To address the computational challenges arising from large-scale longitudinal data, an optimal Poisson subsampling algorithm is proposed for quantile regression. The proposed method can substantially alleviate computational burden. Under some regularity conditions, we derive the asymptotic properties of the estimators from weighted quantile generalized estimating equations. For practical implementation, an efficient algorithm is proposed for parameter estimation. Furthermore, asymptotic theory is established for penalized weighted smooth quantile generalized estimating equations, and regularized parameter estimation is performed within the optimal Poisson subsampling framework. Both numerical simulations and a real data application demonstrate that the proposed optimal Poisson subsampling algorithm outperforms the uniform Poisson subsampling algorithm, and the regularized estimation exhibits satisfactory performance as well.

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