Abstract: Based on clustered data with informative cluster size, two efficient estimation methods are proposed for marginal models. In our procedures, the information of within-cluster correlation and minimum cluster size is fully used; this is not the case with the within-cluster re-sampling (WCR) and cluster-weighted generalized estimating equation (CWGEE) methods. When the correlation model is valid and the minimum cluster size is greater than one, the proposed estimatiors further improve the efficiency of the WCR and CWGEE estimators. As with the WCR estimation procedure, our first estimation method is computationally intensive. To overcome this problem, a second estimation method is developed in which the estimator is asymptotically equivalent to the first one. Asymptotic properties of the estimators are derived. The finite sample properties of the second estimator are investigated through a Monte Carlo simulation; a comparison with the CWGEE estimator is made in the numerical study.
Key words and phrases: Cluster-weighted generalized estimating equation, efficient estimation, informative cluster size, within-cluster re-sampling.