Isaac Scientific Publishing

Journal of Advanced Statistics

Bayesian Approach to Nonlinear Mixed-Effects Quantile Regression Models for Longitudinal Data with Non-normality and Left-censoring

Download PDF (674 KB) PP. 109 - 121 Pub. Date: September 1, 2016

DOI: 10.22606/jas.2016.13001


  • Yangxin Huang*
    School of Mathematics and Computer, Wuhan Textile University, Wuhan 430073, P.R.China and College of Public Health, University of South Florida, Tampa, Florida 33612, USA
  • Jiaqing Chen
    Department of Statistics, Wuhan University of Technology, Wuhan, Hubei, 430070, P.R.China
  • Xiaosun Lu
    Department of Biostatistics, Medpace Inc., Cincinnati, OH 45227, USA


In longitudinal studies, measurements of the same individuals are taken repeatedly through time, but it often happens that some collected data are observed with the following issues. (i) Often, the primary goal is to characterize the change in response over time. Compared with conventional mean regression, quantile regression (QR) can characterize the entire conditional distribution of the outcome variable, and may be more robust to outliers and mis-specification of error distribution. (ii) longitudinal outcomes may suffer from a serious departure of normality in which normality assumption may cause lack of robustness and subsequently lead to invalid inference; and (iii) the response observations may be subject to left-censoring due to a limit of detection. Inferential procedures will become very complicated when one analyzes data with these features together. In this article, Bayesian modeling approach to nonlinear mixed-effects quantile regression models for longitudinal data is developed to study simultaneous impact of multiple data features (non-normality, left-censoring, non-linearity, outliers and heavy-tails). Simulation studies are conducted to assess the performance of the proposed models and methods. A real data example is analyzed to demonstrate the proposed methodology through comparing potential models with different distribution specifications of random-effects.


Asymmetric Laplace distribution, Bayesian inference, Left-censoring, Nonlinear mixedeffects quantile regression, Skew-normal distribution.


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