GEE analysis in joint mean-covariance model for high-dimensional longitudinal data with HPC

High-dimensional covariate longitudinal data is common in various fields. However, estimating a low-dimensional parameter of interest can be challenging due to the presence of high-dimensional nuisance parameters. Traditional methods using generalized estimating equations become ineffective for estimating mean parameters when the working covariance structure is misspecified. In this paper, we first construct generalized estimating equations for regression parameters in a joint mean-covariance model for fixed-dimensional longitudinal data, based on reparameterization of the correlation structure using angles or hyperspherical coordinates. We then utilize a decorrelated matrix to handle parameter estimation for high-dimensional longitudinal data. This model addresses both the parsimonious modelling of correlations without constraints and the challenge of high-dimensional nuisance parameters. The resulting estimators are shown to be consistent and asymptotically normal, with data simulations supporting the effectiveness of the proposed approach.