Clinical Pharmacokinetics

, Volume 45, Issue 4, pp 365–383 | Cite as

Parametric and Nonparametric Population Methods

Their Comparative Performance in Analysing a Clinical Dataset and Two Monte Carlo Simulation Studies
  • Aida Bustad
  • Dimiter Terziivanov
  • Robert Leary
  • Ruediger Port
  • Alan Schumitzky
  • Roger JelliffeEmail author
Original Research Article


Background and objectives

This study examined parametric and nonparametric population modelling methods in three different analyses. The first analysis was of a real, although small, clinical dataset from 17 patients receiving intramuscular amikacin. The second analysis was of a Monte Carlo simulation study in which the populations ranged from 25 to 800 subjects, the model parameter distributions were Gaussian and all the simulated parameter values of the subjects were exactly known prior to the analysis. The third analysis was again of a Monte Carlo study in which the exactly known population sample consisted of a unimodal Gaussian distribution for the apparent volume of distribution (Vd), but a bimodal distribution for the elimination rate constant (ke), simulating rapid and slow eliminators of a drug.


For the clinical dataset, the parametric iterative two-stage Bayesian (IT2B) approach, with the first-order conditional estimation (FOCE) approximation calculation of the conditional likelihoods, was used together with the nonparametric expectation-maximisation (NPEM) and nonparametric adaptive grid (NPAG) approaches, both of which use exact computations of the likelihood.

For the first Monte Carlo simulation study, these programs were also used. A one-compartment model with unimodal Gaussian parameters Vd and ke was employed, with a simulated intravenous bolus dose and two simulated serum concentrations per subject. In addition, a newer parametric expectation-maximisation (PEM) program with a Faure low discrepancy computation of the conditional likelihoods, as well as nonlinear mixed-effects modelling software (NONMEM), both the first-order (FO) and the FOCE versions, were used.

For the second Monte Carlo study, a one-compartment model with an intravenous bolus dose was again used, with five simulated serum samples obtained from early to late after dosing. A unimodal distribution for Vd and a bimodal distribution for ke were chosen to simulate two subpopulations of ‘fast’ and ‘slow’ metabolisers of a drug. NPEM results were compared with that of a unimodal parametric joint density having the true population parameter means and covariance.


For the clinical dataset, the interindividual parameter percent coefficients of variation (CV%) were smallest with IT2B, suggesting less diversity in the population parameter distributions. However, the exact likelihood of the results was also smaller with IT2B, and was 14 logs greater with NPEM and NPAG, both of which found a greater and more likely diversity in the population studied.

For the first Monte Carlo dataset, NPAG and PEM, both using accurate likelihood computations, showed statistical consistency. Consistency means that the more subjects studied, the closer the estimated parameter values approach the true values. NONMEM FOCE and NONMEM FO, as well as the IT2B FOCE methods, do not have this guarantee. Results obtained by IT2B FOCE, for example, often strayed visibly away from the true values as more subjects were studied.

Furthermore, with respect to statistical efficiency (precision of parameter estimates), NPAG and PEM had good efficiency and precise parameter estimates, while precision suffered with NONMEM FOCE and IT2B FOCE, and severely so with NONMEM FO.

For the second Monte Carlo dataset, NPEM closely approximated the true bimodal population joint density, while an exact parametric representation of an assumed joint unimodal density having the true population means, standard deviations and correlation gave a totally different picture.


The smaller population interindividual CV% estimates with IT2B on the clinical dataset are probably the result of assuming Gaussian parameter distributions and/or of using the FOCE approximation. NPEM and NPAG, having no constraints on the shape of the population parameter distributions, and which compute the likelihood exactly and estimate parameter values with greater precision, detected the more likely greater diversity in the parameter values in the population studied.

In the first Monte Carlo study, NPAG and PEM had more precise parameter estimates than either IT2B FOCE or NONMEM FOCE, as well as much more precise estimates than NONMEM FO. In the second Monte Carlo study, NPEM easily detected the bimodal parameter distribution at this initial step without requiring any further information.

Population modelling methods using exact or accurate computations have more precise parameter estimation, better stochastic convergence properties and are, very importantly, statistically consistent. Nonparametric methods are better than parametric methods at analysing populations having unanticipated non-Gaussian or multimodal parameter distributions.


Support Point Conditional Likelihood Clinical Dataset Intravenous Bolus Dose Monte Carlo Simulation Study 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The preparation of this manuscript was supported by US Government grants RR11526, GM65619 and GM068968.

Many thanks to Dr Irina Bondareva of the Institute for Physical-Chemical Medicine, Moscow, Russia, for her very thoughtful help and critiques in the preparation of this manuscript.

The authors have no financial conflicts of interest relevant to the contents of this study.


