Some Simple Methods for Estimating Intraindividual Variability in Nonlinear Mixed Effects Models

Davidian, Marie; Giltinan, David M.

doi:10.2307/2532602

Cited by 57 publications

(60 citation statements)

References 17 publications

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“…The dataset include plasma concentration of 6 individuals measured at 11 time points ranging from 15 [5] used the following biexponential model with power variance function to fit the data.…”

Section: Real Analysismentioning

confidence: 99%

“…Kwan et al [13] used two-compartment open models to analysis the metabolic process. Davidian and Giltinan [5] carried out subsequent analysis and found that heterogeneous * Corresponding Author variability is evident for the indomethacin data through studentized residuals plot. To account for the heterogeneity, Davidian and Giltinan [5] extended the classic random coefficient models by adding a heteroscedasticity function as follows,…”

Section: Introductionmentioning

confidence: 99%

“…Modelling the heterogeneity and identifying covariates that are related to variance can fully characterize the intraindividual variation [5] and provide a better understanding of the research problems [16] . Studying the heteroscedasticity of the model is not only of practical interest, but is also of important theoretical significance.…”

Section: Introductionmentioning

confidence: 99%

“…Davidian and Giltinan [5] extended the generalized least squares (GLS) estimator by pooling information across individuals to estimate the intra-individual variability in nonlinear mixed effects models. In another research, they introduced several estimation methods for nonlinear mixed models with heterogeneity [4], including two stage method and linearization method.…”

Section: Introductionmentioning

confidence: 99%

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Semiparametric hierarchical model with heteroscedasticity

Tian

Pan

2017

Statistics and Its Interface

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Recent work on hierarchical data analysis mainly focuses on the multilevel structure of the mean response. Little research for hierarchical heteroscedasticity was done in the literature. In this paper, we propose a class of hierarchical models with heteroscedasticity and then investigate the semi-parametric statistical inferences. Laplace's approximation is employed to obtain an approximated marginal likelihood function and splines method is used to estimate the unknown functions. We also provide the consistency of the estimators. Simulation studies and real data analysis show that the proposed estimation procedures work well.

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Section: Real Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Semiparametric hierarchical model with heteroscedasticity

Tian

Pan

2017

Statistics and Its Interface

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show abstract

“…If p (b i |ϑ b ) is a normal density, numerical approximation of the integral may be achieved by Gauss-Hermite quadrature. This is a standard deterministic method of approximating an integral by a weighted average of the integrand evaluated at suitably chosen points over a grid, where accuracy increases with the number of grid points (Davidian & Giltinan, 1993). As the integrals over b i in Eq.…”

Section: The Loglikelihoodmentioning

confidence: 99%

Fitting correlated residual error structures in nonlinear mixed-effects models using SAS PROC NLMIXED

Harring

Blozis

2013

Behav Res

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Nonlinear mixed-effects (NLME) models remain popular among practitioners for analyzing continuous repeated measures data taken on each of a number of individuals when interest centers on characterizing individual-specific change. Within this framework, variation and correlation among the repeated measurements may be partitioned into interindividual variation and intraindividual variation components. The covariance structure of the residuals are, in many applications, consigned to be independent with homogeneous variances, σ 2 I n i , not because it is believed that intraindividual variation adheres to this structure, but because many software programs that estimate parameters of such models are not well-equipped to handle other, possibly more realistic, patterns. In this article, we describe how the programmatic environment within SAS may be utilized to model residual structures for serial correlation and variance heterogeneity. An empirical example is used to illustrate the capabilities of the module.

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Bootstrap approach for constructing confidence intervals for population pharmacokinetic parameters. II: a bootstrap modification of standard two-stage (STS) method for phase I trial

Yafune¹,

Ishiguro²

1999

Statist. Med.

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For population pharmacokinetics in phase I trials, the standard two-stage (STS) method is quite appealing, especially to non-statisticians, because the method is theoretically and computationally simple. The method, however, does not take into account the uncertainty in estimating individual-specific parameters and gives biased estimates for population variances of pharmacokinetic parameters. This is one of the main reasons why the STS method is not generally recommended. This paper proposes a simple bootstrap modification of the STS method for estimating confidence intervals of population means and standard deviations of pharmacokinetic parameters in phase I trials. The proposed approach adopts a bootstrap bias correction in estimating population variances of pharmacokinetic parameters. Applications are given to a simulated data set and an actual phase I trial to show how the proposed approach works in practice.

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Some Simple Methods for Estimating Intraindividual Variability in Nonlinear Mixed Effects Models

Cited by 57 publications

References 17 publications

Semiparametric hierarchical model with heteroscedasticity

Semiparametric hierarchical model with heteroscedasticity

Fitting correlated residual error structures in nonlinear mixed-effects models using SAS PROC NLMIXED

Bootstrap approach for constructing confidence intervals for population pharmacokinetic parameters. II: a bootstrap modification of standard two-stage (STS) method for phase I trial

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