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Bayesian joint quantile regression for mixed effects models with censoring and errors in covariates

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Abstract

In this paper, we discuss Bayesian joint quantile regression of mixed effects models with censored responses and errors in covariates simultaneously using Markov Chain Monte Carlo method. Under the assumption of asymmetric Laplace error distribution, we establish a Bayesian hierarchical model and derive the posterior distributions of all unknown parameters based on Gibbs sampling algorithm. Three cases including multivariate normal distribution and other two heavy-tailed distributions are considered for fitting random effects of the mixed effects models. Finally, some Monte Carlo simulations are performed and the proposed procedure is illustrated by analyzing a group of AIDS clinical data set.

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Acknowledgments

The authors thank editors and two reviewers for their constructive comments and valuable suggestions which have greatly improved the paper. The work is partly supported by National Natural Science Foundation of China (Nos. 11501167, 11271368) and Key Scientific Research Project of Henan Province Universities of China (No. 15A110025).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, China

    Yuzhu Tian

  2. Center for Applied Statistics, Renmin University of China, Beijing, 100872, China

    Er’qian Li & Maozai Tian

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  1. Yuzhu Tian
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  2. Er’qian Li
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  3. Maozai Tian
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Correspondence to Yuzhu Tian.

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Tian, Y., Li, E. & Tian, M. Bayesian joint quantile regression for mixed effects models with censoring and errors in covariates. Comput Stat 31, 1031–1057 (2016). https://doi.org/10.1007/s00180-016-0659-1

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  • DOI: https://doi.org/10.1007/s00180-016-0659-1

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