Globally Adaptive Longitudinal Quantile Regression With High Dimensional Compositional Covariates

Abstract

In this work, we propose a longitudinal quantile regression framework that enables a robust characterization of heterogeneous covariate-response associations in the presence of high-dimensional compositional covariates and repeated measurements of both response and covariates. We develop a globally adaptive penalization procedure, which can consistently identify covariate sparsity patterns across a continuum set of quantile levels. The proposed estimation procedure properly aggregates longitudinal observations over time, and ensures the satisfaction of the sum-zero coefficient constraint that is needed for proper interpretation of the effects of compositional covariates. We establish the oracle rate of uniform convergence and weak convergence of the resulting estimators, and further justify the proposed uniform selector of the tuning parameter in terms of achieving global model selection consistency. We derive an efficient algorithm by incorporating existing R packages to facilitate stable and fast computation. Our

Joint modelling of quantile regression for longitudinal data with information observation times and a terminal event

“…Quantile regression approaches have been widely applied to analyze complicated data (Sun, Li & Zhou, 2020). For longitudinal data, quantile regression models were considered by He, Fu & Fung (2003), Koenker (2004), Karlsson (2005), Ma & Wei (2009), and Wang & Fygenson (2009). Recently, Chen, Tang & Zhou (2016) developed a quantile regression method to analyze longitudinal data when the response variable depends on the observation times.…”