In observational studies with delayed entry, causal inference for time-to-event outcomes can be challenging. The challenges arise because, in addition to the potential confounding bias from observational data, the collected data often also suffers from the selection bias due to left truncation, where only subjects with time-to-event (such as death) greater than the enrollment times are included, as well as bias from informative right censoring. To estimate the treatment effects on time-to-event outcomes in such settings, inverse probability weighting (IPW) is often employed. However, IPW is sensitive to model misspecifications, which makes it vulnerable, especially when faced with three sources of biases. Moreover, IPW is inefficient. To address these challenges, we propose a doubly robust framework to handle covariate dependent left truncation and right censoring that can be applied to a wide range of estimation problems, including estimating average treatment effect (ATE) and conditional average treatment effect (CATE). For average treatment effect, we develop estimators that enjoy model double robustness and rate double robustness. For conditional average treatment effect, we develop orthogonal and doubly robust learners that can achieve oracle rate of convergence. Our framework represents the first attempt to construct doubly robust estimators and orthogonal learners for treatment effects that account for all three sources of biases: confounding, selection from covariate-induced dependent left truncation, and informative right censoring. We apply the proposed methods to analyze the effect of midlife alcohol consumption on late-life cognitive impairment, using data from Honolulu Asia Aging Study.

翻译：在具有延迟进入的观察性研究中，针对时间-事件结局的因果推断可能面临挑战。这些挑战源于：除了观察数据中潜在的混杂偏倚外，收集的数据通常还受到左截断（仅纳入时间-事件（如死亡）大于入组时间的个体）导致的选择偏倚，以及信息性右删失带来的偏倚。在此类场景下估计处理对时间-事件结局的效应时，常采用逆概率加权（IPW）方法。然而，IPW对模型设定错误敏感，这使其尤其面对三种偏倚来源时显得脆弱。此外，IPW效率较低。为应对这些挑战，我们提出了一个双重稳健框架来处理协变量相关的左截断与右删失，该框架可应用于广泛的估计问题，包括估计平均处理效应（ATE）和条件平均处理效应（CATE）。对于平均处理效应，我们构建了具有模型双重稳健性和速率双重稳健性的估计量。对于条件平均处理效应，我们开发了正交且双重稳健的学习器，能够达到oracle收敛速率。我们的框架首次尝试构建能够同时处理三种偏倚来源（混杂、协变量诱导的相依左截断选择以及信息性右删失）的处理效应双重稳健估计量与正交学习器。我们应用所提方法，基于檀香山亚洲老龄化研究的数据，分析了中年饮酒对晚年认知障碍的影响。