Motivated by an analysis of single molecular experiments in the study of T-cell signaling, a new model called varying coefficient frailty model with local linear estimation is proposed. Frailty models have been extensively studied, but extensions to nonconstant coefficients are limited to spline-based methods that tend to produce estimation bias near the boundary. To address this problem, we introduce a local polynomial kernel smoothing technique with a modified expectation-maximization algorithm to estimate the unknown parameters. Theoretical properties of the estimators, including their unbiased property near the boundary, are derived along with discussions on the asymptotic bias-variance trade-off. The finite sample performance is examined by simulation studies, and comparisons with existing spline-based approaches are conducted to show the potential advantages of the proposed approach. The proposed method is implemented for the analysis of T-cell signaling. The fitted varying coefficient model provides a rigorous quantification of an early and rapid impact on T-cell signaling from the accumulation of bond lifetime, which can shed new light on the fundamental understanding of how T cells initiate immune responses.

中文翻译：

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变系数脆弱模型在单分子实验中的应用

在分析 T 细胞信号传导研究中的单分子实验的基础上，提出了一种称为局部线性估计的变系数脆弱模型的新模型。脆弱模型已被广泛研究，但非常数系数的扩展仅限于基于样条的方法，这些方法往往会在边界附近产生估计偏差。为了解决这个问题，我们引入了一种局部多项式核平滑技术，该技术采用改进的期望最大化算法来估计未知参数。估计量的理论性质，包括它们在边界附近的无偏性质，与关于渐近偏差-方差权衡的讨论一起推导出来。通过模拟研究检查有限样本性能，并与现有的基于样条的方法进行比较，以显示所提出方法的潜在优势。所提出的方法用于分析 T 细胞信号。拟合的变化系数模型提供了对键寿命积累对 T 细胞信号传导的早期和快速影响的严格量化，这可以为 T 细胞如何启动免疫反应的基本理解提供新的思路。