Pepe M S, Fleming T R
Fred Hutchinson Cancer Research Center, Seattle, Washington 98104.
Biometrics. 1989 Jun;45(2):497-507.
A class of statistics based on the integrated weighted difference in Kaplan-Meier estimators is introduced for the two-sample censored data problem. With positive weight functions these statistics are intuitive for and sensitive against the alternative of stochastic ordering. The standard weighted log-rank statistics are not always sensitive against this alternative, particularly if the hazard functions cross. Qualitative comparisons are made between the weighted log-rank statistics and these weighted Kaplan-Meier (WKM) statistics. A statement of null asymptotic distribution theory is given and the choice of weight function is discussed in some detail. Results from small-sample simulation studies indicate that these statistics compare favorably with the log-rank procedure even under the proportional hazards alternative, and may perform better than it under the crossing hazards alternative.
针对两样本删失数据问题，引入了一类基于Kaplan-Meier估计量的综合加权差异的统计量。对于正权重函数，这些统计量对于随机序的备择假设直观且敏感。标准加权对数秩统计量并非总是对该备择假设敏感，特别是在风险函数交叉时。对加权对数秩统计量和这些加权Kaplan-Meier（WKM）统计量进行了定性比较。给出了零渐近分布理论的陈述，并详细讨论了权重函数的选择。小样本模拟研究的结果表明，即使在比例风险备择假设下，这些统计量也比对数秩检验表现更好，并且在风险函数交叉的备择假设下可能比其表现更佳。
