Longitudinal data arise frequently in biomedical follow-up observation studies. Conditional mean regression and conditional quantile regression are two popular approaches to model longitudinal data. Many results are derived under the case where the response variables are independent of the observation times. In this article, we propose a quantile regression model for the analysis of longitudinal data, where the longitudinal responses are allowed to not only depend on the past observation history but also associate with a terminal event (e.g., death). Non-smoothing estimating equation approaches are developed to estimate parameters, and the consistency and asymptotic normality of the proposed estimators are established. The asymptotic variance is estimated by a resampling method. A majorize-minimize algorithm is proposed to compute the proposed estimators. Simulation studies show that the proposed estimators perform well, and an HIV-RNA dataset is used to illustrate the proposed method.

中文翻译：

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具有信息观察时间和终端事件的纵向数据的分位数回归联合建模

纵向数据经常出现在生物医学后续观察研究中。条件均值回归和条件分位数回归是纵向数据建模的两种流行方法。许多结果都是在响应变量与观测时间无关的情况下得出的。在本文中，我们提出了一种用于分析纵向数据的分位数回归模型，其中纵向响应不仅取决于过去的观察历史，而且还与最终事件（例如死亡）相关。开发了非平滑估计方程方法来估计参数，并建立了所提出的估计量的一致性和渐近正态性。渐近方差是通过重采样方法估计的。提出了一种主要最小化算法来计算所提出的估计量。模拟研究表明，所提出的估计器表现良好，并且使用 HIV-RNA 数据集来说明所提出的方法。