Department of Biostatistics, Harvard School of Public Health, Harvard University, Boston, MA 02115, U.S.A.
Stat Med. 2010 Nov 10;29(25):2581-91. doi: 10.1002/sim.4020.
In two-stage randomization designs, patients are randomized to one of the initial treatments, and at the end of the first stage, they are randomized to one of the second stage treatments depending on the outcome of the initial treatment. Statistical inference for survival data from these trials uses methods such as marginal mean models and weighted risk set estimates. In this article, we propose two forms of weighted Kaplan-Meier (WKM) estimators based on inverse-probability weighting-one with fixed weights and the other with time-dependent weights. We compare their properties with that of the standard Kaplan-Meier (SKM) estimator, marginal mean model-based (MM) estimator and weighted risk set (WRS) estimator. Simulation study reveals that both forms of weighted Kaplan-Meier estimators are asymptotically unbiased, and provide coverage rates similar to that of MM and WRS estimators. The SKM estimator, however, is biased when the second randomization rates are not the same for the responders and non-responders to initial treatment. The methods described are demonstrated by applying to a leukemia data set.
在两阶段随机化设计中，患者被随机分配到初始治疗之一，在第一阶段结束时，根据初始治疗的结果，他们被随机分配到第二阶段治疗之一。这些试验的生存数据的统计推断使用边缘均值模型和加权风险集估计等方法。在本文中，我们提出了两种基于逆概率加权的加权 Kaplan-Meier（WKM）估计量——一种具有固定权重，另一种具有时变权重。我们将它们的性质与标准 Kaplan-Meier（SKM）估计量、基于边缘均值模型的（MM）估计量和加权风险集（WRS）估计量进行了比较。模拟研究表明，两种加权 Kaplan-Meier 估计量都是渐近无偏的，并且与 MM 和 WRS 估计量的覆盖率相似。然而，当第二随机化率对于初始治疗的响应者和非响应者不同时，SKM 估计量是有偏差的。所描述的方法通过应用于白血病数据集进行了演示。
