A COMPARISON OF CLUSTER-SPECIFIC AND POPULATION-AVERAGED APPROACHES FOR ANALYZING CORRELATED BINARY DATA

Clustered or correlated samples of binary responses arise frequently in practice due to repeated measurements or to subsampling the primary sampling units. Several recent approaches address intracluster correlation in binary regression problems including cluster-specific methods such as those based on mixed-effects logistic models and population-averaged methods such as those based on beta-binomial models. This paper considers the interpretations of the regression parameters in these two general approaches. We show that, unlike models for correlated Gaussian outcomes, the parameters of the cluster-specific and population-averaged models for correlated binary data describe different types of effects of the covariates on the response probabilities. In the case of random intercepts, we show that the covariate effects measured by the population-averaged approach are closer to zero than those of the cluster-specific approach when the cluster-specific model holds and that the difference in the magnitude of the covariate effects is increasing with intra-cluster correlation. The case of random slopes is also examined. These results are valid for arbitrary random effects distributions and are demonstrated using data on the ability to obtain samples of breast fluid from women.