In prevalent cohort studies with follow-up, the time-to-event outcome is subject to left truncation when only subjects with event time greater than enrollment time are included. In such studies, subjects with early event times tend not to be captured, leading to selection bias if simply ignoring left truncation. 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 subject to failure 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 first apply the semiparametric theory to find the efficient influence curve of the expectation of an arbitrary transformed survival time in the presence of covariate-induced dependent left truncation. We then use it to further construct estimators that are shown to enjoy double-robustness properties: 1) model double-robustness, that is, they are consistent and asymptotically normal (CAN) when the estimators for the nuisance parameters are both asymptotically linear and one of the two estimators is consistent, but not necessarily both; 2) rate double-robustness, that is, they are CAN when both of the nuisance parameters are consistently estimated and the error product rate under the two nuisance models is faster than root-n. Simulation studies demonstrate the finite sample performance of the estimators.

翻译：常规的脱轨调整方法往往依赖于( quasi-) 独立假设, 减速时间和事件时间会“ 依附” 观察到的区域。 当轨迹时间和事件时间之间有依赖性时, 这种假设会发生故障。 在这样的研究中, 早期事件时间往往不会被捕获, 如果忽略左减速, 导致选择偏差。 常规的脱轨调整方法往往依赖于( quasi-) 独立假设, 即减速时间和事件时间会“ 依赖” 观察到的区域。 当轨迹时间和经测量的调序时间之间可能发生依赖性关系时, 则会发生左减速。 在这样的研究中, 直线时间与经测量值相比, 直线调时间可能会发生偏差, 直线调时间的调速率可能会发生反常变速率, 但对于调模型的精确性能来说, 双向周期性性性性能是。