Abstract: In many longitudinal studies, longitudinal responses are subject to left-censoring and may be correlated with observation times. In this article, we propose a Tobit quantile regression model for the analysis of left-censored longitudinal data with informative observation times and with the longitudinal responses allowed to depend on the past observation history. Estimating equation approaches are developed for parameter estimation, and the resulting estimators are shown to be consistent and asymptotically normal. A modified Majorize-Minimize algorithm is proposed to compute the proposed estimators. Simulation studies show that the proposed estimators perform well. An application to a data set from an AIDS clinical trial study is provided.

Key words and phrases: Bootstrap resampling, estimating equations, informative observation times, left-censored longitudinal data, Tobit quantile regression.