Simultaneous Inference for Semiparametric Nonlinear Mixed‐Effects Models with Covariate Measurement Errors and Missing Responses

Liu, Wei; Wu, Lang

doi:10.1111/j.1541-0420.2006.00687.x

Cited by 78 publications

(108 citation statements)

References 19 publications

(35 reference statements)

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“…Va r i o u s covariate models were investigated in the literature (Carroll et al, 2006;Higgins et al, 1997;Liu and Wu, 2007;Wu, 2002). However, the fundamental assumption of distributions for measurement random errors is normal in these statistical covariate models and this assumption may lack the robustness against departures from normality and/or may violate the agreement with observed data.…”

Section: Measurement Error Models With a Skew-normal Distributionmentioning

confidence: 99%

“…To characterize skewness appeared often in viral loads and CD4 cell counts, we will develop SN Bayesian mixed-effects joint models in conjunction with the three dynamic response models and LME covariate model. To model the covariate CD4 process, we consider empirical polynomial LME models and choose the best model (1) with quadratic (l = 3) based on AIC/BIC model selection criteria as suggested by Liu and Wu (2007) and Wu (2002). We thus adapted the quadratic polynomial as the SN covariate model (1) with u ik = v ik = (1,s ik ,s 2 ik ) T for the CD4 trajectory as follows.…”

Section: Data and Modelsmentioning

confidence: 99%

“…Following studies in (Liu and Wu, 2007;Wu and Zhang, 2002), we set ψ 0 (t) = φ 0 (t) ≡ 1 and take the same natural cubic splines in the approximations (3) with q ≤ p. The values of p and q are determined based on the AIC/BIC which suggest the following function for w(t ij ) + h i (t ij ) with p = 3 and q = 1 in the model (14) below.…”

Section: Data and Modelsmentioning

confidence: 99%

“…Recent research indicates that the first-phase decay rate of viral response to treatment is a potentially useful biomarker for ARV potency . Even though various statistical modeling and analysis methods have been applied for estimating the parameters of HIV dynamics such as linear and nonlinear regression (Perelson, 1997), linear mixed-effects (LME) and nonlinear mixed-effects (NLME) modeling approach Wu, 2004), nonparametric NLME modeling approach (Liu and Wu, 2007;Liang et al, 2003;Wu and Zhang, 2002;, joint model approach via Monte Carlo EM algorithm (Liu and Wu, 2007;Wu, 2002;Wu, 2004) and Bayesian NLME modeling approach via Markov Chain Monte Carlo (MCMC) procedure (Huang, 2006;Huang and Dagne, 2010), it is not clear which model should be used to estimate the first-phase decay rate. More importantly, in all of these models at least one of the following three important issues standout.…”

Section: Introductionmentioning

confidence: 99%

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Simultaneous Bayesian Inference for Linear, Nonlinear and Semiparametric Mixed-Effects Models with Skew-Normality and Measurement Errors in Covariates

Huang

Ren²,

Dagne³

2011

The International Journal of Biostatistics

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In recent years, various mixed-effects models have been suggested for estimating viral decay rates in HIV dynamic models for complex longitudinal data. Among those models are linear mixed-effects (LME), nonlinear mixed-effects (NLME), and semiparametric nonlinear mixedeffects (SNLME) models. However, a critical question is whether these models produce coherent estimates of viral decay rates, and if not, which model is appropriate and should be used in practice. In addition, one often assumes that a model random error is normally distributed, but the normality assumption may be unrealistic, particularly if the data exhibit skewness. Moreover, some covariates such as CD4 cell count may be often measured with substantial errors. This paper addresses these issues simultaneously by jointly modeling the response variable with skewness and a covariate process with measurement errors using a Bayesian approach to investigate how estimated parameters are changed or different under these three models. A real data set from an AIDS clinical trial study was used to illustrate the proposed models and methods. It was found that there was a significant incongruity in the estimated decay rates in viral loads based on the three mixed-effects models, suggesting that the decay rates estimated by using Bayesian LME or NLME joint models should be interpreted differently from those estimated by using Bayesian SNLME joint models. The findings also suggest that the Bayesian SNLME joint model is preferred to other models because an arbitrary data truncation is not necessary; and it is also shown that the models with a skew-normal distribution and/or measurement errors in covariate may achieve reliable results when the data exhibit skewness.

