Inference for censored quantile regression models in longitudinal studies

Wang, Huixia Judy; Fygenson, Mendel

doi:10.1214/07-aos564

Cited by 79 publications

(82 citation statements)

References 33 publications

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“…Maximizing the likelihood leads to unbiased point estimate, but ALD may not represent the true distribution of error density. At the same time the density function f(y|η) might not be differentiable with respect to η. Alternatively, some other methods are available to provide inference for quantile regression with longitudinal data, such as the rank score test proposed by Wang and Fygenson (2009) recently, and the block bootstrap method which has been applied in the works of Buchinsky (1995) and Lipsitz et al (1997). In this study, we consider the latter method to construct tests and the confidence intervals for β τ .…”

Section: Confidence Intervals For Parametersmentioning

confidence: 99%

Mixed-Effects Models for Conditional Quantiles with Longitudinal Data

Liu¹,

Bottai²

2009

The International Journal of Biostatistics

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We propose a regression method for the estimation of conditional quantiles of a continuous response variable given a set of covariates when the data are dependent. Along with fixed regression coefficients, we introduce random coefficients which we assume to follow a form of multivariate Laplace distribution. In a simulation study, the proposed quantile mixed-effects regression is shown to model the dependence among longitudinal data correctly and estimate the fixed effects efficiently. It performs similarly to the linear mixed model at the central location when the regression errors are symmetrically distributed, but provides more efficient estimates when the errors are over-dispersed. At the same time, it allows the estimation at different locations of conditional distribution, which conveys a comprehensive understanding of data. We illustrate an application to clinical data where the outcome variable of interest is bounded within a closed interval.

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Section: Confidence Intervals For Parametersmentioning

confidence: 99%

Mixed-Effects Models for Conditional Quantiles with Longitudinal Data

Liu¹,

Bottai²

2009

The International Journal of Biostatistics

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“…Koenker [81] generalized his previous work on QR to longitudinal data via penalized least squares method. Other methods or algorithms used to QR includes Barrodale-Roberts algorithm [82], Expectation-Maximization (EM) algorithm [83], Monte Carlo Expectation-Maximization (MCEM) algorithm [13,84,85], and Bayesian approach by Markov chain Monte Carlo (MCMC) procedure [86][87][88][89][90][91][92][93]. Longitudinal QR has been rapidly expanded in many areas, including investment and finance [94,95], economics [96], environmental science [97,98], geography [99], public health [100,101] and biomedical research [102][103][104][105].…”

Section: Qr Models For Longitudinal Datamentioning

confidence: 99%

Quantile Regression Models and Their Applications: A Review

Huang¹,

Zhang²,

Chen³

et al. 2017

J Biom Biostat

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Quantile regression (QR) has received increasing attention in recent years and applied to wide areas such as investment, finance, economics, medicine and engineering. Compared with conventional mean regression, QR can characterize the entire conditional distribution of the outcome variable, may be more robust to outliers and misspecification of error distribution, and provides more comprehensive statistical modeling than traditional mean regression. QR models could not only be used to detect heterogeneous effects of covariates at different quantiles of the outcome, but also offer more robust and complete estimates compared to the mean regression, when the normality assumption violated or outliers and long tails exist. These advantages make QR attractive and are extended to apply for different types of data, including independent data, time-to-event data and longitudinal data. Consequently, we present a brief review of QR and its related models and methods for different types of data in various application areas.Citation: Huang Q, Zhang H, Chen J, He M (2017) Quantile Regression Models and Their Applications: A Review. J Biom Biostat 8: 354.

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“…By utilizing this property, under independent data setting, [31] developed Bayesian QR, [19] and [33] studied the Bayesian estimation procedure for the Tobit QR model with censored data, and [32] proposed a likelihood-based goodness-of-fit test for QR. More recently, QRbased linear mixed-effects models have been considered via different methods for longitudinal data [20,21,23,24,25,26,27,28,29].…”

Section: Nonlinear Quantile Regression For Independent Datamentioning

confidence: 99%

“…In order to have a zero mean vector for the random-effects b i , we assume the location parameter µ = − 2/πδ; see [11] and [12] in detail. The proposed NLMEQR model (4) along with the Tobit model provides a generalization and extension of commonly adopted QR models for longitudinal data in the literature [20,23,24,25,21,26,27,28,29] by the following facts that (i) linear QR-based models are extended to nonlinear QR formulation; (ii) Tobit model is introduced to deal with the inaccurate observations below LOD as left-censoring (or missing values) which are predicted using fully Bayesian predictive distributions; and (iii) random-effects are assumed to follow an SN distribution which offers a robust alternative to the usual symmetric normal distribution, a special case of the SN distribution when ∆ = 0.…”

Section: Quantile Regression-based Models For Longitudinal Datamentioning

confidence: 99%

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

Huang¹,

Chen²,

Lu³

2016

JAS

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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.

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Inference for censored quantile regression models in longitudinal studies

Cited by 79 publications

References 33 publications

Mixed-Effects Models for Conditional Quantiles with Longitudinal Data

Mixed-Effects Models for Conditional Quantiles with Longitudinal Data

Quantile Regression Models and Their Applications: A Review

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

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