Flexible Bayesian quantile regression for independent and clustered data

Biostatistics
Brian J ReichHuixia J Wang

Abstract

Quantile regression has emerged as a useful supplement to ordinary mean regression. Traditional frequentist quantile regression makes very minimal assumptions on the form of the error distribution and thus is able to accommodate nonnormal errors, which are common in many applications. However, inference for these models is challenging, particularly for clustered or censored data. A Bayesian approach enables exact inference and is well suited to incorporate clustered, missing, or censored data. In this paper, we propose a flexible Bayesian quantile regression model. We assume that the error distribution is an infinite mixture of Gaussian densities subject to a stochastic constraint that enables inference on the quantile of interest. This method outperforms the traditional frequentist method under a wide array of simulated data models. We extend the proposed approach to analyze clustered data. Here, we differentiate between and develop conditional and marginal models for clustered data. We apply our methods to analyze a multipatient apnea duration data set.

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Citations

Feb 22, 2012·Journal of the American Statistical Association·Mi-Ok Kim, Yunwen Yang
Jul 13, 2013·Biometrics·Brian J Reich, Luke B Smith
Sep 16, 2011·Journal of the Royal Statistical Society. Series C, Applied Statistics·Susan M Paddock, Thomas A Louis
Mar 21, 2015·Biostatistics·Yuanyuan TangSteven Lipshultz
Dec 3, 2016·Statistical Methods in Medical Research·Maria Francesca MarinoMarco Alfò
Jul 31, 2013·The International Journal of Biostatistics·Nora FenskeMichael Höhle
Sep 21, 2018·International Journal of Environmental Research and Public Health·Chawarat Rotejanaprasert, Andrew B Lawson
Aug 1, 2019·Journal of the Royal Statistical Society. Series C, Applied Statistics·Marco Geraci
May 11, 2016·Biometrical Journal. Biometrische Zeitschrift·Cherry GuptaDebjayoti Sinha
Sep 1, 2015·The Annals of Applied Statistics·Luke B SmithBrian J Reich
Sep 15, 2020·The British Journal of Mathematical and Statistical Psychology·Xin TongJianhui Zhou
Oct 1, 2021·Behavior Research Methods·Seohyun KimJeffrey P Boichuk
Jan 7, 2022·Health Care Management Science·Mani SuleimanVural Aksakalli

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