Assessment of a Modified Sandwich Estimator for Generalized Estimating Equations with Application to Opioid Poisoning in MIMIC-IV ICU Patients

Longitudinal data is encountered frequently in many healthcare research areas to include the critical care environment. Repeated measures from the same subject are expected to correlate with each other. Models with binary outcomes are commonly used in this setting. Regression models for correlated binary outcomes are frequently fit using generalized estimating equations (GEE). The Liang and Zeger sandwich estimator is often used in GEE to produce unbiased standard error estimation for regression coefficients in large sample settings, even when the covariance structure is misspecified. The sandwich estimator performs optimally in balanced designs when the number of participants is large with few repeated measurements. The sandwich estimator’s asymptotic properties do not hold in small sample and rare-event settings. Under these conditions, the sandwich estimator underestimates the variances and is biased downwards. Here, the performance of a modified sandwich estimator is compared to the traditional Liang-Zeger estimator and alternative forms proposed by authors Morel, Pan, and Mancl-DeRouen. Each estimator’s performance was assessed with 95% coverage probabilities for the regression coefficients using simulated data under various combinations of sample sizes and outcome prevalence values with independence and autoregressive correlation structures. This research was motivated by investigations involving rare-event outcomes in intensive care unit settings.