Varying coefficient models are useful for modeling longitudinal data and have been extensively studied in the past decade. Motivated by commonly encountered dichotomous outcomes in medical and health cohort studies, we propose a two-step method to estimate the regression coefficient functions in a logistic varying coefficient model for a longitudinal binary outcome. The model depicts time-varying covariate effects without imposing stringent parametric assumptions. The proposed estimation is simple and can be conveniently implemented using existing statistical packages such as SAS and R. We study asymptotic properties of the proposed estimators which lead to asymptotic inference and also develop bootstrap inferential procedures to test whether the coefficient functions are indeed time-varying or are equal to zero. The proposed methodology is illustrated with the analysis of a smoking cessation data set. Simulations are used to evaluate the performance of the proposed method compared to an alternative estimation method based on local maximum likelihood.

中文翻译：

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纵向数据逻辑变系数建模的两步估计方法

变系数模型对于纵向数据建模非常有用，并且在过去十年中得到了广泛的研究。受医疗和健康队列研究中常见的二分结果的启发，我们提出了一种两步法来估计纵向二元结果的逻辑变量系数模型中的回归系数函数。该模型描述了随时间变化的协变量效应，而没有强加严格的参数假设。所提出的估计很简单，可以方便地使用现有的统计软件包（如 SAS 和 R）来实现。我们研究了所提出的估计量的渐近特性，这导致渐近推理，并开发了引导推理程序来测试系数函数是否确实是随时间变化的或等于零。通过对戒烟数据集的分析来说明所提出的方法。与基于局部最大似然的替代估计方法相比，模拟用于评估所提出方法的性能。