A comparison of a bayesian population method with two methods as implemented in commercially available software

  • J. E. Bennett
  • J. C. Wakefield


In this paper we describe and discuss three specific estimation procedures that are available within commercially available population software packages. The first version of NONMEM (1) was released in 1979 and later versions are the standard analysis tools in both industry and academia. Recently, two commercially available pieces of software have become available. PPHARM was released during 1994 and POPKAN was released in 1995. We provide descriptions and critique the FOCE method within NONMEM, the two-step algorithm within PPHARM and the Markov chain Monte Carlo method that is utilized by POPKAN. We use simulated data generated from a monoexponential model to evaluate the parameter estimation capabilities of these methods within the three software tools. In particular we investigate the effect on parameter estimation of increasing both interindividual and intraindividual variability.

Key words

population pharmacokinetics parameter estimation simulation mixed effects models NONMEM PPHARM POPKAN 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. L. Beal and L. B. Sheiner.NONMEM User's Guide Version I. Division of Clinical Pharmacology, University of California, San Francisco, 1979.Google Scholar
  2. 2.
    J.-L. Steimer, A. Mallet, J.-L. Golmard, and J.-L. Boisvieux. Alternative approaches to estimation of population pharmacokinetic parameters: Comparison with the nonlinear mixed-effects model.Drug Metab. Rev. 15:265–292 (1984).PubMedCrossRefGoogle Scholar
  3. 3.
    A. Racine-Poon. A Bayesian approach to nonlinear random effects models.Biometrics 41:1015–1023 (1985).PubMedCrossRefGoogle Scholar
  4. 4.
    M. J. Lindstrom and D. M. Bates. Nonlinear mixed effects models for repeated measures data.Biometrics 46:673–687 (1990).PubMedCrossRefGoogle Scholar
  5. 5.
    E. F. Vonesh and R. L. Carter. Mixed-effects nonlinear regression for unbalanced repeated measures.Biometrics 48:1–17 (1992).PubMedCrossRefGoogle Scholar
  6. 6.
    J. C. Wakefield, A. F. M. Smith, A. Racine-Poon, and A. E. Gelfand. Bayesian analysis of linear and nonlinear population models using the Gibbs sampler.Appl. Statist. 41:201–221 (1994).CrossRefGoogle Scholar
  7. 7.
    A. Mallet. A maximum likelihood estimation method for random coefficient regression models.Biometrika 73:645–656 (1986).CrossRefGoogle Scholar
  8. 8.
    M. Davidian and A. R. Gallant. The nonlinear mixed effects model with a smooth random effects density.Biometrika 80:475–488 (1993).CrossRefGoogle Scholar
  9. 9.
    M. Davidian and D. M. Giltinan.Nonlinear Models for Repeated Measures Data, Chapman and Hall, 1995.Google Scholar
  10. 10.
    L. Yuh, S. Beal, M. Davidian, F. Harrison, A. Hester, K. Kowalski, E. Vonesh, and R. Wolfinger. Population pharmacokinetic/pharmacodynamic methodology and applications: A bibliography.Biometrics 50:566–575 (1994).PubMedCrossRefGoogle Scholar
  11. 11.
    L. B. Sheiner and S. L. Beal. Evaluation of methods for estimating population pharmacokinetic parameters. I. Michaelis-Menten model: Routine clinical pharmacokinetic data.J. Pharmacokin. Biopharm. 8:533–571 (1980).CrossRefGoogle Scholar
  12. 12.
