Brueckner Matthias, Titman Andrew, Jaki Thomas
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, U.K.
Biometrics. 2019 Mar;75(1):110-120. doi: 10.1111/biom.12952. Epub 2018 Aug 2.
Instrumental variable methods allow unbiased estimation in the presence of unmeasured confounders when an appropriate instrumental variable is available. Two-stage least-squares and residual inclusion methods have recently been adapted to additive hazard models for censored survival data. The semi-parametric additive hazard model which can include time-independent and time-dependent covariate effects is particularly suited for the two-stage residual inclusion method, since it allows direct estimation of time-independent covariate effects without restricting the effect of the residual on the hazard. In this article, we prove asymptotic normality of two-stage residual inclusion estimators of regression coefficients in a semi-parametric additive hazard model with time-independent and time-dependent covariate effects. We consider the cases of continuous and binary exposure. Estimation of the conditional survival function given observed covariates is discussed and a resampling scheme is proposed to obtain simultaneous confidence bands. The new methods are compared to existing ones in a simulation study and are applied to a real data set. The proposed methods perform favorably especially in cases with exposure-dependent censoring.
当存在合适的工具变量时，工具变量法能够在存在未测量混杂因素的情况下进行无偏估计。两阶段最小二乘法和残差纳入法最近已被应用于删失生存数据的加法风险模型。半参数加法风险模型可以包括与时间无关和与时间有关的协变量效应，特别适合于两阶段残差纳入法，因为它允许直接估计与时间无关的协变量效应，而无需限制残差对风险的影响。在本文中，我们证明了在具有与时间无关和与时间有关的协变量效应的半参数加法风险模型中，两阶段残差纳入估计量的回归系数的渐近正态性。我们考虑连续暴露和二元暴露的情况。讨论了给定观察到的协变量时条件生存函数的估计，并提出了一种重采样方案以获得同时置信带。在模拟研究中将新方法与现有方法进行了比较，并将其应用于一个真实数据集。所提出的方法表现良好，尤其是在存在与暴露有关的删失的情况下。
