An asymptotic analysis of the logrank test.
An asymptotic analysis of the logrank test.
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DOI：
10.1023/a:1009648914586
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发表时间：
1997-01-01
影响因子：
1.3
通讯作者：
Strawderman, R L
中科院分区：
文献类型：
--
作者：
Strawderman, R L
在独立同分布观测下，给出了对数秩统计量的零分布及其在局部比例风险下的分布的渐近展开式。这些结果来自Gu（1992）和Taniguchi（1992）的工作，很容易解释，并为以前在模拟研究中观察到的对数秩检验的许多行为特征提供了一些理论依据。我们主要关注（i）治疗组失衡下通常的正态近似的不足;以及（ii）治疗组失衡对功效和样本量计算的影响。基于Konishi（1991）的结果，还推导出对数秩统计量的简单转换，发现当存在治疗组失衡时，在无生存差异的零假设下，对数秩统计量的标准正态近似值显著改善。
Asymptotic expansions for the null distribution of the logrank statistic and its distribution under local proportional hazards alternatives are developed in the case of iid observations. The results, which are derived from the work of Gu (1992) and Taniguchi (1992), are easy to interpret, and provide some theoretical justification for many behavioral characteristics of the logrank test that have been previously observed in simulation studies. We focus primarily upon (i) the inadequacy of the usual normal approximation under treatment group imbalance; and, (ii) the effects of treatment group imbalance on power and sample size calculations. A simple transformation of the logrank statistic is also derived based on results in Konishi (1991) and is found to substantially improve the standard normal approximation to its distribution under the null hypothesis of no survival difference when there is treatment group imbalance.