Various methods of modeling correlated binary data are compared as applied to data from health services research. The methods include the standard logistic regression, a simple adjustment of the standard errors of logistic regression by a single inflator, the weighted logistic regression, the generalized estimating equation, the beta-binomial model, and two proposed bootstrap methods. First, these approaches are compared for a fixed set of predictors by individual tests of significance. Next, several subsets of predictors are compared through the AIC criterion, whenever applicable.