Skip to main content
PMC home page
The AAPS Journal logoLink to The AAPS Journal
. 2007 Mar 2;9(1):E60–E83. doi: 10.1208/aapsj0901007

A survey of population analysis methods and software for complex pharmacokinetic and pharmacodynamic models with examples

Robert J Bauer 1,✉, Serge Guzy 1, Chee Ng 2
PMCID: PMC2751305  PMID: 17408237

Abstract

An overview is provided of the present population analysis methods and an assessment of which software packages are most appropriate for various PK/PD modeling problems. Four PK/PD example problems were solved using the programs NONMEM VI beta version, PDx-MCPEM, S-ADAPT, MONOLIX, and WinBUGS, informally assessed for reasonable accuracy and stability in analyzing these problems. Also, for each program we describe their general interface, ease of use, and abilities. We conclude with discussing which algorithms and software are most suitable for which types of PK/PD problems. NONMEM FO method is accurate and fast with 2-compartment models, if intra-individual and interindividual variances are small. The NONMEM FOCE method is slower than FO, but gives accurate population values regardless of size of intra- and interindividual errors. However, if data are very sparse, the NONMEM FOCE method can lead to inaccurate values, while the Laplace method can provide more accurate results. The exact EM methods (performed using S-ADAPT, PDx-MCPEM, and MONOLIX) have greater stability in analyzing complex PK/PD models, and can provide accurate results with sparse or rich data. MCPEM methods perform more slowly than NONMEM FOCE for simple models, but perform more quickly and stably than NONMEM FOCE for complex models. WinBUGS provides accurate assessments of the population parameters, standard errors and 95% confidence intervals for all examples. Like the MCPEM methods, WinBUGS's efficiency increases relative to NONMEM when solving the complex PK/PD models.

Keywords: population, pharmacokinetics, pharmaco-dhnamics, clinical, software, computation methods

Full Text

The Full Text of this article is available as a PDF (340.6 KB).

