Joint modelling of quantile regression for longitudinal data with information observation times and a terminal event

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.