Statistical methods for longitudinal and clustered designs with binary responses

Dependent binary response data arise frequently in practice due to repeated measurements in longitudinal studies or to subsampling primary sampling units as in fields such as teratology and ophthalmology. Several classes of approaches have recently been proposed to analyse such repeated binary outcome data. The different classes of approaches measure different effects of covariates on binary responses and address different statistical questions. This article compares the different classes of approaches in terms of parameter interpretation and magnitude, standard errors of model parameters and Wald tests for covariate effects. The results help to clarify the substantive questions which data analysts can address with each approach, as well as why the covariate effects measured by different approaches may be different. Finally, I will provide guidelines to the advantages and disadvantages of alternative approaches for analysing dependent binary responses. Simulations and example data illustrate these findings.