Overstuffed sandwiches and separation anxiety: finite-sample variance estimation for penalized GEE with near-separated binary data

TL;DR

This paper develops a new finite-sample variance estimator for penalized GEE in near-separated binary data, improving inference accuracy in small samples.

Contribution

It introduces a novel variance correction method, $ ilde{V}_{AR}$, that accounts for finite-sample bias and leverage effects, outperforming existing corrections.

Findings

$ ilde{V}_{AR}$ provides conservative or near-nominal error control in small samples.

Standard corrections often overadjust or are anti-conservative in low-event, small-$N$ settings.

The proposed method is effective even with $N=10$ and unbalanced designs.

Abstract

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.