高维纵向数据在信息性簇大小下的惩罚加权广义估计方程

近年来，高维纵向数据在科学研究中的应用日益广泛，惩罚广义估计方程(GEE)是分析此类数据的常用方法。然而，当响应变量与簇的大小存在关联时，即所谓的“信息性簇大小”现象，传统GEE方法的优良特性会受到影响。针对这一问题，本文通过系统分析信息性簇大小的影响机制，创新性地提出一种加权GEE方法，有效解决了信息性簇大小带来的偏差问题，并将其进一步扩展至高维数据情况下的惩罚版本。研究表明，惩罚加权GEE方法在模型选择和参数估计方面均具有相合性。本文从理论上证明了，在假设真实模型已知(即Oracle)的条件下，所提出的惩罚加权GEE估计量在渐近意义上等价于Oracle估计量。该结果表明，惩罚加权GEE方法不仅保留了GEE方法的优良性质，而且对信息性簇大小具有稳健性，从而大大拓展了该方法在复杂实际场景中的应用范围。通过模拟研究和实际数据分析表明，惩罚加权GEE方法在各项性能指标上均显著优于现有的替代方法。

High-dimensional longitudinal data have become increasingly prevalent in recent studies, and penalized generalized estimating equations(GEEs) are often used to model such data. However, the desirable properties of the GEE method can break down when the outcome of interest is associated with cluster size, a phenomenon known as informative cluster size. In this article, we address this issue by formulating the effect of informative cluster size and proposing a novel weighted GEE approach to mitigate its impact, while extending the penalized version for high-dimensional settings. We show that the penalized weighted GEE approach achieves consistency in both model selection and estimation. Theoretically, we establish that the proposed penalized weighted GEE estimator is asymptotically equivalent to the Oracle estimator, assuming that the true model is known. This result indicates that the penalized weighted GEE approach retains the excellent properties of the GEE method and is robust to informative cluster sizes, thereby extending its applicability to more complex situations. Simulations and a real data application further demonstrate that the penalized weighted GEE outperforms the existing alternative methods.