A novel gibbs maximum a posteriori (GMAP) approach on bayesian nonlinear mixed-effects population pharmacokinetics (PK) models

Journal of Biopharmaceutical Statistics

Volumn 19, Issue 4, 2009, Pages 700-720

  Kim, Seongho ^a   Hall, Stephen D ^a   Li, Lang ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

Bayesian model; Gibbs Maximum a Posteriori (GMAP); Monte Carlo Markov Chain (MCMC); Pharmacokinetics (PK)

Indexed keywords

MIDAZOLAM;

ALGORITHM; ARTICLE; BAYES THEOREM; CONTROLLED STUDY; DATA ANALYSIS; GIBBS MAXIMUM A POSTERIOR; INTRAVENOUS DRUG ADMINISTRATION; METHODOLOGY; MONTE CARLO METHOD; PERFORMANCE MEASUREMENT SYSTEM; PHARMACOKINETICS; PRIORITY JOURNAL; SIMULATION; STATISTICAL MODEL; VALIDITY;

ALGORITHMS; BAYES THEOREM; BIAS (EPIDEMIOLOGY); CLINICAL TRIALS AS TOPIC; COMPUTER SIMULATION; DATA INTERPRETATION, STATISTICAL; HUMANS; INFUSIONS, INTRAVENOUS; MARKOV CHAINS; MIDAZOLAM; MODELS, STATISTICAL; MONTE CARLO METHOD; NONLINEAR DYNAMICS; REPRODUCIBILITY OF RESULTS;

EID: 70449635585     PISSN: 10543406     EISSN: 15205711     Source Type: Journal    
DOI: 10.1080/10543400902964159     Document Type: Article

References (29)

1. Beal, S. L., Sheiner, L. B. (1982). Estimating population kinetics. Crit. Rev. Biomed. Eng. 8:195-222.
2. Bennett, J. E., Racine-Poon, A., Wakefield, J. C. (1996). MCMC for nonlinear hierarchical models. In: Gilks, W. R., Richardson, S., Spiegelhalter, D. J., eds. Markov Chain Monte Carlo in Practice. London: Chapman and Hall, pp. 337-339.
3. Broyden, C. G. (1970). The convergence of a class of double-rank minimization algorithms: 2. the new algorithm. IMA Journal of Applied Mathematics 6:222-231.
4. Damien, P., Wakefield, J., Walker, S. (1999). Gibbs sampling for Bayesian nonconjugate and hierarchical models by using auxiliary variables. Journal of the Royal Statistical Society B 61:331-344.
5. Davidian, M., Gallant, A. R. (1992). Smooth nonparametric maximum likelihood estimation for population pharmacokinetics, with application to quinidine. Journal of Pharmacokinetics and Pharmacodynamics 20:529-556.
6. Delyon, B., Lavielle, M., Moulines, E. (1999). Convergence of a stochastic approximation version of the EM algorithm. The Annals of Statistics 27:94-128.
7. van Dyk, D. A., Meng, X. L. (2001). The art of data augmentation. Journal of Computational and Graphical Statistics 10:1-50.
8. Ette, E. I., Miller, R., Gillespie, W. R., Huang, S. M., Lesko, L., Williams, R. (1997). The population approach: FDA experience. In: Balant, L. P., Aarons, L., eds. Concentration and Dose, the Population Approach: Measuring and Managing Variability in Response, Commission of the European Communities. Brussels: European Cooperation in the field of Scientific and Technical Research, pp. 271-275.
9. Geman, S., Geman, D. (1984). Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6:721-741.
10. Gilks, W. R. (1996). Full conditional distributions. In: Gilks, W. R., Richardson, S., Spiegelhalter, D. J., eds. Markov Chain Monte Carlo in Practice. London: Chapman and Hall, pp. 75-88.
11. Gilks, W. R., Roberts, G. O. (1996). Strategies for improving MCMC. In: Gilks, W. R., Richardson, S., Spiegelhalter, D. J., eds. Markov Chain Monte Carlo in Practice. London: Chapman and Hall, pp. 89-114.
12. Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57:97-109.
13. Li, L., Yu, M., Chin, R., Lucksiri, A., Flockhart, D. A., Hall, S. D. (2007). Drugdrug interaction prediction: a Bayesian meta-analysis approach. Statistics in Medicine 26:3700-3721.
14. Lindstrom, M. J., Bates, D. M. (1990). Nonlinear mixed-effects models for repeated measures data. Biometrics 46:673-687.
15. Liu, J., Wong, W. H., Kong, A. (1994). Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes. Biometrika 81:27-40.
16. Liu, J. S., Wong, W. H., Kong, A. (1995). Covariance structure and convergence rate of the Gibbs sampler with various scans. Journal of the Royal Statistical Society B 57:157-169.
17. Mallet, A. (1986). A maximum likelihood estimation method for random coefficient regression models. Biometrika 73:645-656.
18. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., Teller, E. (1953). Equation of state calculations by fast computer machines. Journal of Chemical Physics 21:1087-1092.
19. Raftery, A. E., Lewis, S. (1992). How many iterations in the Gibbs sampler? In: Bernardo, M., Berger, J. O., Dawid, A. P., Smith, A. F. M., eds. Bayesian Biostatistics 4. Oxford: Oxford University Press, pp. 763-773.
20. Raftery, A. E., Lewis, S. (1996). Implementing MCMC. In: Gilks, W. R., Richardson, S., Spiegelhalter, D. J., eds. Markov Chain Monte Carlo in Practice. London: Chapman and Hall, pp. 115-130.
21. Roberts, G. O. (1996). Markov chain concepts related to sampling algorithms. In: Gilks, W. R., Richardson, S., Spiegelhalter, D. J., eds. Markov Chain Monte Carlo in Practice. London: Chapman and Hall, pp. 45-57.
22. Sheiner, L. B., Beal, S. L. (1982). Bayesian individualization of pharmacokinetics: simple implementation and comparison with non-Bayesian methods. Journal of Pharmceutical Science 71:1344-1348.
23. Smith, A. F. M., Gelfand, A. E. (1992). Bayesian statistics without tears: a samplingresampling perspective. The American Statistician 46:84-88.
24. Smith, A. F. M., Roberts, G. O. (1993). Bayesian computation via the Gibbs sampler and relater Markov chain Monte Carlo methods. Journal of the Royal Statistical Society B 55:3-23.
25. Tanner, M. A., Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association 82:528-550.
26. Tierney, L. (1994). Markov chains for exploring posterior distributions (with discussion). Annals of Statistics 22:1701-1762.
27. Vonesh, E. F., Carter, R. L. (1992). Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics 48:1-17.
28. Wakefield, J. C., Smith, A. F. M., Racine-Poon, A., Gelfand, A. E. (1994). Bayesian analysis of linear and nonlinear population models by using the Gibbs sampler. Applied Statistics 43:201-221.
29. Wolfinger, R. (1993). Laplace's approximation for nonlinear mixed models. Biometrika 80:791-795.