Clustered data are common in medical research. Typically, one is interested in a regression model for the association between an outcome and covariates. Two complications that can arise when analysing clustered data are informative cluster size (ICS) and confounding by cluster (CBC). ICS and CBC mean that the outcome of a member given its covariates is associated with, respectively, the number of members in the cluster and the covariate values of other members in the cluster. Standard generalised linear mixed models for cluster-specific inference and standard generalised estimating equations for population-average inference assume, in general, the absence of ICS and CBC. Modifications of these approaches have been proposed to account for CBC or ICS. This article is a review of these methods. We express their assumptions in a common format, thus providing greater clarity about the assumptions that methods proposed for handling CBC make about ICS and vice versa, and about when different methods can be used in practice. We report relative efficiencies of methods where available, describe how methods are related, identify a previously unreported equivalence between two key methods, and propose some simple additional methods. Unnecessarily using a method that allows for ICS/CBC has an efficiency cost when ICS and CBC are absent. We review tools for identifying ICS/CBC. A strategy for analysis when CBC and ICS are suspected is demonstrated by examining the association between socio-economic deprivation and preterm neonatal death in Scotland.
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