References

  • 1.Csajka C, Verotta D. Pharmacokinetic-pharmacodynamic modelling: history and perspectives. J Pharmacokinet Pharmacodyn. 2006;33:227–279. doi: 10.1007/s10928-005-9002-0. [DOI] [PubMed] [Google Scholar]
  • 2.Sheiner LB, Beal SL. Evaluation of methods for estimating population pharmacokinetics parameters. I. Michaelis-Menten model: routine clinical pharmacokinetic data. J Pharmacokinet Biopharm. 1980;8:553–571. doi: 10.1007/BF01060053. [DOI] [PubMed] [Google Scholar]
  • 3.Pillai G, Mentre F, Steimer JL. Non-linear mixed effects modeling—from methodology and software development to driving implementation in drug development science. J Pharmacokinet Pharmacodyn. 2005;32:161–183. doi: 10.1007/s10928-005-0062-y. [DOI] [PubMed] [Google Scholar]
  • 4.mandema JW. Population pharmacokinetics and pharmacodynamics. In: Welling PG, Tse FLS, editors. Pharmacokinetics. 2nd ed. New York, NY: Marcel Dekker, Inc.; 1995. pp. 411–450. [Google Scholar]
  • 5.Roe DJ. Comparison of population pharmacokinetic modeling methods using simulated data: results from the population modeling workgroup. Stat Med. 1997;16:1241–1262. doi: 10.1002/(SICI)1097-0258(19970615)16:11<1241::AID-SIM527>3.0.CO;2-C. [DOI] [PubMed] [Google Scholar]
  • 6.Aarons L. Software for population pharmacokinetics and pharmacodynamics. Clin Pharmacokinet. 1999;36:255–264. doi: 10.2165/00003088-199936040-00001. [DOI] [PubMed] [Google Scholar]
  • 7.Mentre F, Mallet A, Steiner JL. Hyperparameter estimation using stochastic approximation with application to population. pharmacokinetics. Biometrics. 1988;44:673–683. doi: 10.2307/2531582. [DOI] [PubMed] [Google Scholar]
  • 8.Bauer RJ, Guzy S. Monte Carlo parametric expectation maximization (MC-PEM) method for analyzing population pharmacokinetic/ pharmacodynamic data. In: D'Argenio DZ, editor. Advanced Methods of Pharmacokinetic and Pharmacodynamic Systems Analysis. Boston, MA: Kluwer Academic Publishers; 2004. pp. 135–163. [Google Scholar]
  • 9.Best NG, Tan KK, Spiegelhalter DJ. Estimation of population pharmacokinetics using the Gibbs sampler. J Pharmacokinet Biopharm. 1995;23:407–435. doi: 10.1007/BF02353641. [DOI] [PubMed] [Google Scholar]
  • 10.Lunn DJ, Best N, Thomas A, Wakefield J, Spiegelhalter D. Bayesian analysis of population PK/PD models: general concepts and software. J Pharmacokinet Pharmacodyn. 2002;29:271–307. doi: 10.1023/A:1020206907668. [DOI] [PubMed] [Google Scholar]
  • 11.Beal SL, Sheiner LB. NONMEM Users Guide—Part VII. Hanover, MD: Globomax, Inc; 1992. [Google Scholar]
  • 12.Users Guides NONMEM. [computer program]. Version V. Hanover, MD: Globomax, Inc; 1989–1998.
  • 13.PDx-MCPEM Users Guide [computer program]. Version 1.0. Hanover, MD: Globomax, Inc; 2006.
  • 14.S-ADAPT/MCPEM User's Guide [computer program]. Version 1.52. Berkeley, CA.; 2006.
  • 15.Monolix Users Manual [computer program]. Version 1.1. Orsay, France: Laboratoire de Mathematiques, U. Paris-Sud; 2005.
  • 16.PKBUGS software [computer program]. Version 2.0. Cambridge, UK: MRC Biostatistics Unit, 2006.
  • 17.Davidian M, Giltinan DM. Nonlinear Models for Repeated Measurement Data. New York, NY: Chapman and Hall; 1995. [Google Scholar]
  • 18.Lindstrom ML, Bates DM. Nonlinear mixed effects models for repeated measures data. Biometrics. 1990;46:673–687. doi: 10.2307/2532087. [DOI] [PubMed] [Google Scholar]
  • 19.Pinheiro JC, Bates DM. Approximations to the Log-likelihood function in the nonlinear mixed-effects model. J Comput Graph Statist. 1995;4:12–35. doi: 10.2307/1390625. [DOI] [Google Scholar]
  • 20.Beal SL, Sheiner LB. Estimating population kinetics. Crit Rev Biomed Eng. 1982;8:195–222. [PubMed] [Google Scholar]
  • 21.Ette EI, Kelman AW, Howie CA, Whiting B. Analysis of animal pharmacokinetic data: performance of the one point per animal design. J Pharmacokinet Biopharm. 1995;23:551–566. doi: 10.1007/BF02353461. [DOI] [PubMed] [Google Scholar]
  • 22.Ette EI, Sun H, Ludden TM. Balanced designs in longitudinal population pharmacokinetic studies. J Clin Pharmacol. 1998;38:417–423. doi: 10.1002/j.1552-4604.1998.tb04446.x. [DOI] [PubMed] [Google Scholar]
  • 23.Jones CD, Sun H, Ette EI. Designing cross-sectional population pharmacokinetic studies: implications for pediatric and animal studies. Clin Res Pr Drug Regul Aff. 1996;13:133–165. doi: 10.3109/10601339609035949. [DOI] [Google Scholar]
  • 24.White DB, Walawander CA, Tung Y, Grasela TH. An evaluation of point and interval estimates in population pharmacokinetics using NONMEM analysis. J Pharmacokinet Biopharm. 1991;19:87–112. doi: 10.1007/BF01062194. [DOI] [PubMed] [Google Scholar]
  • 25.SAS online documentation, SAS/STAT Users Guide, NLMIXED procedure [computer program]. Version 8. Cary, NC: SAS Institute, Inc.; 2005.
  • 26.Jonsson S, Kjellsson MC, Karlsson MO. Estimating bias in population parameters for some models for repeated measures ordinals data using NONMEM and NLMIXED. J Pharmacokinet Pharmacodyn. 2004;31:299–320. doi: 10.1023/B:JOPA.0000042738.06821.61. [DOI] [PubMed] [Google Scholar]
