Mean estimating equation approach to analysing cluster-correlated data with nonignorable cluster sizes

Most methods for analysing cluster-correlated biological data implicitly assume the ignorability of cluster sizes. When this assumption fails, the resulting inferences may be asymptotically invalid. Hoffman et al. (2001) proposed a simple but computationally intensive method, based on a large number of within-cluster resamples and associated separate estimating equations, that leads to asymptotically valid inferences whether the cluster sizes are ignorable or not. We study a simple method, based on a single inverse cluster size-weighted estimating equation, that avoids resampling and yet leads to asymptotically valid inferences. Simulation results are presented to assess the performance of the proposed method. We also propose Wald tests for ignorability of cluster sizes.