Cause-Specific Cumulative Incidence Estimation and the Fine and Gray Model Under Both Left Truncation and Right Censoring
Cause-Specific Cumulative Incidence Estimation and the Fine and Gray Model Under Both Left Truncation and Right Censoring
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DOI：
10.1111/j.1541-0420.2010.01420.x
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发表时间：
2011-03-01
期刊：
影响因子：
1.9
通讯作者：
Geskus, Ronald B.
中科院分区：
文献类型：
--
作者：
Geskus, Ronald B.
在具有左截断和/或右截尾数据的竞争风险设置中，特定原因累积关联函数的标准估计量可以用两种可选形式编写。一种是加权经验累积分布函数，另一种是乘积极限估计量。这种等价性提出了用左截断和右截断分析时间到事件数据的另一种观点：仍然处于风险中或经历过较早竞争事件的个体从审查和截断机制中获得权重。因此，对累积尺度的推断可以使用标准程序的加权版本来执行。这适用于特定原因累积关联函数的估计，以及Fine和Gray比例子分布风险模型中回归参数的估计。我们证明，通过适当的过滤，一个鞅性质成立，允许以与标准Cox比例风险模型相同的方式导出比例子分布风险模型的渐近结果。如果生存分析的标准软件允许包含与时间相关的权重，则可以使用该软件对特定原因的累积发生率函数和亚分布风险的回归进行估计。我们将在R统计包中展示其实现。采用比例亚分布风险模型研究了日历周期作为确定性外部时变协变量（可视为左截断的特例）对艾滋病相关和非艾滋病相关累积死亡率的影响。
The standard estimator for the cause-specific cumulative incidence function in a competing risks setting with left truncated and/or right censored data can be written in two alternative forms. One is a weighted empirical cumulative distribution function and the other a product-limit estimator. This equivalence suggests an alternative view of the analysis of time-to-event data with left truncation and right censoring: individuals who are still at risk or experienced an earlier competing event receive weights from the censoring and truncation mechanisms. As a consequence, inference on the cumulative scale can be performed using weighted versions of standard procedures. This holds for estimation of the cause-specific cumulative incidence function as well as for estimation of the regression parameters in the Fine and Gray proportional subdistribution hazards model. We show that, with the appropriate filtration, a martingale property holds that allows deriving asymptotic results for the proportional subdistribution hazards model in the same way as for the standard Cox proportional hazards model. Estimation of the cause-specific cumulative incidence function and regression on the subdistribution hazard can be performed using standard software for survival analysis if the software allows for inclusion of time-dependent weights. We show the implementation in the R statistical package. The proportional subdistribution hazards model is used to investigate the effect of calendar period as a deterministic external time varying covariate, which can be seen as a special case of left truncation, on AIDS related and non-AIDS related cumulative mortality.