Centre for Mathematical Sciences, School of Engineering, Computing and Mathematics, University of Plymouth, Plymouth, UK.
South West Transplant Centre, University Hospitals Plymouth NHS Trust, Plymouth, UK.
Stat Methods Med Res. 2023 Oct;32(10):1902-1918. doi: 10.1177/09622802231188516. Epub 2023 Aug 9.
Time-to-event semi-competing risk endpoints may be correlated when both events occur on the same individual. These events and the association between them may also be influenced by individual characteristics. In this article, we propose copula survival models to estimate hazard ratios of covariates on the non-terminal and terminal events, along with the effects of covariates on the association between the two events. We use the Normal, Clayton, Frank and Gumbel copulas to provide a variety of association structures between the non-terminal and terminal events. We apply the proposed methods to model semi-competing risks of graft failure and death for kidney transplant patients. We find that copula survival models perform better than the Cox proportional hazards model when estimating the non-terminal event hazard ratio of covariates. We also find that the inclusion of covariates in the association parameter of the copula models improves the estimation of the hazard ratios.
时间事件半竞争风险终点可能在同一个体上同时发生时相关。这些事件及其之间的关联也可能受到个体特征的影响。在本文中，我们提出了 Copula 生存模型来估计协变量对非终端和终端事件的风险比，以及协变量对两个事件之间关联的影响。我们使用正态 Copula、Clayton Copula、Frank Copula 和 Gumbel Copula 来提供非终端和终端事件之间的各种关联结构。我们将提出的方法应用于肾移植患者移植物失败和死亡的半竞争风险模型。我们发现，在估计协变量对非终端事件的风险比时，Copula 生存模型比 Cox 比例风险模型表现更好。我们还发现，在 Copula 模型的关联参数中包含协变量可以提高风险比的估计。
