We describe a multinomial overdispersion model (MOM) that leads to the specification of the first two moments of the outcome and allows the estimation of the global parameters using generalized estimating equations (GEE). Similar models have been extensively studied for correlated normal and binomial data but much less so for correlated multinomial data. We also introduce a Global Blinding Index as a target parameter and illustrate the application of the GEE method to its estimation from 1) a clinical trial with clustering by practitioner and 2) a meta-analysis on psychiatric disorders.
In addition, we examine empirically the impact of a small number of clusters, high variability in cluster sizes and the magnitude of the intra-class correlation on the performance of the GEE estimators of the Global Blinding Index using the data simulated from different models. We use simulated data to compare these estimators with the inverse-variance weighted estimators and a maximum-likelihood estimator, derived under the Dirichlet-multinomial model.