We consider varying-coefficient models for mixed synchronous and asynchronous longitudinal covariates, where asynchronicity refers to the misalignment of longitudinal measurement times within an individual. We propose three different methods of parameter estimation and inference. The first method is a one-step approach that estimates non-parametric regression functions for synchronous and asynchronous longitudinal covariates simultaneously. The second method is a two-step approach in which synchronous longitudinal covariates are regressed with the longitudinal response by centering the synchronous longitudinal covariates first and, in the second step, the residuals from the first step are regressed with asynchronous longitudinal covariates. The third method is the same as the second method except that in the first step, we omit the asynchronous longitudinal covariate and include a non-parametric intercept in the regression analysis of synchronous longitudinal covariates and the longitudinal response. We further construct simultaneous confidence bands for the non-parametric regression functions to quantify the overall magnitude of variation. Extensive simulation studies provide numerical support for the theoretical findings. The practical utility of the methods is illustrated on a dataset from the ADNI study.

翻译：我们考虑混合同步与异步纵向协变量的变系数模型，其中异步性指个体内纵向测量时间的不对齐。我们提出了三种参数估计与推断方法。第一种方法是一步法，同时估计同步与异步纵向协变量的非参数回归函数。第二种方法是两步法，首先通过中心化同步纵向协变量对纵向响应进行回归，第二步将第一步的残差对异步纵向协变量进行回归。第三种方法除第一步在同步纵向协变量与纵向响应的回归分析中省略异步纵向协变量并包含非参数截距项外，其余与第二种方法相同。我们进一步构建非参数回归函数的联合置信带以量化整体变异幅度。大量模拟研究为理论结果提供了数值支持。ADNI研究数据集验证了该方法的实际应用价值。