# Optional subsampling for generalized estimating equations in growing-dimensional longitudinal Data

## TL;DR

This paper introduces an optimal Poisson subsampling method for generalized estimating equations to efficiently analyze large-scale longitudinal data with high-dimensional covariates, addressing computational challenges.

## Contribution

It develops a novel subsampling algorithm with proven asymptotic properties and practical two-step probability construction for large-scale longitudinal data analysis.

## Key findings

- Method remains effective under misspecified correlation matrices.
- Achieves computational efficiency in large datasets.
- Demonstrated successful application on real CHFS data.

## Abstract

As a powerful tool for longitudinal data analysis, the generalized estimating equations have been widely studied in the academic community. However, in large-scale settings, this approach faces pronounced computational and storage challenges. In this paper, we propose an optimal Poisson subsampling algorithm for generalized estimating equations in large-scale longitudinal data with diverging covariate dimension, and establish the asymptotic properties of the resulting estimator. We further derive the optimal Poisson subsampling probability based on A- and L-optimality criteria. An approximate optimal Poisson subsampling algorithm is proposed, which adopts a two-step procedure to construct these probabilities. Simulation studies are conducted to evaluate the performance of the proposed method under three different working correlation matrices. The results show that the method remains effective even when the working correlation matrices are misspecified. Finally, we apply the proposed method to the CHFS dataset to illustrate its empirical performance.