Ning Jing, Qin Jing, Shen Yu
Division of Biostatistics, School of Public Health, The University of Texas, Houston, TX 77030, U.S.A.
J R Stat Soc Series B Stat Methodol. 2010 Nov 1;72(5):609-630. doi: 10.1111/j.1467-9868.2010.00742.x.
Testing the equality of two survival distributions can be difficult in a prevalent cohort study when non random sampling of subjects is involved. Due to the biased sampling scheme, independent censoring assumption is often violated. Although the issues about biased inference caused by length-biased sampling have been widely recognized in statistical, epidemiological and economical literature, there is no satisfactory solution for efficient two-sample testing. We propose an asymptotic most efficient nonparametric test by properly adjusting for length-biased sampling. The test statistic is derived from a full likelihood function, and can be generalized from the two-sample test to a k-sample test. The asymptotic properties of the test statistic under the null hypothesis are derived using its asymptotic independent and identically distributed representation. We conduct extensive Monte Carlo simulations to evaluate the performance of the proposed test statistics and compare them with the conditional test and the standard logrank test for different biased sampling schemes and right-censoring mechanisms. For length-biased data, empirical studies demonstrated that the proposed test is substantially more powerful than the existing methods. For general left-truncated data, the proposed test is robust, still maintains accurate control of type I error rate, and is also more powerful than the existing methods, if the truncation patterns and right-censoring patterns are the same between the groups. We illustrate the methods using two real data examples.
在一项现患队列研究中，当涉及到非随机抽样时，检验两个生存分布的相等性可能会很困难。由于抽样方案存在偏差，独立删失假设常常会被违反。尽管长度偏倚抽样导致的有偏推断问题在统计学、流行病学和经济学文献中已得到广泛认可，但对于有效的两样本检验尚无令人满意的解决方案。我们通过适当调整长度偏倚抽样提出了一种渐近最有效的非参数检验。检验统计量源自一个完全似然函数，并且可以从两样本检验推广到k样本检验。在原假设下，利用其渐近独立同分布表示推导检验统计量的渐近性质。我们进行了广泛的蒙特卡罗模拟，以评估所提出检验统计量的性能，并针对不同的偏倚抽样方案和右删失机制将它们与条件检验和标准对数秩检验进行比较。对于长度偏倚数据，实证研究表明所提出的检验比现有方法具有更强的检验效能。对于一般的左截断数据，如果组间截断模式和右删失模式相同，所提出的检验是稳健的，仍能准确控制第一类错误率，并且也比现有方法具有更强的检验效能。我们使用两个实际数据示例来说明这些方法。
