Association models for periodontal disease progression: a comparison of methods for clustered binary data

We investigate population-averaged (PA) and cluster-specific (CS) associations for clustered binary logistic regression in the context of a longitudinal clinical trial that investigated the association between tooth-specific visual elastase kit results and periodontal disease progression within 26 weeks of follow-up. We address estimation of population-averaged logistic regression models with generalized estimating equations (GEE), and conditional likelihood (CL) and mixed effects (ME) estimation of CS logistic regression models. Of particular interest is the impact of clusters that do not provide information for conditional likelihood methods (non-informative clusters) on inferences based upon the various methodologies. The empirical and analytical results indicate that CL methods yield smaller test statistics than ME methods when non-informative clusters exist, and that CL estimates are less efficient than ME estimates under certain conditions. Moreover, previously reported relationships between population-averaged and cluster-specific parameters appear to hold for the corresponding estimates in the presence of these clusters.