Augmented mixed models for clustered proportion data

Often in biomedical research, we deal with continuous (clustered) proportion responses ranging between zero and one quantifying the disease status of the cluster units. Interestingly, the study population might also consist of relatively disease-free as well as highly diseased subjects, contributing to proportion values in the interval [0, 1]. Regression on a variety of parametric densities with support lying in (0, 1), such as beta regression, can assess important covariate effects. However, they are deemed inappropriate due the presence of zeros and/or ones. To evade this, we introduce a class of general proportion density (GPD), and further augment the probabilities of zero and one to this GPD, controlling for the clustering. Our approach is Bayesian, and presents a computationally convenient framework amenable to available freeware.Bayesian case-deletion influence diagnostics based on q-divergence measures are automatic from the MCMC output. The methodology is illustrated using both simulation studies and application to a real dataset from a clinical periodontology study.