Semiparametric partial Linear quantile regression of longitudinal data with time varying coefficients and informative observation times

Abstract

Regression analysis of longitudinal data has been a popular topic in many fields for long time. However, only limited research exists for the case where observation times may be informative and for quantile regression of longitudinal data. In particular, to our knowledge, there does not exist any established method for quantile regression of longitudinal data with informative observation times, the focus of this paper. More specifically, we will discuss this problem and present a semiparametric partial linear model with time-varying coefficients. For estimation, B-splines are used to approximate the time-varying coefficients and in addition to the estimation approach, model checking and selection procedures are also provided. The latter can be used to determine the covariates that indeed have time-varying effects on the longitudinal process of interest. The proposed method could identify the underlying true model structure and estimate the parameters simultaneously. Also we establish the convergence rate of the proposed estimators and the asymptotic normality of the estimated time-independent regression parameters. For the assessment of the finite sample performance of the proposed methods, an extensive simulation study is conducted and suggests that they work well for practical situations. Finally they are applied to a set of longitudinal medical cost data on chronic heart failure patients that motivated this study.