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The risk difference scale is often of primary interest when evaluating public health impacts of interventions on binary outcomes. However, few investigators report findings in terms of additive interaction, probably because the models typically used for binary outcomes implicitly measure interaction on the multiplicative scale. One measure with which to assess additive interaction from multiplicative models is the relative excess risk due to interaction (RERI). The RERI measure has been applied in many contexts, but one limitation of previous approaches is that clustering in data has rarely been considered. We evaluated the RERI metric for the setting of clustered data using both population-averaged and cluster-conditional models. In simulation studies, we found that estimation and inference for the RERI using population-averaged models was straightforward. However, frequentist implementations of cluster-conditional models including random intercepts often failed to converge or produced degenerate variance estimates. We developed a Bayesian implementation of log binomial random-intercept models, which represents an attractive alternative for estimating the RERI in cluster-conditional models. We applied the methods to an observational study of adverse birth outcomes in mothers with human immunodeficiency virus, in which mothers were clustered within clinical research sites.

Estimating the Relative Excess Risk Due to Interaction in Clustered-Data Settings