Statistics and Its Interface

Volume 8 (2015)

Number 2

Special Issue on Modern Bayesian Statistics (Part II)

Guest Editor: Ming-Hui Chen (University of Connecticut)

Quantile regression for censored mixed-effects models with applications to HIV studies

Pages: 203 – 215

DOI: http://dx.doi.org/10.4310/SII.2015.v8.n2.a8

Authors

Victor H. Lachos (Department of Statistics, Campinas States University, Cidade Universitária-Barão Geraldo, Campinas, Brazil)

Ming-Hui Chen (Department of Statistics, University of Connecticut, Storrs, Conn., U.S.A.)

Carlos A. Abanto-Valle (Department of Statistics, Federal University of Rio de Janeiro, Brazil)

Caio L. N. Azevedo (Department of Statistics, Campinas States University, Cidade Universitária-Barão Geraldo, Campinas, Brazil)

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 the $p\,$th 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.

Keywords

censored regression model, HIV viral load, quantile regression, asymmetric Laplace distribution, Gibbs sampling

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