Many methods have been developed for analyzing survival data which are commonly right-censored. These methods, however, are challenged by complex features pertinent to the data collection as well as the nature of data themselves. Typically, biased samples caused by left-truncation (or length-biased sampling) and measurement error often accompany survival analysis. While such data frequently arise in practice, little work has been available to simultaneously address these features. In this paper, we explore valid inference methods for handling left-truncated and right-censored survival data with measurement error under the widely used Cox model. We first exploit a flexible estimator for the survival model parameters which does not require specification of the baseline hazard function. To improve the efficiency, we further develop an augmented nonparametric maximum likelihood estimator. We establish asymptotic results and examine the efficiency and robustness issues for the proposed estimators. The proposed methods enjoy appealing features that the distributions of the covariates and of the truncation times are left unspecified. Numerical studies are reported to assess the finite sample performance of the proposed methods.

中文翻译：

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具有协变量测量误差的左截断和右删失生存数据的半参数方法

已经开发了许多方法来分析通常经过右删失的生存数据。然而，这些方法受到与数据收集相关的复杂特征以及数据本身的性质的挑战。通常，由左截断（或长度偏置采样）和测量误差引起的有偏样本通常伴随着生存分析。虽然这些数据在实践中经常出现，但几乎没有工作可以同时解决这些特征。在本文中，我们探索了在广泛使用的 Cox 模型下处理具有测量误差的左截断和右删失生存数据的有效推理方法。我们首先为生存模型参数开发一个灵活的估计器，它不需要指定基线风险函数。为了提高效率，我们进一步开发了一个增强的非参数最大似然估计器。我们建立渐近结果并检查建议估计量的效率和稳健性问题。所提出的方法具有吸引人的特征，即协变量的分布和截断时间的分布未指定。据报道，数值研究用于评估所提出方法的有限样本性能。