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Section: Measurement Error Models With a Skew-normal Distributionmentioning

confidence: 99%

Section: Data and Modelsmentioning

confidence: 99%

Section: Data and Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simultaneous Bayesian Inference for Linear, Nonlinear and Semiparametric Mixed-Effects Models with Skew-Normality and Measurement Errors in Covariates

Huang

Ren²,

Dagne³

2011

The International Journal of Biostatistics

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“…However, the covariates such as CD4 cell count are often measured with substantial errors. Thus measurement error in covariates is another typical feature of longitudinal data and statistical inference without considering measurement errors in covariates may result in biased results (Huang and Dagne (2011), Liu and Wu (2007), Wu (2002)). …”

Section: Introductionmentioning

confidence: 99%

Simultaneous Bayesian Inference for Longitudinal Data with Asymmetry, Left-censoring and Covariates Measured with Errors

Huang

Dagne

2012

JJSS

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It is a common practice to analyze complex longitudinal data using flexible nonlinear mixed-effects (NLME) models with normality assumption. However, a serious departure of normality may cause lack of robustness and subsequently lead to invalid inference and unreasonable estimates. Covariates are usually introduced in such models to partially explain inter-subject variations, but some covariates may be often measured with substantial errors. Moreover, the response observations may be subject to left-censoring due to a detection limit. Inferential procedures can be complicated dramatically when data with asymmetric (skewed) characteristics, leftcensoring and measurement errors are observed. In the literature, there has been considerable interest in accommodating either skewness, censoring or covariate measurement errors in such models, but there is relatively little work concerning all of the three features simultaneously. In this article, we jointly investigate a skew-t NLME model for response (with left-censoring) process and a skew-t nonparametric mixedeffects model for covariate (with measurement errors) process. We propose a robust skew-t Bayesian modeling approach in a general form to analyze data in capturing the effects of skewness, censoring and measurement errors in covariates simultaneously. A real data example is offered to illustrate the methodologies. The proposed modeling alternative offers important advantages in the sense that the model can be easily fitted in freely available software and the computational effort for the model with a skew-t distribution is almost equivalent to that of the model with a standard normal distribution.

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A longitudinal study of children's aggressive behaviours based on multivariate mixed models with incomplete data

Liu

2009

Can J Statistics

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The authors consider children's behavioural and emotional problems and their relationships with possible predictors. They propose a multivariate transitional mixed‐effects model for a longitudinal study and simultaneously address non‐ignorable missing data in responses and covariates, measurement errors in covariates, and multivariate modelling of the responses and covariate processes. A real dataset is analysed in details using the proposed method with some interesting results. The Canadian Journal of Statistics 37: 435–452; 2009 © 2009 Statistical Society of Canada

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Simultaneous Inference for Semiparametric Nonlinear Mixed‐Effects Models with Covariate Measurement Errors and Missing Responses

Cited by 78 publications

References 19 publications

Simultaneous Bayesian Inference for Linear, Nonlinear and Semiparametric Mixed-Effects Models with Skew-Normality and Measurement Errors in Covariates

Simultaneous Bayesian Inference for Linear, Nonlinear and Semiparametric Mixed-Effects Models with Skew-Normality and Measurement Errors in Covariates

Simultaneous Bayesian Inference for Longitudinal Data with Asymmetry, Left-censoring and Covariates Measured with Errors

A longitudinal study of children's aggressive behaviours based on multivariate mixed models with incomplete data

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