Robust Joint Non-linear Mixed-Effects Models and Diagnostics for Censored HIV Viral Loads with CD4 Measurement Error

Bandyopadhyay, Dipankar; Castro, Luis M.; Lachos, Víctor H.; Pinheiro, Hildete Prisco

doi:10.1007/s13253-014-0195-9

Cited by 11 publications

(22 citation statements)

References 33 publications

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“…To alleviate such limitations, it is natural to replace the multivariate normally-distributed random effects and within-subject errors of the MNLMM by a broader family, such as the multivariate skew-normal distribution [51], the multivariate skew-t distribution [52], the multivariate skew-elliptical distribution [53], or the multivariate skew-normal independent distribution [54,55]. The proposed methods are readily extendable to carry out ML estimation of the multivariate version of skew-family nonlinear mixed models.…”

Section: Discussionmentioning

confidence: 99%

Approximate Methods for Maximum Likelihood Estimation of Multivariate Nonlinear Mixed-Effects Models

Wang

2015

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Multivariate nonlinear mixed-effects models (MNLMM) have received increasing use due to their flexibility for analyzing multi-outcome longitudinal data following possibly nonlinear profiles. This paper presents and compares five different iterative algorithms for maximum likelihood estimation of the MNLMM. These algorithmic schemes include the penalized nonlinear least squares coupled to the multivariate linear mixed-effects (PNLS-MLME) procedure, Laplacian approximation, the pseudo-data expectation conditional maximization (ECM) algorithm, the Monte Carlo EM algorithm and the importance sampling EM algorithm. When fitting the MNLMM, it is rather difficult to exactly evaluate the observed log-likelihood function in a closed-form expression, because it involves complicated multiple integrals. To address this issue, the corresponding approximations of the observed log-likelihood function under the five algorithms are presented. An expected information matrix of parameters is also provided to calculate the standard errors of model parameters. A comparison of computational performances is investigated through simulation and a real data example from an AIDS clinical study.

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Section: Discussionmentioning

confidence: 99%

Approximate Methods for Maximum Likelihood Estimation of Multivariate Nonlinear Mixed-Effects Models

Wang

2015

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“…This model is the so-called normal NLMEC (N-NLMEC) model. To overcome the sometimes unrealistic assumption of normality of the random effects distribution, a more robust model, named as the skew-normal nonlinear mixed-effects model with censored response (SN-NLMEC) has been proposed (see Bandyopadhyay et al 12 ). Under this model, it is assumed that…”

Section: The Hiv Dynamicmentioning

confidence: 99%

“…Moreover, a variation in the intercept among individuals is also observed. In Figure 1 In Figure 2 we present the estimated trajectories for 9 randomly chosen patients after fitting the SN-NLMEC model 12 . From this figure, it is clear that such model provides biased estimated trajectories.…”

Section: The Actg 315 Clinical Trialmentioning

confidence: 99%

“…For example, Matos et al 8 proposed an EM algorithm for linear and nonlinear mixedeffects models with censored response (LMEC/NLMEC) using the multivariate Student's-t distribution while, in turn, Lachos et al 9 adopted a Bayesian approach to carry out posterior inference for censored linear and nonlinear mixed-effects models considering a class of thick-tail distributions (the so called normal/independent proposed by Lange and Sinsheimer 10 ) as the joint distribution of the error term and random effects. On the other hand, and under a Bayesian framework, Bandyopadhyay et al 11 studied censored linear mixed-effects models considering both skewness and heavy tails, while Bandyopadhyay et al 12 proposed a skewed censored nonlinear mixed-effect model under the presence of measurement error.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian semiparametric modeling for HIV longitudinal data with censoring and skewness

Castro

Wang

Lachos

et al. 2018

Stat Methods Med Res

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In biomedical studies, the analysis of longitudinal data based on Gaussian assumptions is common practice. Nevertheless, more often than not, the observed responses are naturally skewed, rendering the use of symmetric mixed effects models inadequate. In addition, it is also common in clinical assays that the patient's responses are subject to some upper and/or lower quantification limit, depending on the diagnostic assays used for their detection. Furthermore, responses may also often present a nonlinear relation with some covariates, such as time. To address the aforementioned three issues, we consider a Bayesian semiparametric longitudinal censored model based on a combination of splines, wavelets, and the skew-normal distribution. Specifically, we focus on the use of splines to approximate the general mean, wavelets for modeling the individual subject trajectories, and on the skew-normal distribution for modeling the random effects. The newly developed method is illustrated through simulated data and real data concerning AIDS/HIV viral loads.

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“…A variety of proposals (both classical and Bayesian) exist in this direction that uses the univariate or multivariate Student’s- t distribution (Pinheiro et al 2001; Lin and Lee 2006, 2007) in the context of LME/NLME models. Some Bayesian propositions in the context of heavy-tailed LMEC/NLMEC models include Lachos et al (2011) who advocated the use of the normal/independent density (Lange and Sinsheimer 1993), while Bandyopadhyay et al (2012, 2015) studied the LMEC model considering both skewness and heavy-tails. Very recently, Matos et al (2013b) proposed a full maximum-likelihood (ML) based inference using a computationally convenient exact ECM algorithm for the LMEC/NLMEC models using the multivariate Student’s- t distribution (henceforth, the t -LMEC/NLMEC model).…”

Section: Introductionmentioning

confidence: 99%

Influence assessment in censored mixed-effects models using the multivariate Student’s-t distribution

Matos

Bandyopadhyay

Castro

et al. 2015

Journal of Multivariate Analysis

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In biomedical studies on HIV RNA dynamics, viral loads generate repeated measures that are often subjected to upper and lower detection limits, and hence these responses are either left- or right-censored. Linear and non-linear mixed-effects censored (LMEC/NLMEC) models are routinely used to analyse these longitudinal data, with normality assumptions for the random effects and residual errors. However, the derived inference may not be robust when these underlying normality assumptions are questionable, especially the presence of outliers and thick-tails. Motivated by this, Matos et al. (2013b) recently proposed an exact EM-type algorithm for LMEC/NLMEC models using a multivariate Student’s-t distribution, with closed-form expressions at the E-step. In this paper, we develop influence diagnostics for LMEC/NLMEC models using the multivariate Student’s-t density, based on the conditional expectation of the complete data log-likelihood. This partially eliminates the complexity associated with the approach of Cook (1977, 1986) for censored mixed-effects models. The new methodology is illustrated via an application to a longitudinal HIV dataset. In addition, a simulation study explores the accuracy of the proposed measures in detecting possible influential observations for heavy-tailed censored data under different perturbation and censoring schemes.

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Robust Joint Non-linear Mixed-Effects Models and Diagnostics for Censored HIV Viral Loads with CD4 Measurement Error

Cited by 11 publications

References 33 publications

Approximate Methods for Maximum Likelihood Estimation of Multivariate Nonlinear Mixed-Effects Models

Approximate Methods for Maximum Likelihood Estimation of Multivariate Nonlinear Mixed-Effects Models

Bayesian semiparametric modeling for HIV longitudinal data with censoring and skewness

Influence assessment in censored mixed-effects models using the multivariate Student’s-t distribution

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