Censored mixed-effects models for irregularly observed repeated measures with applications to HIV viral loads

Matos, Larissa A.; Castro, Luis M.; Lachos, Víctor H.

doi:10.1007/s11749-016-0486-2

Cited by 21 publications

(23 citation statements)

References 30 publications

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“…Finally, we would like to emphasize the importance of ensuring the constraints to be scientifically sensible before applying constrained statistical inference. For example, some HIV studies 26 considered longer follow‐up periods during which the constraints of positive viral decay rates were less likely to hold due to long‐term complications such as drug side‐effects or loss/attenuation of efficacy. In that case, a constrained test may not be applicable.…”

Section: Discussionmentioning

confidence: 99%

Multiparameter one‐sided tests for nonlinear mixed effects models with censored responses

Zhou

2021

Statistics in Medicine

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Nonlinear mixed‐effects (NLME) models are commonly used in longitudinal studies such as pharmacokinetics and HIV viral dynamics studies. NLME models are often derived based on underlying data‐generating mechanisms, therefore the parameters in these models often have natural physical interpretations that may suggest reasonable constraints on certain parameters. For example, the HIV viral decay rates for populations receiving anti‐HIV treatments may be reasonably expected to be nonnegative. Hypothesis testing for these parameters should incorporate practically reasonable constraints to increase statistical power. Motivated from HIV viral dynamic models, in this article we propose multiparameter one‐sided or constrained tests for NLME models with censored responses, for example, viral dynamic models with viral loads subject to lower detection limits. We propose approximate likelihood‐based tests that are computationally efficient. We evaluate the tests via simulations and show that the proposed tests are more powerful than the corresponding two‐sided or unrestricted tests. We apply the proposed tests to two AIDS datasets with new findings.

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Section: Discussionmentioning

confidence: 99%

Multiparameter one‐sided tests for nonlinear mixed effects models with censored responses

Zhou

2021

Statistics in Medicine

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“…Following the work of Matos et al, the individual score can be determined as

bolds false(y_{i} false| bold-italicθ false) = \frac{\partial \log f false(y_{i} false| bold-italicθ false)}{\partial bold-italicθ} = E ((), \frac{\partial ℓ_{i c} false(bold-italicθ false| y_{c i} false)}{\partial bold-italicθ} false| V_{i}, C_{i}, bold-italicθ)

, where ℓ i c ( θ | y c i ) is the complete data log‐likelihood formed from the observation y c i (see the work of Louis). Then, the empirical information matrix is given by

I_{e} false(\overset{θ}{true} false| boldy false) = true \sum_{i = 1}^{n} {\overset{s}{true}}_{i} {\overset{s}{true}}_{i}^{⊤},

where

{\overset{s}{true}}_{i} = ((), {\overset{s}{true}}_{i, β_{1}}, …, {\overset{s}{true}}_{i, β_{p}}, {\overset{s}{true}}_{i, σ_{1}^{2}}, …, {\overset{s}{true}}_{i, σ_{r *}^{2}}, {\overset{s}{true}}_{i, α_{1}}, …, {\overset{s}{true}}_{i, α_{q *}}, {\overset{s}{true}}_{i, ϕ_{1}}, {\overset{s}{true}}_{i, ϕ_{2}}, {\overset{s}{true}}_{i, ν},)

…”

Section: Estimation Of the Likelihood And Standard Errorsmentioning

confidence: 99%

“…Following the work of Matos et al, 5 the individual score can be determined as sboldyibold-italicθ=∂ log fboldyi|θ∂θ=E∂ℓicθboldyci∂θboldVi,boldCi,θ where ℓ ic ( θ | y ci ) is the complete data log-likelihood formed from the observation y ci (see the work of Louis 28 ). Then, the empirical information matrix is given by boldIebold-italicθtrue^boldy=true∑i=1nbolds^ibolds^i⊤, where trues^i=trues^i,β1, …,trues^i,βp,trues^i,σ12, …,...…”

Section: Estimation Of the Likelihood And Standard Errorsmentioning

confidence: 99%

“…From the statistical viewpoint, this situation presents the problem of censored statistical models in which the observed response lies in a restricted interval (to the left, right, or both of them). Moreover, since the HIV data are generally obtained from follow-up studies (AIDS clinical trials), censored linear and nonlinear mixed effects models 4 and regression models with a specific correlation structure of the error terms 5 are considered to study in detail the effects of specific antiretroviral (ARV) therapies in infected subjects.…”

Section: Introductionmentioning

confidence: 99%

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Flexible longitudinal linear mixed models for multiple censored responses data

Lachos

Matos

Castro

et al. 2018

Statistics in Medicine

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In biomedical studies and clinical trials, repeated measures are often subject to some upper and/or lower limits of detection. Hence, the responses are either left or right censored. A complication arises when more than one series of responses is repeatedly collected on each subject at irregular intervals over a period of time and the data exhibit tails heavier than the normal distribution. The multivariate censored linear mixed effect (MLMEC) model is a frequently used tool for a joint analysis of more than one series of longitudinal data. In this context, we develop a robust generalization of the MLMEC based on the scale mixtures of normal distributions. To take into account the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is considered. For this complex longitudinal structure, we propose an exact estimation procedure to obtain the maximum-likelihood estimates of the fixed effects and variance components using a stochastic approximation of the EM algorithm. This approach allows us to estimate the parameters of interest easily and quickly as well as to obtain the standard errors of the fixed effects, the predictions of unobservable values of the responses, and the log-likelihood function as a byproduct. The proposed method is applied to analyze a set of AIDS data and is examined via a simulation study.

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“…Further, and still using this dataset, Matos et al. 24 proposed a censored nonlinear mixed-effects model using a damped exponential correlation structure for the error term. For a more detailed description of the HIV/AIDS study, we refer the interested reader to Lederman et al.…”

Section: Preliminariesmentioning

confidence: 99%

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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Censored mixed-effects models for irregularly observed repeated measures with applications to HIV viral loads

Cited by 21 publications

References 30 publications

Multiparameter one‐sided tests for nonlinear mixed effects models with censored responses

Multiparameter one‐sided tests for nonlinear mixed effects models with censored responses

Flexible longitudinal linear mixed models for multiple censored responses data

Bayesian semiparametric modeling for HIV longitudinal data with censoring and skewness

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