Li Ruosha, Peng Limin
Ruosha Li, University of Pittsburgh, Pittsburgh, USA.
Emory University, Atlanta, USA.
J R Stat Soc Series B Stat Methodol. 2015 Jan;77(1):107-130. doi: 10.1111/rssb.12063.
In this work, we study quantile regression when the response is an event time subject to potentially dependent censoring. We consider the semi-competing risks setting, where time to censoring remains observable after the occurrence of the event of interest. While such a scenario frequently arises in biomedical studies, most of current quantile regression methods for censored data are not applicable because they generally require the censoring time and the event time be independent. By imposing rather mild assumptions on the association structure between the time-to-event response and the censoring time variable, we propose quantile regression procedures, which allow us to garner a comprehensive view of the covariate effects on the event time outcome as well as to examine the informativeness of censoring. An efficient and stable algorithm is provided for implementing the new method. We establish the asymptotic properties of the resulting estimators including uniform consistency and weak convergence. The theoretical development may serve as a useful template for addressing estimating settings that involve stochastic integrals. Extensive simulation studies suggest that the proposed method performs well with moderate sample sizes. We illustrate the practical utility of our proposals through an application to a bone marrow transplant trial.
在这项工作中，我们研究当响应变量为事件发生时间且可能受到相依删失影响时的分位数回归。我们考虑半竞争风险情形，即感兴趣事件发生后删失时间仍可观测。虽然这种情形在生物医学研究中经常出现，但当前大多数针对删失数据的分位数回归方法并不适用，因为它们通常要求删失时间和事件发生时间相互独立。通过对事件发生时间响应与删失时间变量之间的关联结构施加相当温和的假设，我们提出了分位数回归方法，这使我们能够全面了解协变量对事件发生时间结果的影响，并检验删失的信息性。我们提供了一种高效且稳定的算法来实现新方法。我们建立了所得估计量的渐近性质，包括一致相合性和弱收敛性。理论发展可为处理涉及随机积分的估计问题提供有用的模板。大量的模拟研究表明，所提出的方法在中等样本量下表现良好。我们通过应用于一项骨髓移植试验来说明我们方法的实际效用。
