Quantile regression analysis of censored longitudinal data with irregular outcome-dependent follow-up

In many observational longitudinal studies, the outcome of interest presents a skewed distribution, is subject to censoring due to detection limit or other reasons, and is observed at irregular times that may follow a outcome-dependent pattern. In this work, we consider quantile regression modeling of such longitudinal data, because quantile regression is generally robust in handling skewed and censored outcomes and is flexible to accommodate dynamic covariate-outcome relationships. Specifically, we study a longitudinal quantile regression model that specifies covariate effects on the marginal quantiles of the longitudinal outcome. Such a model is easy to interpret and can accommodate dynamic outcome profile changes over time. We propose estimation and inference procedures that can appropriately account for censoring and irregular outcome-dependent follow-up. Our proposals can be readily implemented based on existing software for quantile regression. We establish the asymptotic properties of the proposed estimator, including uniform consistency and weak convergence. Extensive simulations suggest good finite-sample performance of the new method. We also present an analysis of data from a long-term study of a population exposed to polybrominated biphenyls (PBB), which uncovers an inhomogeneous PBB elimination pattern that would not be detected by traditional longitudinal data analysis.