title: Quantile regression for censored mixed-effects models with applications to HIV studies.
abstract: HIV RNA viral load measures are often subjected to some upper and lower detection limits depending on the quantification assays. Hence, the responses are either left or right censored. Linear/nonlinear mixed-effects models, with slight modifications to accommodate censoring, are routinely used to analyze this type of data. Usually, the inference procedures are based on normality (or elliptical distribution) assumptions for the random terms. However, those analyses might not provide robust inference when the distribution assumptions are questionable. In this paper, we discuss a fully Bayesian quantile regression inference using Markov Chain Monte Carlo (MCMC) methods for longitudinal data models with random effects and censored responses. Compared to the conventional mean regression approach, quantile regression can characterize the entire conditional distribution of the outcome variable, and is more robust to outliers and misspecification of the error distribution. Under the assumption that the error term follows an asymmetric Laplace distribution, we develop a hierarchical Bayesian model and obtain the posterior distribution of unknown parameters at thepth level, with the median regression (p= 0.5) as a special case. The proposed procedures are illustrated with two HIV AIDS studies on viral loads that were initially analyzed using the typical normal (censored) mean regression mixed-effects models, as well as a simulation study.
authors.affiliation: Department of Statistics, Campinas States University, Rua Sergio Buarque de Holanda, 651, Cidade Universitária-Barãao Geraldo, CEP: 13083-859, Campinas, SP, Brazil, hlachos@ime.unicamp.br.
authors.forename: Victor H
authors.initials: VH
authors.lastname: Lachos
authors.affiliation: Department of Statistics, University of Connecticut, 215 Glenbrook Rd, U-4120, Storrs, CT 06269, USA, ming-hui.chen@uconn.edu.
authors.forename: Ming-Hui
authors.initials: MH
authors.lastname: Chen
authors.affiliation: Departament of Statistics, Federal University of Rio de Janeiro, Caixa Postal 68530, CEP: 21945-970, Rio de Janeiro, Brazil.
authors.forename: Carlos A
authors.initials: CA
authors.lastname: Abanto-Valle
authors.affiliation: Department of Statistics, Campinas States University, Rua Sergio Buarque de Holanda, 651, Cidade Universitária-Barãao Geraldo, CEP: 13083-859, Campinas, SP, Brazil, cnaber@ime.unicamp.br.
authors.forename: Caio L N
authors.initials: CL
authors.lastname: Azevedo
keywords: Asymmetric Laplace distribution; Censored regression model; Gibbs sampling; HIV viral load; Quantile regression