Penalized generalized estimating equations (PGEE) stabilize point estimation for longitudinal binary data under near-separation, but inference still depends on how the sandwich variance is corrected. Existing corrections for PGEE can overadjust in high-leverage directions, require restrictive pooling assumptions, or add global regularization without explaining the bias. We establish first-order asymptotics for PGEE along convergent interior-root sequences and derive a matrix characterization of the parameter-specific overcorrection induced by full leverage adjustment. Finite-sample calibration is limited by both mean bias and the variability of leverage-corrected variance estimates. We propose $\hat{V}_{AR}$, which keeps the score-level leverage correction and adds a finite-sample upward translation dominated at first order by the finite-population factor, with a smaller centering term. In simulations, $\hat{V}_{AR}$ gives conservative or near-nominal type I error in low-event, small-$N$ settings, including $N = 10$, where several standard corrections remain anti-conservative and pooling estimators are unavailable for unbalanced designs.

翻译：惩罚广义估计方程(PGEE)通过稳定近分离条件下纵向二元数据的点估计，但其推断仍取决于夹心方差校正方式。现有PGEE校正方法存在以下问题：在高杠杆方向过度调整、需要严格的合并假设、或引入全局正则化却未解释偏差。我们建立了沿收敛内根序列的PGEE一阶渐近性质，并推导了全杠杆调整引起的参数特定过度校正的矩阵表征。有限样本校准受均值偏差和杠杆校正方差估计变异性的双重限制。我们提出$\hat{V}_{AR}$方法，该方法保留得分级杠杆校正，并增加一阶主导项为有限总体因子的有限样本上平移（附带更小的中心化项）。模拟研究表明，在低事件、小样本量（含$N = 10$）场景中，$\hat{V}_{AR}$能提供保守或接近名义水平的I类错误率，而若干标准校正方法仍显不足，且合并估计量无法用于非平衡设计。