Finite-Sample Adjustments in Estimating Equations for Correlated Overdispersed Count Outcomes With Application to Cluster Randomized Trials.

Generalized estimating equations (GEE) produce population-averaged estimates of treatment effects in marginal mean models for correlated count outcomes, when intra-cluster correlations are considered as nuisance parameters. For joint inference of marginal means and correlations, paired estimating equations have been proposed. With a small number of clusters, matrix-adjusted estimating equations (MAEE) were introduced to correct finite-sample bias in correlation parameter estimates. This article extends the GEE/MAEE method by adding a third estimating equation for the scale parameter (3EE/MAEE) and demonstrates its superior performance for correlated count outcomes. In simulations, 3EE/MAEE reduced bias of ICC estimates and better maintained the nominal coverage of confidence intervals compared to its uncorrected counterpart. The performance of different bias-corrected sandwich variance estimators as well as working negative binomial (NB) and Poisson models is also evaluated. The 3EE/MAEE method is applied to overdispersed correlated count outcomes from a real-world, stepped wedge cluster randomized trial.