险模型中，幸存者之间的二元脆弱性分布收敛于极限分布。这概括了 Abbring 和 van den Berg (Biometrika 94(1):87–99, 2007 ) 的结果，他们表明在单个法术持续时间模型中，脆弱性分布收敛到伽玛分布。由此产生的限制分布在伽马分布的分区方面具有解释，并允许生存变量之间的正相关和负相关。这一结果为竞争风险模型中的脆弱性提供了一个自然而灵活的规范。