Schaubel Douglas E, Wei Guanghui
Department of Biostatistics, University of Michigan, Ann Arbor, Michigan 48109-2029, U.S.A. Amgen Inc., South San Francisco, California 94080, USA.
Biometrics. 2011 Mar;67(1):29-38. doi: 10.1111/j.1541-0420.2010.01449.x.
In medical studies of time-to-event data, nonproportional hazards and dependent censoring are very common issues when estimating the treatment effect. A traditional method for dealing with time-dependent treatment effects is to model the time-dependence parametrically. Limitations of this approach include the difficulty to verify the correctness of the specified functional form and the fact that, in the presence of a treatment effect that varies over time, investigators are usually interested in the cumulative as opposed to instantaneous treatment effect. In many applications, censoring time is not independent of event time. Therefore, we propose methods for estimating the cumulative treatment effect in the presence of nonproportional hazards and dependent censoring. Three measures are proposed, including the ratio of cumulative hazards, relative risk, and difference in restricted mean lifetime. For each measure, we propose a double inverse-weighted estimator, constructed by first using inverse probability of treatment weighting (IPTW) to balance the treatment-specific covariate distributions, then using inverse probability of censoring weighting (IPCW) to overcome the dependent censoring. The proposed estimators are shown to be consistent and asymptotically normal. We study their finite-sample properties through simulation. The proposed methods are used to compare kidney wait-list mortality by race.
在医学研究的事件发生时间数据中，估计治疗效果时，非比例风险和依存性删失是非常常见的问题。处理随时间变化的治疗效果的传统方法是对时间依赖性进行参数化建模。这种方法的局限性包括难以验证指定函数形式的正确性，以及在存在随时间变化的治疗效果的情况下，研究者通常感兴趣的是累积治疗效果而非瞬时治疗效果。在许多应用中，删失时间并非独立于事件时间。因此，我们提出了在存在非比例风险和依存性删失的情况下估计累积治疗效果的方法。我们提出了三种度量方法，包括累积风险比、相对风险和受限平均寿命差异。对于每种度量方法，我们提出了一种双重逆加权估计量，其构建方式是首先使用治疗加权逆概率（IPTW）来平衡特定治疗的协变量分布，然后使用删失加权逆概率（IPCW）来克服依存性删失。所提出的估计量被证明是一致的且渐近正态的。我们通过模拟研究了它们的有限样本性质。所提出的方法用于比较不同种族的肾脏等待名单死亡率。
