All Title Author
Keywords Abstract

PLOS ONE  2013 

Bayesian Inference for Generalized Linear Mixed Model Based on the Multivariate t Distribution in Population Pharmacokinetic Study

DOI: 10.1371/journal.pone.0058369

Full-Text   Cite this paper   Add to My Lib

Abstract:

This article provides a fully Bayesian approach for modeling of single-dose and complete pharmacokinetic data in a population pharmacokinetic (PK) model. To overcome the impact of outliers and the difficulty of computation, a generalized linear model is chosen with the hypothesis that the errors follow a multivariate Student t distribution which is a heavy-tailed distribution. The aim of this study is to investigate and implement the performance of the multivariate t distribution to analyze population pharmacokinetic data. Bayesian predictive inferences and the Metropolis-Hastings algorithm schemes are used to process the intractable posterior integration. The precision and accuracy of the proposed model are illustrated by the simulating data and a real example of theophylline data.

References

[1]  Ette EI, Williams PJ (2004) Population pharmacokinetics ii: estimation methods. Ann Pharmacother 38: 1907–1915.
[2]  Ette E, Williams P, Lane J (2004) Population pharmacokinetics iii: design, analysis, and application of population pharmacokinetic studies. Ann Pharmacother 38: 2136–2144.
[3]  Laird N, Ware JH (1982) Random-effects models for longitudinal data. Biometrics 38: 963–974.
[4]  Sheiner LB, Beal S (1982) Bayesian individualization of pharmacokinetics: simple implementation and comparison with non-Bayesian methods. Journal of Pharmaceutical Sciences 71: 1344–8.
[5]  Wakefield J (2004) Non-linear regression modeling methods and models in statistics. New York: Wiley. 119–153 p.
[6]  Vonesh E (1992) Nonlinear models for the analysis of longitudinal data. Statistics in Medicine 11: 1929–1954.
[7]  Davidian M, Giltinan D (1995) Nonlinear models for repeated measurement data. Statistics in Medicine 15: 1462–1463.
[8]  Salway R, Wakefield J (2008) Gamma generalized linear models for pharmacokinetic data. Biometrics 64: 620–626.
[9]  Wade JR, Kelman AW, Howie CA, Whiting B (1993) Effect of misspecification of the absorption process on subsequent parameter estimation in population analysis. J Pharmacokinet Biopharm 21: 209–222.
[10]  Liu I, Mukherjee B, Suesse T, Sparrow D, Park SK (2007) Graphical diagnostics to check model misspecification for the proportional odds regression model. Statistics in Medicine 28: 412–29.
[11]  Wang J (2005) A semi-parametric approach to fitting a nonlinear mixed PK/PD model with an effect compartment using SAS. Pharm Stat 4: 59–69.
[12]  Wakefield J (1996) Bayesian individualization via sampling-based methods. J Pharmacokinet Pharmacodyn 24: 103–131.
[13]  Gimenez O, Choquet R (2010) Individual heterogeneity in studies on marked animals using numerical integration: Capture-Recapture Mixed Models. Eco Soc America 91: 951–957.
[14]  Chib S, Bradley PC (1999) On MCMC sampling in hierarchical longitudinal models. Stat Comput 9: 17–26.
[15]  Gomez E, Gomez-Villegas MA, Marin JM (1998) A multivariate generalization of the power exponential family of distribution. Commun Stat Theory Methods 27: 589–600.
[16]  Robert V (1994) Usefulness and limits of a computer program using a Bayesian one-compartment model for adapting amikacin therapy in critically ill patients. Int J Biomed Comput 36: 153–154.
[17]  Debasis K, Amit M (1998) Estimating the parameters of the linear compartment model. Journal of Statistical Planning and Inference 70: 317–334.
[18]  James WT (2009) Yates (2009) An implementation of the Expectation-Maximization (EM) algorithm for population pharmacokinetic–pharmacodynamic modeling in ACSLXTREME. Comput Methods Programs Biomed 96: 49–62.
[19]  Adeline S, Marc L, France M (2006) Extension of the SAEM algorithm to left-censored data in nonlinear mixed-effects model: Application to HIV dynamics model. Statistics & Data Analysis 51: 1562–1574.
[20]  Natarajan R, Kass RE (2000) Reference Bayesian methods for generalized linear mixed models. Am Stat 95: 227–237.
[21]  Upton RT, Guentert JF, Wallace TW, Powell SJ, Sansom L, et al. (1982) Intraindividual variability in theophylline pharmacokinetics: Statistical verification in 39 of 60 healthy young adults. J Pharmacokinet Pharmacodyn 10: 123–134.
[22]  Worsley KJ, Friston KJ (1995) Analysis of fMRI time-series revisited-again. Neurolmage 2: 173–181.
[23]  Geweke J (1993) Bayesian treatment of The Student’s t linear model. J Econom 8: 19–41.
[24]  Wakefield J (1991) Bayesian analysis of linear and non-linear population models by using the Gibbs sampler. J R Stat Soc Ser C Appl Stat 43: 201–221.
[25]  Fong Y, Rue H, Wakefield J (2010) Bayesian inference for generalized linear mixed models. Biostatistics 11: 397–412.

Full-Text

comments powered by Disqus