Tsai Tsung-Hsien, Tsai Wei-Yann, Chi Yunchan, Chang Sheng-Mao
Department of Statistics, National Cheng Kung University, Tainan, Taiwan.
Department of Biostatistics, Columbia University, New York City, U.S.A.
Biometrics. 2016 Mar;72(1):232-41. doi: 10.1111/biom.12378. Epub 2015 Sep 10.
The confidence intervals for the ratio of two median residual lifetimes are developed for left-truncated and right-censored data. The approach of Su and Wei (1993) is first extended by replacing the Kaplan-Meier survival estimator with the estimator of the conditional survival function (Lynden-Bell, 1971). This procedure does not involve a nonparametric estimation of the probability density function of the failure time. However, the Su and Wei type confidence intervals are very conservative even for larger sample size. Therefore, this article proposes an alternative confidence interval for the ratio of two median residual lifetimes, which is not only without nonparametric estimation of the density function of failure times but is also computationally simpler than the Su and Wei type confidence interval. A simulation study is conducted to examine the accuracy of these confidence intervals and the implementation of these confidence intervals to two real data sets is illustrated.
针对左截断和右删失数据，推导了两个中位数剩余寿命之比的置信区间。首先扩展了苏和魏（1993）的方法，用条件生存函数的估计量（林登 - 贝尔，1971）替代了卡普兰 - 迈耶生存估计量。此过程不涉及失效时间概率密度函数的非参数估计。然而，即使对于较大的样本量，苏和魏型置信区间也非常保守。因此，本文提出了一种用于两个中位数剩余寿命之比的替代置信区间，它不仅无需对失效时间的密度函数进行非参数估计，而且在计算上比苏和魏型置信区间更简单。进行了一项模拟研究以检验这些置信区间的准确性，并说明了将这些置信区间应用于两个真实数据集的情况。
