Varying coefficient models are widely used to characterize dynamic associations between longitudinal outcomes and covariates. Existing work on varying coefficient models, however, all assumes that observation times are independent of the longitudinal outcomes, which is often violated in real-world studies with outcome-driven or otherwise informative visit schedules. Such informative observation times can lead to biased estimation and invalid inference using existing methods. In this article, we develop estimation and inference procedures for varying coefficient models that account for informative observation times. We model the observation time process as a general counting process under a proportional intensity model, with time-varying covariates summarizing the observed history. To address potential bias, we incorporate inverse intensity weighting into a sieve estimation framework, yielding closed-form coefficient function estimators via weighted least squares. We establish consistency, convergence rates, and asymptotic normality of the proposed estimators, and construct pointwise confidence intervals for the coefficient functions. Extensive simulation studies demonstrate that the proposed weighted method substantially outperforms the conventional unweighted method when observation times are informative. Finally, we provide an application of our method to the Alzheimer's Disease Neuroimaging Initiative study.

翻译：变系数模型被广泛用于刻画纵向结局与协变量之间的动态关联。然而，现有关于变系数模型的研究均假设观测时间独立于纵向结局，这一假设在实际研究中常因结局驱动或其他信息性访视计划而被违背。此类信息性观测时间若使用现有方法进行分析，可能导致估计偏倚与推断失效。本文针对存在信息性观测时间的变系数模型，提出了相应的估计与推断方法。我们将观测时间过程建模为比例强度模型下的通用计数过程，其中时变协变量用于概括已观测历史。为消除潜在偏倚，我们将逆强度加权引入筛估计框架，通过加权最小二乘法得到具有闭式解的系数函数估计量。我们证明了所提估计量的一致性、收敛速率及渐近正态性，并构建了系数函数的逐点置信区间。大量模拟研究表明，当观测时间具有信息性时，所提出的加权方法显著优于传统的未加权方法。最后，我们将该方法应用于阿尔茨海默病神经影像学倡议研究。