Timelines of longitudinal studies are often anchored by specific events. In the absence of the fully observed anchoring event times, the study timeline becomes undefined, and the traditional longitudinal analysis loses its temporal reference. In this paper, we considered an analytical situation where the anchoring events are interval censored. We demonstrated that by expressing the regression parameter estimators as stochastic functionals of a plug‐in estimate of the unknown anchoring event time distribution, the standard longitudinal models could be extended to accommodate the situation of less well‐defined timelines. We showed that for a broad class of longitudinal models, the functional parameter estimates are consistent and asymptotically normally distributed with a $\sqrt{n}$ convergence rate under mild regularity conditions. Applying the developed theory to linear mixed‐effects models, we further proposed a hybrid computational procedure that combines the strengths of the Fisher's scoring method and the expectation‐expectation (EM) algorithm for model parameter estimation. We conducted a simulation study to validate the asymptotic properties and to assess the finite sample performance of the proposed method. A real data example was used to illustrate the proposed method. The method fills in a gap in the existing longitudinal analysis methodology for data with less well‐defined timelines.

中文翻译：

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具有区间删失锚定事件的纵向模型中的随机函数估计

纵向研究的时间表通常以特定事件为基础。在缺乏充分观察到的锚定事件时间的情况下，研究时间线变得不确定，传统的纵向分析失去了时间参考。在本文中，我们考虑了一种对锚定事件进行区间删失的分析情况。我们证明，通过将回归参数估计量表示为未知锚定事件时间分布的插件估计的随机函数，可以扩展标准纵向模型以适应时间线定义不太明确的情况。我们表明，对于一类广泛的纵向模型，函数参数估计是一致的并且渐近正态分布$\sqrt{n}$温和规律性条件下的收敛速度。将所发展的理论应用于线性混合效应模型，我们进一步提出了一种混合计算程序，结合了费舍尔评分方法和模型参数估计的期望-期望（EM）算法的优点。我们进行了模拟研究来验证渐进特性并评估所提出方法的有限样本性能。使用真实数据示例来说明所提出的方法。该方法填补了现有纵向分析方法中针对时间线不太明确的数据的空白。