Jeong Jong-Hyeon, Jung Sin-Ho, Costantino Joseph P
Department of Biostatistics, University of Pittsburgh, Pittsburgh, PA 15261, USA.
Biometrics. 2008 Mar;64(1):157-63. doi: 10.1111/j.1541-0420.2007.00826.x. Epub 2007 May 14.
A simple approach to the estimation of the median residual lifetime is proposed for a single group by inverting a function of the Kaplan-Meier estimators. A test statistic is proposed to compare two median residual lifetimes at any fixed time point. The test statistic does not involve estimation of the underlying probability density function of failure times under censoring. Extensive simulation studies are performed to validate the proposed test statistic in terms of type I error probabilities and powers at various time points. One of the oldest data sets from the National Surgical Adjuvant Breast and Bowel Project (NSABP), which has more than a quarter century of follow-up, is used to illustrate the method. The analysis results indicate that, without systematic post-operative therapy, a significant difference in median residual lifetimes between node-negative and node-positive breast cancer patients persists for about 10 years after surgery. The new estimates of the median residual lifetime could serve as a baseline for physicians to explain any incremental effects of post-operative treatments in terms of delaying breast cancer recurrence or prolonging remaining lifetimes of breast cancer patients.
通过对Kaplan-Meier估计量的函数求逆，为单个组提出了一种估计中位剩余寿命的简单方法。提出了一个检验统计量，用于比较在任何固定时间点的两个中位剩余寿命。该检验统计量不涉及对删失情况下失效时间的潜在概率密度函数的估计。进行了广泛的模拟研究，以根据不同时间点的I型错误概率和检验功效来验证所提出的检验统计量。使用来自国家外科辅助乳腺和肠道项目（NSABP）的最古老数据集之一（该数据集有超过四分之一个世纪的随访数据）来说明该方法。分析结果表明，在没有系统性术后治疗的情况下，淋巴结阴性和淋巴结阳性乳腺癌患者的中位剩余寿命在术后约10年内仍存在显著差异。中位剩余寿命的新估计值可以作为医生解释术后治疗在延迟乳腺癌复发或延长乳腺癌患者剩余寿命方面的任何增量效果的基线。
