Abstract: This paper describes a flexible nonparametric quantile regression model for longitudinal data. The basic elements of the model consist of a time-dependent power transformation on the longitudinal dependent variable and a varying-coefficient model for conditional quantiles. A two-step estimation procedure is proposed to fit the model, and its consistency is established. Tuning parameters are chosen with generalized cross validation in conjunction with a Schwarz-type information criterion. The proposed method is illustrated by data on the time evolution of CD4 cell counts in HIV-1 infected patients under three different treatments. The quantile regression approach for longitudinal data enables construction of a pointwise prediction band for CD4 cell counts trajectories without requiring parametric distributional assumptions.
Key words and phrases: Longitudinal data, power transformation, quantile regression, varying-coefficient models.