- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 250909, 13 pages
Empirical Likelihood Estimation for Population Pharmacokinetic Study Based on Generalized Linear Model
1Department of Mathematics, Southeast University, Nanjing 210096, China
2Department of Mathematics, China Pharmaceutical University, Nanjing 210009, China
3State Key Laboratory of Natural Medicines, China Pharmaceutical University, Nanjing 210009, China
Received 29 September 2012; Accepted 18 November 2012
Academic Editor: Li Weili
Copyright © 2012 Fang-rong Yan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- N. M. Laird and J. H. Ware, “Random-effects models for longitudinal data,” Biometrics, vol. 38, no. 4, pp. 963–974, 1982.
- L. B. Sheiner, B. Rosenberg, and V. V. Marathe, “Estimation of population characteristics of pharmacokinetic parameters from routine clinical data,” Journal of Pharmacokinetics and Biopharmaceutics, vol. 5, no. 5, pp. 445–479, 1977.
- R. Salway and J. Wakefield, “Gamma generalized linear models for pharmacokinetic data,” Biometrics, vol. 64, no. 2, pp. 620–626, 2008.
- J. Wakefield, “Non-linear regression modeling,” in Methods and Models in Statistics, pp. 119–153, Imperial College Press, 2004.
- E. F. Vonesh, “Non-linear models for the analysis of longitudinal data,” Statistics in Medicine, vol. 11, no. 14-15, pp. 1929–1954, 1992.
- M. Davidian and D. Giltinan, “Nonlinear models for repeated measurement data,” Journal of the American Statistical Association, vol. 5, no. 13, pp. 1462–1463, 1995.
- C. E. McCulloch, “Maximum likelihood algorithms for generalized linear mixed models,” Journal of the American Statistical Association, vol. 92, no. 437, pp. 162–170, 1997.
- J. Wakefield, A. F. M. Smith, A. R. Poon, and A. E. Gelfand, “Bayesian analysis of linear and non-linear population models by using the gibbs sampler,” Journal of the Royal Statistical Society, vol. 43, no. 1, pp. 201–221, 1994.
- A. B. Owen, “Empirical likelihood ratio confidence intervals for a single functional,” Biometrika, vol. 75, no. 2, pp. 237–249, 1988.
- A. B. Owen, Empirical Likelihood, Chapman & Hall, New York, NY, USA, 2001.
- J. Qin and J. Lawless, “Empirical likelihood and general estimating equations,” The Annals of Statistics, vol. 22, no. 1, pp. 300–325, 1994.
- J. Qin and J. Lawless, “Estimating equations, empirical likelihood and constraints on parameters,” The Canadian Journal of Statistics, vol. 23, no. 2, pp. 145–159, 1995.
- G. Li, “Nonparametric likelihood ratio estimation of probabilities for truncated data,” Journal of the American Statistical Association, vol. 90, no. 431, pp. 997–1003, 1995.
- B. Y. Jing, “Two-sample empirical likelihood method,” Statistics & Probability Letters, vol. 24, no. 4, pp. 315–319, 1995.
- S. J. Wang, L. F. Qian, and R. J. Carroll, “Generalized empirical likelihood methods for analyzing longitudinal data,” Biometrika, vol. 97, no. 1, pp. 79–93, 2010.
- K. Y. Liang and S. L. Zeger, “Longitudinal data analysis using generalized linear models,” Biometrika, vol. 73, no. 1, pp. 13–22, 1986.
- C. N. Morris, “Natural exponential families with quadratic variance functions,” The Annals of Statistics, vol. 10, no. 1, pp. 65–80, 1982.
- J. A. Nelder and D. Pregibon, “An extended quasilikelihood function,” Biometrika, vol. 74, no. 2, pp. 221–232, 1987.
- E. D. Kolaczyk, “Empirical likelihood for generalized linear models,” Statistica Sinica, vol. 4, no. 1, pp. 199–218, 1994.
- L. G. Xue and L. X. Zhu, “Empirical likelihood semiparametric regression analysis for longitudinal data,” Biometrika, vol. 94, no. 4, pp. 921–937, 2007.
- W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, Cambridge University Press, New York, NY, USA, 2nd edition, 1992.
- R. A. Upton, J. F. Thiercelin, and T. W. Guentert, “Intraindividual variability in theophylline pharmacokinetics: statistical verification in 39 of 60 healthy young adults,” Journal of Pharmacokinetics and Biopharmaceutics, vol. 10, no. 2, pp. 123–134, 1982.
- F. R. Yan, Y. Huang, and T. Lu, “Bayesian inference for generalized linear mixed modeling based on the multivariate t distribution in population pharmacokinetic study,” Journal of Pharmacokinetics and Pharmacodynamics. In press.
- A. B. Owen, “Empirical likelihood confidence regions,” Annals of Statistics, vol. 19, no. 1, pp. 90–120, 1990.