A Grouped GEE Framework for Quantile Regression in Heterogeneous Longitudinal Data Analysis

ABSTRACT In longitudinal data analysis, identifying subgroups of subjects with heterogeneous parameters is crucial for understanding complex data structures. To address the challenges posed by within‐subject correlation and heteroscedasticity across subjects, we propose a novel grouped generalized estimating equation (GEE) method for quantile regression (QR). Under the assumption that subjects can be partitioned into a finite number of groups, where individuals within the same group share identical regression coefficients at a given quantile level, we develop a computationally efficient three‐step algorithm that simultaneously performs subject grouping, estimates QR coefficients and infers the correlation matrix. Theoretically, we establish the asymptotic distribution of the group‐specific QR coefficient estimator by demonstrating its asymptotic equivalence to the infeasible estimator with known group membership, even when both dimensions of the longitudinal data diverge. Numerical studies and theoretical analysis show that incorporating the estimated correlation matrix significantly improves the efficiency of both coefficient estimation and group identification, which provides an efficient and flexible framework for analysing heterogeneous longitudinal data.