In prevalent cohort studies with follow-up, the time-to-event outcome is subject to left truncation leading to selection bias. For estimation of the distribution of time-to-event, conventional methods adjusting for left truncation tend to rely on the (quasi-)independence assumption that the truncation time and the event time are "independent" on the observed region. This assumption is violated when there is dependence between the truncation time and the event time possibly induced by measured covariates. Inverse probability of truncation weighting leveraging covariate information can be used in this case, but it is sensitive to misspecification of the truncation model. In this work, we apply the semiparametric theory to find the efficient influence curve of an expected (arbitrarily transformed) survival time in the presence of covariate-induced dependent left truncation. We then use it to construct estimators that are shown to enjoy double-robustness properties. Our work represents the first attempt to construct doubly robust estimators in the presence of left truncation, which does not fall under the established framework of coarsened data where doubly robust approaches are developed. We provide technical conditions for the asymptotic properties that appear to not have been carefully examined in the literature for time-to-event data, and study the estimators via extensive simulation. We apply the estimators to two data sets from practice, with different right-censoring patterns.

翻译：在具有随访的现患队列研究中，结局事件时间会因左删失而产生选择偏倚。为估计事件时间的分布，传统调整左删失的方法通常依赖于（准）独立性假设，即观测区域内的删失时间与事件时间"独立"。当删失时间与事件时间因测量协变量产生依赖关系时，该假设不再成立。此时可利用协变量信息的逆删失概率加权法，但其对删失模型的误设定敏感。本研究应用半参数理论，推导了在协变量诱导依赖左删失下期望（任意变换）生存时间的有效影响曲线，并据此构建了具有双重稳健性的估计量。这是首次在左删失场景下构建双重稳健估计量的尝试，该场景不适用于现有构建双重稳健方法的粗化数据框架。我们给出了文献中针对生存数据尚未被仔细考察的渐近性质技术条件，并通过大量模拟研究评估了估计量的表现。最后，我们将该估计量应用于两个具有不同右删失模式的实际数据集。