We study the multiplicative hazards model with intermittently observed longitudinal covariates and time-varying coefficients. For such models, the existing ad hoc approach, such as the last value carried forward, is biased. We propose a kernel weighting approach to get an unbiased estimation of the non-parametric coefficient function and establish asymptotic normality for any fixed time point. Furthermore, we construct the simultaneous confidence band to examine the overall magnitude of the variation. Simulation studies support our theoretical predictions and show favorable performance of the proposed method. A data set from Alzheimer's Disease Neuroimaging Initiative study is used to illustrate our methodology.

翻译：我们研究了具有间歇观测纵向协变量和时变系数的乘性风险模型。对于此类模型，现有的临时性方法（如末次观测值结转法）存在偏差。我们提出了一种核加权方法来获得非参数系数函数的无偏估计，并为任意固定时间点建立了渐近正态性。此外，我们构建了同时置信带来检验变异的整体幅度。模拟研究支持了我们的理论预测，并显示了所提方法的良好性能。我们使用来自阿尔茨海默病神经影像学倡议研究的一个数据集来阐述我们的方法。