Williams R L
Research Triangle Institute, NC 27709-2194, USA.
Lifetime Data Anal. 1995;1(2):171-86. doi: 10.1007/BF00985768.
A simple variance estimator for product-limit survival functions is demonstrated for survival times with nested errors. Such data arise whenever survival times are observed within clusters of related observations. Greenwood's formula, which assumes independent observations, is not appropriate in this situation. A robust variance estimator is developed using Taylor series linearized values and the between-cluster variance estimator commonly used in multi-stage sample surveys. A simulation study shows that the between-cluster variance estimator is approximately unbiased and yields confidence intervals that maintain the nominal level for several patterns of correlated survival times. The simulation study also shows that Greenwood's formula underestimates the variance when the survival times are positively correlated within a cluster and yields confidence intervals that are too narrow. Extension to life table methods is also discussed.
针对具有嵌套误差的生存时间，展示了一种用于乘积限生存函数的简单方差估计器。只要在相关观测值的聚类中观察到生存时间，就会出现此类数据。假设观测值独立的格林伍德公式在这种情况下并不适用。利用泰勒级数线性化值和多阶段抽样调查中常用的聚类间方差估计器，开发了一种稳健的方差估计器。一项模拟研究表明，聚类间方差估计器近似无偏，并且对于几种相关生存时间模式，其产生的置信区间能保持名义水平。模拟研究还表明，当聚类内生存时间呈正相关时，格林伍德公式会低估方差，并且产生的置信区间过窄。还讨论了对生命表方法的扩展。
