  We propose a novel inference procedure for linear combinations of
high-dimensional regression coefficients in generalized estimating equations
(GEE), which are widely used to analyze correlated data. Our estimator for this
more general inferential target, obtained via constructing projected estimating
equations, is shown to be asymptotically normally distributed under certain
regularity conditions. We also introduce a data-driven cross-validation
procedure to select the tuning parameter for estimating the projection
direction, which is not addressed in the existing procedures. We demonstrate
the robust finite-sample performance, especially in estimation bias and
confidence interval coverage, of the proposed method via extensive simulations,
and apply the method to a longitudinal proteomic study of COVID-19 plasma
samples to investigate the proteomic signatures associated with disease
severity.
