Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, Quebec, Canada H3A 1A2.
Stat Med. 2010 Mar 30;29(7-8):915-23. doi: 10.1002/sim.3807.
We propose two bootstrap-based methods to correct the standard errors (SEs) from Cox's model for within-cluster correlation of right-censored event times. The cluster-bootstrap method resamples, with replacement, only the clusters, whereas the two-step bootstrap method resamples (i) the clusters, and (ii) individuals within each selected cluster, with replacement. In simulations, we evaluate both methods and compare them with the existing robust variance estimator and the shared gamma frailty model, which are available in statistical software packages. We simulate clustered event time data, with latent cluster-level random effects, which are ignored in the conventional Cox's model. For cluster-level covariates, both proposed bootstrap methods yield accurate SEs, and type I error rates, and acceptable coverage rates, regardless of the true random effects distribution, and avoid serious variance under-estimation by conventional Cox-based standard errors. However, the two-step bootstrap method over-estimates the variance for individual-level covariates. We also apply the proposed bootstrap methods to obtain confidence bands around flexible estimates of time-dependent effects in a real-life analysis of cluster event times.
我们提出了两种基于 bootstrap 的方法来校正 Cox 模型中右删失事件时间的簇内相关的标准误差（SE）。簇引导法仅对簇进行有放回的重采样，而两步引导法对（i）簇和（ii）每个选定簇中的个体进行有放回的重采样。在模拟中，我们评估了这两种方法，并将它们与现有的稳健方差估计量和共享伽马 frailty 模型进行了比较，这些模型在统计软件包中都可用。我们模拟了具有潜在聚类水平随机效应的聚类事件时间数据，这些随机效应在传统的 Cox 模型中被忽略。对于聚类水平的协变量，两种提议的引导法都产生了准确的 SE 和误差率，并且接受了可接受的覆盖范围，无论真实的随机效应分布如何，并且避免了传统的基于 Cox 的标准误差的严重方差低估。然而，两步引导法高估了个体水平协变量的方差。我们还将提出的引导法应用于实际的聚类事件时间分析中，以获得时变效应的灵活估计的置信带。
