This article discusses nonparametric estimation of a survival function in the presence of measurement errors on the observation of the failure time of interest. One situation where such issues arise would be clinical studies of chronic diseases where the observation on the time to the failure event of interest such as the onset of the disease relies on patient recall or chart review of electronic medical records. It is easy to see that both situations can be subject to measurement errors. To resolve this problem, we propose a simulation extrapolation approach to correct the bias induced by the measurement error. To overcome potential computational difficulties, we use spline regression to approximate the unspecified extrapolated coefficient function of time, and establish the asymptotic properties of our proposed estimator. The proposed method is applied to nonparametric estimation based on interval-censored data. Extensive numerical experiments involving both simulated and actual study datasets demonstrate the feasibility of this proposed estimation procedure.

中文翻译：

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在感兴趣的失效时间存在测量误差的情况下，对生存函数进行非参数估计

本文讨论了在观察感兴趣的失效时间时存在测量误差的情况下生存函数的非参数估计。出现此类问题的一种情况是慢性疾病的临床研究，其中对感兴趣的故障事件（例如疾病发作）的时间的观察依赖于患者回忆或电子病历的图表审查。很容易看出，这两种情况都可能出现测量误差。为了解决这个问题，我们提出了一种模拟外推方法来纠正由测量误差引起的偏差。为了克服潜在的计算困难，我们使用样条回归来近似未指定的时间外推系数函数，并建立我们提出的估计器的渐近属性。该方法适用于基于区间删失数据的非参数估计。涉及模拟和实际研究数据集的大量数值实验证明了所提出的估计程序的可行性。