A Comparison of Variance Estimators for Logistic Regression Models Estimated Using Generalized Estimating Equations (<scp>GEE</scp>) in the Context of Observational Health Services Research

In observational health services research, researchers often use clustered data to estimate the independent association between individual outcomes and several cluster-level covariates after adjusting for individual-level characteristics. Generalized estimating equations are a popular method for estimating generalized linear models using clustered data. The conventional Liang-Zeger variance estimator is known to result in estimated standard errors that are biased low when the number of clusters in small. Alternative variance estimators have been proposed for use when the number of clusters is low. Previous studies focused on these alternative variance estimators in the context of cluster randomized trials, which are often characterized by a small number of clusters and by an outcomes regression model that often consists of a single cluster-level variable (the treatment/exposure variable). We addressed the following questions: (i) which estimator is preferred for estimating the standard errors of cluster-level covariates for logistic regression models with multiple binary and continuous cluster-level variables in addition to subject-level variables; (ii) in such settings, how many clusters are required for the Liang-Zeger variance estimator to have acceptable performance for estimating the standard errors of cluster-level covariates. We suggest that when estimating standard errors: (i) when the number of clusters is < 15 use the Kauermann-Carroll estimator; (ii) when the number of clusters is between 15 and 40 use the Fay-Graubard estimator; (iii) when the number of clusters exceeds 40, use the Liang-Zeger estimator or the Fay-Graubard estimator. When estimating confidence intervals, we suggest using the Mancl-DeRouen estimator with a t-distribution.