    L. B. Sheiner and S. L. Beal. Evaluation of methods for estimating pharmacokinetic parameters. II. Biexponential model and experimental pharmacokinetic data.J. Pharmacokin. Biopharm. 9:635–651 (1981).CrossRefGoogle Scholar
  13. 13.
    L. B. Sheiner and S. L. Beal. Evaluation of methods for estimating population pharmacokinetic parameters. III. Monoexponential model: Routine clinical pharmacokinetic data.J. Pharmacokin. Biopharm. 11:303–319 (1983).CrossRefGoogle Scholar
  14. 14.
    T. H. Grasela, E. J. Antal, R. J. Townsend, and R. B. Smith. An evaluation of population pharmacokinetics in therapeutic trials. Part I. Comparison of methodologies.Clin. Pharmacol. Ther. 39:605–612 (1986).PubMedCrossRefGoogle Scholar
  15. 15.
    A. Racine-Poon and A. F. M. Smith. Population models. In D. Berry (ed.),Statistical Methodology in the Pharmaceutical Sciences, Marcel-Dekker, New York, 1990, pp. 139–162.Google Scholar
  16. 16.
    S. L. Beal and L. B. Sheiner. Estimating population kinetics.CRC Crit. Rev. Biomed. Eng. 8:195–222 (1982).Google Scholar
  17. 17.
    L. B. Sheiner, B. Rosenburg and V. V. Marathe. Estimation of population characteristics of pharmacokinetic parameters from routine clinical data.J. Pharmacokin. Biopharm. 5:445–479 (1977).CrossRefGoogle Scholar
  18. 18.
    N. M. Laird and J. H. Ware. Random-effects models for longitudinal data.Biometrics 38:963–974 (1982).PubMedCrossRefGoogle Scholar
  19. 19.
    M. J. Lindstrom and D. M. Bates. Newton-Raphson and EM algorithms for linear mixed-effects models for repeated-measures data.J. Am. Statist. Assoc. 83:1014–1022 (1988).Google Scholar
  20. 20.
    S. L. Beal and L. B. Sheiner.NONMEM User's Guide Version IV, Part VII. Conditional Estimation Methods, University of California, San Francisco, 1992.Google Scholar
  21. 21.
    J. C. Wakefield and S. G. Walker. A Bayesian population approach to initial dose selection.Statist. Med. (in press).Google Scholar
  22. 22.
    N. H. G. Holford and L. B. Sheiner. Understanding the dose-effect relationship.Clin. Pharmacokin.6:429–453 (1981).CrossRefGoogle Scholar
  23. 23.
    J. C. Pinheiro and D. M. Bates. Approximations to the loglikelihood function in the nonlinear mixed effects model.J. Comput. Graph. Statist. (1995).Google Scholar
  24. 24.
    R. Wolfinger. Laplace's approximation for nonlinear mixed models.Biometrika 80:791–795 (1993).CrossRefGoogle Scholar
  25. 25.
    E. F. Vonesh. A note on the Laplace's approximation for nonlinear mixed-effects models.Biometrika 83:447–452 (1996).CrossRefGoogle Scholar
  26. 26.
    L. Tierney and J. B. Kadane. Accurate approximations for posterior moments and marginal densities.J. Am. Statist. Assoc. 81:82–86 (1986).CrossRefGoogle Scholar
  27. 27.
    J.-L. Steimer, S. Vozeh, A. Racine, N. G. Holford, and R. O'Neill. The population approach: Rationale, methods and applications in clinical pharmacology and drug development. InHandbook of Experimental Pharmacology, Vol. 110, Pharmacokinetics of Drugs, Springer-Verlag, Heidelberg, 1994.Google Scholar
  28. 28.
    F. Mentré and G. Gomeni. A two step iterative algorithm for estimation in nonlinear mixed effect models with an evaluation in population pharmacokinetics.J. Biopharm. Statist. 5:141–158 (1995).CrossRefGoogle Scholar
  29. 29.
    G. Prévost. Estimation of a normal probability density function from samples measured with non-negligible and non-constant dispersion. Internal Report, Andersa-Gerbios, 2 avenue du ler mai, F-91120 Palaiseau, 1977.Google Scholar
