Cortese Giuliana, Holmboe Stine A, Scheike Thomas H
Department of Statistical Sciences, University of Padua, Padua, Italy.
Department of Growth and Reproduction, Rigshospitalet, Copenhagen, Denmark.
Stat Med. 2017 May 20;36(11):1803-1822. doi: 10.1002/sim.7222. Epub 2017 Jan 20.
The hazard ratios resulting from a Cox's regression hazards model are hard to interpret and to be converted into prolonged survival time. As the main goal is often to study survival functions, there is increasing interest in summary measures based on the survival function that are easier to interpret than the hazard ratio; the residual mean time is an important example of those measures. However, because of the presence of right censoring, the tail of the survival distribution is often difficult to estimate correctly. Therefore, we consider the restricted residual mean time, which represents a partial area under the survival function, given any time horizon τ, and is interpreted as the residual life expectancy up to τ of a subject surviving up to time t. We present a class of regression models for this measure, based on weighted estimating equations and inverse probability of censoring weighted estimators to model potential right censoring. Furthermore, we show how to extend the models and the estimators to deal with delayed entries. We demonstrate that the restricted residual mean life estimator is equivalent to integrals of Kaplan-Meier estimates in the case of simple factor variables. Estimation performance is investigated by simulation studies. Using real data from Danish Monitoring Cardiovascular Risk Factor Surveys, we illustrate an application to additive regression models and discuss the general assumption of right censoring and left truncation being dependent on covariates. Copyright © 2017 John Wiley & Sons, Ltd.
Cox回归风险模型得出的风险比难以解释，也难以转换为延长的生存时间。由于主要目标通常是研究生存函数，因此人们越来越关注基于生存函数的汇总指标，这些指标比风险比更易于解释；剩余平均时间就是这些指标中的一个重要例子。然而，由于存在右删失，生存分布的尾部往往难以正确估计。因此，我们考虑受限剩余平均时间，它表示在任何时间范围τ下生存函数下的部分面积，并被解释为在时间t存活的个体直至τ的剩余预期寿命。我们基于加权估计方程和删失逆概率加权估计量，为该指标提出了一类回归模型，以对潜在的右删失进行建模。此外，我们展示了如何扩展模型和估计量以处理延迟进入的情况。我们证明，在简单因子变量的情况下，受限剩余平均寿命估计量等同于Kaplan-Meier估计量的积分。通过模拟研究考察了估计性能。使用来自丹麦心血管危险因素监测调查的真实数据，我们说明了在加法回归模型中的应用，并讨论了右删失和左截断依赖于协变量的一般假设。版权所有© 2017约翰威立父子有限公司。
