Wang Yuyao, Ying Andrew, Xu Ronghui
Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA.
Department of Statistics and Data Science, The Wharton School, University of Pennsylvania, 265 South 37th Street, Philadelphia, Pennsylvania 19104, USA.
Biometrika. 2024 Feb 10;111(3):789-808. doi: 10.1093/biomet/asae005. eCollection 2024 Sep.
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 the 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 can be used in this case, but it is sensitive to misspecification of the truncation model. In this work, we apply semiparametric theory to find the efficient influence curve of the expectation of an 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 were 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 datasets from practice, with different right-censoring patterns.
在有随访的现患队列研究中，事件发生时间结局存在左截断问题，从而导致选择偏倚。对于事件发生时间分布的估计，传统的针对左截断进行调整的方法往往依赖于截断时间和事件时间在观察区域内相互独立的准独立性假设。当截断时间和事件时间之间存在依赖关系（可能由测量的协变量引起）时，这一假设就会被违背。在这种情况下，可以使用截断加权的逆概率方法，但它对截断模型的错误设定很敏感。在这项工作中，我们应用半参数理论来找到在存在协变量引起的依赖左截断情况下，任意变换生存时间期望的有效影响曲线。然后我们用它来构建具有双重稳健性的估计量。我们的工作是在存在左截断的情况下构建双重稳健估计量的首次尝试，这种情况不属于已建立的粗化数据框架，而双重稳健方法正是在该框架下发展起来的。我们为渐近性质提供了技术条件，这些条件在关于事件发生时间数据的文献中似乎尚未得到仔细研究，并且通过广泛的模拟研究了这些估计量。我们将这些估计量应用于来自实践的两个数据集，这两个数据集具有不同的右删失模式。