  30. 30.
    J. M. Kinowski, M. Rodier, F. Bressolle, D. Fabre, V. Augey, J. L. Richard, M. Galtier, and R. Gomeni. Bayesian estimation ofp-aminohippurate clearance by a limited sampling strategy.J. Pharm. Sci. 84:307–311 (1995).PubMedCrossRefGoogle Scholar
  31. 31.
    J. M. Kinowski, F. Bressolle, M. Rodier, V. Augey, D. Fabre, J. L. Richard, M. Galtier, and R. Gomeni. A limited sampling model with Bayesian estimation to determine insulin pharmacokinetics using the population data modelling program P-PHARM.Clin. Pharmacokin. 9:260–269 (1995).Google Scholar
  32. 32.
    A. P. Dempster, N. M. Laird, and D. B. Rubin. Maximum likelihood from incomplete data via the EM algorithm (with discussion).J. Roy. Statist. Soc. B 39:1–38 (1977).Google Scholar
  33. 33.
    S. G. Walker. An EM algorithm for nonlinear random effects models.Biometrics 52:934–944 (1996).CrossRefGoogle Scholar
  34. 34.
    A. E. Gelfand, S. E. Hills, A. Racine-Poon, and A. F. M. Smith. Illustration of Bayesian inference in normal data models using Gibbs sampling.J. Am. Statist. Assoc. 85:972–985 (1990).CrossRefGoogle Scholar
  35. 35.
    L. Tierney. Markov chains for exploring posterior distributions.Ann. Statist. 22:1701–1762 (1994).CrossRefGoogle Scholar
  36. 36.
    J. E. Bennett, A. Racine-Poon, and J. C. Wakefield. Markov chain Monte Carlo for nonlinear hierarchical models. In W. R. Gilks, S. Richardson, and D. J. Spiegelhalter (eds.),Markov Chain Monte Carlo in Practice, Chapman and Hall, London, 1995.Google Scholar
  37. 37.
    J. C. Wakefield. An expected loss approach to the design of dosage regimens via sampling-based methods.Statistician 43:13–29 (1994).CrossRefGoogle Scholar
  38. 38.
    J. C. Wakefield. Bayesian individualization via a sampling-based methods.J. Pharmacokin. Biopharm. 24:103–131 (1996).CrossRefGoogle Scholar
  39. 39.
    J. C. Wakefield. The Bayesian analysis of population pharmacokinetic models.J. Am. Statist. Assoc. 91:62–75 (1966).CrossRefGoogle Scholar
  40. 40.
    J. C. Wakefield and A. Racine-Poon. An application of Bayesian population pharmacokinetic/pharmacodynamic models to dose recommendation.Statist. Med. 14:971–986 (1995).CrossRefGoogle Scholar
  41. 41.
    A. Racine-Poon and J. C. Wakefield. Bayesian analysis of population pharmacokinetic and instantaneous pharmacodynamic relationships. In D. Berry and D. Stangl (eds.),Bayesian Biostatistics, Marcel Dekker, New York, 1996.Google Scholar
  42. 42.
    W. R. Gilks, N. G. Best, and K. K. C. Tan. Adaptive Rejection Metropolis sampling within Gibbs sampling.Appl. Statist. 44:455–472 (1995).CrossRefGoogle Scholar
  43. 43.
    N. G. Best, K. K. C. Tan, W. R. Gilks, and D. J. Spiegelhalter. Estimation of population pharmacokinetics using the Gibbs sampler.J. Pharmacokin. Biopharm. 23:407–424 (1995).CrossRefGoogle Scholar
  44. 44.
    PPHARM.User's manual, SIMED Scientific Software Development, Créteil, France, (1995).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • J. E. Bennett
    • 1
  • J. C. Wakefield
    • 2
  1. 1.Department of MathematicsImperial College of Science, Technology and MedicineLondonUK
  2. 2.Department of Epidemiology and Public HealthImperial College School of Medicine at St Mary'sLondonUK

Personalised recommendations