Correcting the Variance of Effect Sizes Based on Binary Outcomes for Clustering

Researchers conducting systematic reviews and meta-analyses often encounter studies in which the research design is a well conducted cluster randomized trial, but the statistical analysis does not take clustering into account. For example, the study might assign treatments by clusters but the analysis may not take into account the clustered treatment assignment. Alternatively, the analysis of the primary outcome of the study might take clustering into account, but the reviewer might be interested in another outcome for which only summary data are available in a form that does not take clustering into account. This article provides expressions for the approximate variance of risk differences, log risk ratios, and log odds ratios computed from clustered binary data, using the intraclass correlations. An example illustrates the calculations. References to empirical estimates of intraclass correlations are provided.