Shu Xu, Schaubel Douglas E
Novartis Pharmaceuticals, One Health Plaza, East Hanover, NJ 07936, USA.
Department of Biostatistics, University of Michigan, 1415 Washington Heights, Ann Arbor, MI 48109-2029, USA.
Stat Biosci. 2017 Dec;9(2):470-488. doi: 10.1007/s12561-016-9168-6. Epub 2016 Sep 26.
In studies featuring a sequence of ordered events, gap times between successive events are often of interest. Despite the rich literature in this area, very few methods for comparing gap times have been developed. We propose methods for estimating a hazard ratio connecting the first and second gap times. Specifically, a two-stage procedure is developed based on estimating equations. At the first stage, a proportional hazards model is fitted for the first gap time. Weighted estimating equations are then solved at the second stage to estimate the hazard ratio between the first and second gap times. The proposed estimator has a closed form and, being analogous to a standardized mortality ratio, is easy to interpret. Large sample properties of the proposed estimators are derived, with simulation studies used to evaluate finite sample characteristics. Extension of the approach to accommodate a piecewise constant hazard ratio is considered. The proposed methods are applied to contrast repeat (second) versus primary (first) liver transplants with respect to graft failure, based on national registry data.
在以一系列有序事件为特征的研究中，连续事件之间的间隔时间常常受到关注。尽管该领域已有丰富的文献，但用于比较间隔时间的方法却很少被开发出来。我们提出了估计连接第一个和第二个间隔时间的风险比的方法。具体而言，基于估计方程开发了一个两阶段程序。在第一阶段，针对第一个间隔时间拟合一个比例风险模型。然后在第二阶段求解加权估计方程，以估计第一个和第二个间隔时间之间的风险比。所提出的估计量具有封闭形式，并且类似于标准化死亡率比，易于解释。推导了所提出估计量的大样本性质，并通过模拟研究来评估有限样本特征。考虑了将该方法扩展以适应分段常数风险比的情况。基于国家登记数据，将所提出的方法应用于对比重复（第二次）与初次（第一次）肝移植在移植物失败方面的情况。
