We study the multiplicative hazards model with intermittently observed longitudinal covariates and time-varying coefficients. For such models, the existing {\it 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 cerebral infarction is used to illustrate our methodology.

翻译：我们研究了含有间歇性观测纵向协变量及时变系数的乘性风险模型。对于此类模型，现有{\it 临时}方法（如末次观测值结转法）存在偏差。我们提出一种核加权方法以获取非参数系数函数的无偏估计，并建立任意固定时间点的渐近正态性。此外，我们构建了同时置信带以检验变异的整体幅度。模拟研究支持了我们的理论预测，并展示了所提方法的优越性能。通过脑梗死数据集演示了该方法的应用。