Quantile regression of longitudinal data with informative observation times

Longitudinal data are frequently encountered in medical follow-up studies and economic research. Conditional mean regression and conditional quantile regression are often used to fit longitudinal data. Many methods focused on the cases where the observation times are independent of the response variables or conditionally independent of them given the covariates. Few papers have considered the case where the response variables depend on the observation times or observation times are random variables associated with a counting process. In this paper, we propose a marginally conditional quantile regression approach for modeling longitudinal data with random observing times and informative observation times. Estimators of the parameters in the proposed conditional quantile regression are derived by constructing non-smooth estimating equations when the observation times follow a counting process. Consistency and asymptotic normality for these estimators are established. Asymptotic variance is estimated based on a resampling method. A simulation study is conducted and suggests that the finite sample performance of the proposed approach is very good, and an illustrative approach is provided.