Additive hazards model is often used to complement the proportional hazards model in the analysis of failure time data. Statistical inference of additive hazards model with time-dependent longitudinal covariates requires the availability of the whole trajectory of the longitudinal process, which is not realistic in practice. The commonly used last value carried forward approach for intermittently observed longitudinal covariates can induce biased parameter estimation. The more principled joint modeling of the longitudinal process and failure time data imposes strong modeling assumptions, which is difficult to verify. In this paper, we propose methods that weigh the distance between the observational time of longitudinal covariates and the failure time, resulting in unbiased regression coefficient estimation. We establish the consistency and asymptotic normality of the proposed estimators. Simulation studies provide numerical support for the theoretical findings. Data from an Alzheimer’s study illustrate the practical utility of the methodology.

在故障时间数据分析中，加性风险模型通常用于补充比例风险模型。具有时间相关纵向协变量的加性风险模型的统计推断需要纵向过程的整个轨迹的可用性，这在实践中是不现实的。间歇性观察到的纵向协变量常用的最后一个值结转方法会导致参数估计有偏差。纵向过程和失效时间数据的更有原则的联合建模强加了强大的建模假设，这很难验证。在本文中，我们提出了权衡纵向协变量的观察时间与失效时间之间的距离的方法，从而得到无偏回归系数估计。我们建立了提议的估计量的一致性和渐近正态性。模拟研究为理论发现提供了数值支持。来自阿尔茨海默氏症研究的数据说明了该方法的实用性。