title: Augmented mixed models for clustered proportion data.
abstract: 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 to the presence of zeros and/or ones. To evade this, we introduce a class of general proportion density, and further augment the probabilities of zero and one to this general proportion density, 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 Markov chain Monte Carlo output. The methodology is illustrated using both simulation studies and application to a real dataset from a clinical periodontology study.
authors.affiliation: 1 Division of Biostatistics, University of Minnesota School of Public Health, Minneapolis, USA.
authors.forename: Dipankar
authors.initials: D
authors.lastname: Bandyopadhyay
authors.affiliation: 2 Departamento de Estatística, Universidade Estadual de Campinas, Campinas, SP, Brazil.
authors.forename: Diana M
authors.initials: DM
authors.lastname: Galvis
authors.affiliation: 2 Departamento de Estatística, Universidade Estadual de Campinas, Campinas, SP, Brazil.
authors.forename: Victor H
authors.initials: VH
authors.lastname: Lachos
mesh_terms: D001499:Bayes Theorem; D056808:Biostatistics / Q000379:methods; D016000:Cluster Analysis; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D016208:Databases, Factual / Q000706:statistics & numerical data; D006801:Humans; D008390:Markov Chains; D015233:Models, Statistical; D009010:Monte Carlo Method; D010510:Periodontal Diseases / Q000175:diagnosis; D016016:Proportional Hazards Models; D012044:Regression Analysis; D012984:Software
keywords: Bayesian; Kullback-Leibler divergence; augment; dispersion models; periodontal disease; proportion data