  • 27.Schumitzky A. EM algorithms and two stage methods in pharmacokinetics population analysis. In: D'Argenio DZ, editor. Advanced Methods of Pharmacokinetic and Pharmacodynamic Systems Analysis. Boston, MA: Kluwer Academic Publishers; 1995. pp. 145–160. [Google Scholar]
  • 28.Mentre F, Gomeni R. A two-step iterative algorithm for estimation in nonlinear mixed-effect models with an evaluation in population pharmacokinetics. J Biopharm Stat. 1995;5:141–158. doi: 10.1080/10543409508835104. [DOI] [PubMed] [Google Scholar]
  • 29.Walker S. An EM algorithm for nonlinear random effects models. Biometrics. 1996;52:934–944. doi: 10.2307/2533054. [DOI] [Google Scholar]
  • 30.Lavielle M. SAEM in MATLAB: an alternative to linearization (software presentation). Presented at: PAGE Meeting; June 17–18, 2004; Uppsala, Sweden. Uppsala, Sweden: Population Approach Group Europe; 2004: Abstract 544.
  • 31.Steimer JL, Mallet A, Golmard JL, Boisvieux JF. Alternative approaches to estimation of population pharmacokinetic parameters: comparison with the nonlinear mixed-effect model. Drug Metab Rev. 1984;15:265–292. doi: 10.3109/03602538409015066. [DOI] [PubMed] [Google Scholar]
  • 32.Lindstrom MJ, Bates DM. Newton-Raphson and EM algorithms for linear mixed-effects models for repeated-measures data. J Am Stat Assoc. 1988;83:1014–1022. doi: 10.2307/2290128. [DOI] [Google Scholar]
  • 33.Aarons L. The estimation of population pharmacokinetic parameters using an EM algorithm. Comput Methods Programs Biomed. 1993;41:9–16. doi: 10.1016/0169-2607(93)90062-P. [DOI] [PubMed] [Google Scholar]
  • 34.Thermo Kinetica software [computer program]. Version 4.4.1. Waltham, MA: Thermo Electron Corporation; 1997–2007.
  • 35.Gomeni R, Pineau G, Mentre F. Population kinetics and conditional assessment of the optimal dosage regimen using the P-PHARM software package. Anticancer Res. 1994;14:2321–2326. [PubMed] [Google Scholar]
  • 36.Popkinetics software [computer program]. Version 1.0. University of Washington Seattle; 2006.
  • 37.Zhou Z, Rodman JH, Flynn PM, Robbins BL, Wilcox CK, D'Argenio DZ. Model for intracellular lamivudine metabolism in peripheral blood mononuclear cells ex vivo and in human immunodeficiency virus type 1-infected adolescents. Antimicrob Agents Chemother. 2006;50:2686–2694. doi: 10.1128/AAC.01637-05. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 38.Dokoumetzidis A, Aarons L. Propagation of population pharmacokinetic information using a Bayesian approach: comparison with meta-analysis. J Pharmacokinet Pharmacodyn. 2005;32:401–418. doi: 10.1007/s10928-005-0048-9. [DOI] [PubMed] [Google Scholar]
  • 39.Gilks WR. Full conditional distributions. In: Gilks WR, Richardson S, Spiegelhalter DJ, editors. Markov Chain Monte Carlo in Practice. New York, NY: Chapman and Hall; 1996. pp. 75–88. [Google Scholar]
  • 40.Gilks WR, Richardson S, Spiegelhalter DJ. Introducing Markov chain Monte Carlo. In: Gilks WR, Richardson S, Spiegelhalter DJ, editors. Markov Chain Monte Carlo in Practice. New York, NY: Chapman and Hall; 1996. pp. 1–19. [Google Scholar]
  • 41.Bennett JE, Racine-Poon A, Wakefield AJ. MCMC for nonlinear heirarchical models. In: Gilks WR, Richardson S, Spiegelhalter DJ, editors. Markov Chain Monte Carlo in Practice. New York, NY: Chapman and Hall; 1996. pp. 339–357. [Google Scholar]
  • 42.Gueroguieva I, Aarons L, Rowland M. Diazepam pharmacokinetics from preclinical to Phase 1 using a Bayesian population physiologically based pharmacokinetics model with informative prior distributions in Winbugs. J Pharmacokinet Pharmacodyn. 2006;33:1–24. doi: 10.1007/s10928-005-0004-8. [DOI] [PubMed] [Google Scholar]
  • 43.ADAPT II Users Guide . Pharmacokinetic/Pharmacodynamic Systems Analysis Software. [computer program]. Version (Release) 4. Los Angeles, CA: Biomedical Simulations Resource, University of Southern California; 1997. [Google Scholar]
  • 44.Ng CM, Joshi A, Dedrick R, Garovoy M, Bauer R. Pharmacokinetic-pharmacodynamic-efficacy analysis of efalizumab in patients with moderate to severe psoriasis. Pharm Res. 2005;22:1088–1100. doi: 10.1007/s11095-005-5642-4. [DOI] [PubMed] [Google Scholar]
  • 45.Mu S, Ludden TM. Estimation of population pharmacokinetic parameters in the presence of non-compliance. J Pharmacokinet Pharmacodyn. 2003;30:53–81. doi: 10.1023/A:1023297426153. [DOI] [PubMed] [Google Scholar]
  • 46.Duffull SB, Kirkpatrick CJ, Green B, Holford NH. Analysis of population pharmcokinetic data using NONMEM and Winbugs. J Biopharm Stat. 2005;15:53–73. doi: 10.1081/BIP-200040824. [DOI] [PubMed] [Google Scholar]
  • 47.Girard P, Mentre F. A comparison of estimation methods in nonlinear mixed effects models using a blind analysis. Presented at: PAGE Meeting; June 16–17, 2005; Pamplona, Spain. Population Approach Group Europe; 2005: Abstract 834.

Articles from The AAPS Journal are provided here courtesy of American Association of Pharmaceutical Scientists

RESOURCES