Quantile Regression Analysis of Censored Longitudinal Data with Irregular Outcome-Dependent Follow-Up

Abstract

Summary 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.

Globally Adaptive Longitudinal Quantile Regression With High Dimensional Compositional Covariates

“…Many longitudinal quantile regression models studied in literature (for example, Lipsitz et al, 1997;Wang and Fygenson, 2009;Sun et al, 2016;Cho et al, 2016;Gao and Liu, 2019) bear similar forms to model (2.1) or (2.2) but do not involve the zero-sum coefficient constraint. In addition, they were investigated under the locally concerned perspective.…”

ICT as a Key Determinant of Efficiency: A Bootstrap-Censored Quantile Regression (BCQR) Analysis for Vietnamese Banks

“…Since the EF does not follow a normal distribution, OLS and Tobit/truncated regressions may not be appropriate. For instance, Galvao (2011) and Sun et al (2016) argued that, compared to the mean regression, quantile regression is more robust and can deal with data with various distributions. We therefore argue that the second-stage regression, particularly for our case, must not only account for the truncated/censored characteristic of EF but also its skewed distribution.…”

Semi-Parametric Sensitivity Analysis for Trials with Irregular and Informative Assessment Times

“…Bůžková and Lumley [6] adapted this method to allow an intensity function with discontinuities, as could occur when many participants are assessed exactly at the targeted assessment times. Pullenayegum and Feldman [27] combined inverse-intensity weighting with a model for the increments of the outcome process to form a doubly robust estimator, while Sun et al [35] extended inverse-intensity weighting to the setting of quantile regression.…”