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We group approaches to modeling correlated binary data according to data recorded cross-sectionally as opposed to data recorded longitudinally; according to models that are population-averaged as opposed to subject-specific; and according to data with time-dependent covariates as opposed to time-independent covariates. Standard logistic regression models are appropriate for cross-sectional data. However, for longitudinal data, methods such as generalized estimating equations (GEE) and generalized method of moments (GMM) are commonly used to fit population-averaged models, while random-effects models such as generalized linear mixed models (GLMM) are used to fit subject-specific models. Some of these methods account for time-dependence in covariates while others do not. This paper addressed these approaches with an illustration using a Medicare dataset as it relates to rehospitalization. In particular, we compared results from standard logistic models, GEE models, GMM models, and random-effects models by analyzing a binary outcome for four successive hospitalizations. We found that these procedures address differently the correlation among responses and the feedback from response to covariate. We found marginal GMM logistic regression models to be more appropriate when covariates are classified as time-dependent in comparison to GEE models. We also found conditional random-intercept models with time-dependent covariates decomposed into components to be more appropriate when time-dependent covariates are present in comparison to ordinary random-effects models. We used the SAS procedures GLIMMIX, NLMIXED, IML, GENMOD, and LOGISTIC to analyze the illustrative dataset, as well as unique programs written using the R language.

Modeling Correlated Binary Outcomes with Time-Dependent Covariates