  1. 1.
    Schumitzky A. The nonparametric maximum likelihood approach to pharmacokinetic population analysis. Proceedings of the 1993 Western Simulation Multiconference: Simulation for Health Care; 1993 Jan 17–19; La Jolla (CA): San Diego (CA): Society for Computer Simulation, 1993: 95–100. (Also available as Technical Report 92–3. Los Angeles [CA]: Laboratory of Applied Pharmacokinetics, USC School of Medicine, 1992)Google Scholar
  2. 2.
    Schumitzky A. Nonparametric EM algorithms for estimating prior distributions. Appl Math Comput 1991; 45: 143–57CrossRefGoogle Scholar
  3. 3.
    Schumitzky A. EM algorithms and two stage methods in pharmacokinetic population analysis. In: D’Argenio DZ, editor. Advanced methods of pharmacokinetic and pharmacodynamic systems analysis II. New York: Plenum Press, 1995: 145–60Google Scholar
  4. 4.
    Leary R, Jelliffe R, Schumitzky A, et al. A unified parametric/nonparametric approach to population PK/PD modeling. Annual Meeting of the Population Approach Group in Europe; 2002 Jun 6–7; ParisGoogle Scholar
  5. 5.
    Beal S, Sheiner L. NONMEM user’s guide I: users basic guide. San Francisco (CA): Division of Clinical Pharmacology, University of California, 1979Google Scholar
  6. 6.
    Sheiner L. The population approach to pharmacokinetic data analysis: rationale and standard data analysis methods. Drug Metab Rev 1984; 15: 153–71PubMedCrossRefGoogle Scholar
  7. 7.
    Beal S. Population pharmacokinetic data and parameter estimation based on their first two statistical moments. Drug Metab Rev 1984; 15: 173–93PubMedCrossRefGoogle Scholar
  8. 8.
    Rowland M, Sheiner L, Steimer JL, editors. Variability in drug therapy: description, estimation, and control. New York: Raven Press, 1985Google Scholar
  9. 9.
    Davidian M, Giltinan D. Nonlinear models for repeated measurement data. New York: Chapman and Hall, 1995Google Scholar
  10. 10.
    Jelliffe R, Schumitzky A, Van Guilder M, et al. User manual for version 10.7 of the USC*PACK Collection of PC Programs, USC Laboratory of Applied Pharmacokinetics. Los Angeles (CA): USC School of Medicine, 1995 Dec 1Google Scholar
  11. 11.
    Sheiner L, Beal S, Rosenberg B, et al. Forecasting individual pharmacokinetics. Clin Pharmacol Ther 1979; 26: 294–305PubMedGoogle Scholar
  12. 12.
    Jelliffe R. Explicit determination of laboratory assay error patterns: a useful aid in therapeutic drug monitoring (no. DM 89–4 [DM56]). Drug Monit Toxicol 1989; 10 (4)Google Scholar
  13. 13.
    Jelliffe R, Schumitzky A, Van Guilder M, et al. Individualizing drug dosage regimens: roles of population pharmacokinetic and dynamic models, bayesian fitting, and adaptive control. Ther Drug Monit 1993; 15: 380–93PubMedCrossRefGoogle Scholar
  14. 14.
    De Groot M. Probability and statistics. 2nd ed. (reprinted 1989). Reading (MA): Addison-Wesley, 1986: 420–3Google Scholar
  15. 15.
    Lindsay B. The geometry of mixture likelihoods: a general theory. Ann Stat 1983; 11: 86–94CrossRefGoogle Scholar
  16. 16.
    Mallet A. A maximum likelihood estimation method for random coefficient regression models. Biometrika 1986; 73: 645–56CrossRefGoogle Scholar
  17. 17.
    Maire P, Barbaut X, Girard P, et al. Preliminary results of three methods for population pharmacokinetic analysis (NONMEM, NPML, NPEM) of amikacin in geriatric and general medicine patients. Int J Biomed Comput 1994; 36: 139–41PubMedCrossRefGoogle Scholar
  18. 18.
    Spieler G, Schumitzky A. Asymptotic properties of extended least squares estimates with application to population pharmacokinetics. Proceedings of the American Statistical Association, Biopharmaceutical Section. 1993 Aug 8–12; San Francisco (CA). Alexandria (VA): American Statistical Association, 1993: 177–82. (Also available as Technical Report 92–4. Los Angeles [CA]: Laboratory of Applied Pharmacokinetics, USC School of Medicine, 1992)Google Scholar
  19. 19.
    Vonesh E, Chinchilli V. Linear and nonlinear models for analysis of repeated measurements. New York: Marcel Dekker, 1997Google Scholar
  20. 20.
    Leary R, Jelliffe R, Schumitzky A, et al. Improved computational methods for statistically consistent and efficient PK/PD population analysis [poster]. Annual Meeting of the Population Approach Group in Europe; 2003 Jun 12–13; VeronaGoogle Scholar
  21. 21.
    Bennet JE, Racine-Poon A, Wakefield JC. Markov chain Monte Carlo for nonlinear hierarchical models. In: Gilks WR, Richardson S, Spiegelhalter DJ, editors. Markov chain Monte Carlo in practice. London: Chapman and Hall, 1996: 339–57Google Scholar
  22. 22.
    Bertilsson L. Geographic/interracial differences in polymorphic drug oxidation. Clin Pharmacokinet 1995; 29: 192–209PubMedCrossRefGoogle Scholar
  23. 23.
    Bustad A, Jelliffe R, Terziivanov D. A comparison of parametric and nonparametric methods of population pharmacokinetic modeling [poster]. Annual Meeting of the American Society for Clinical Pharmacology and Therapeutics; 2002 Mar 26; Atlanta (GA)Google Scholar
  24. 24.
    Jelliffe R. Estimation of creatinine clearance in patients with unstable renal function, without a urine specimen. Am J Nephrol 2002; 22: 320–4PubMedCrossRefGoogle Scholar
  25. 25.
    Beal L, Sheiner L, editors. NONMEM version V.1.1 users guides. San Francisco (CA): University of California, 1999Google Scholar
  26. 26.
    Girard P, Mentre F. A comparison of estimation methods in nonlinear mixed effects models using a blind analysis [online]. 14th meeting of the Population Approach Group in Europe; 2005 Jun 16–17; Pamplona. Available from URL: [Accessed 2006 Jan 20]Google Scholar
  27. 27.
    Terziivanov D, Bozhinova K, Dimitrova V, et al. Nonparametric expectation maximisation (NPEM) population analysis of caffeine disposition from sparse data in adult Caucasians: systemic caffeine clearance as a biomarker for cytochrome P4501A2 activity. Clin Pharmacokinet 2003; 42: 1393–409PubMedCrossRefGoogle Scholar
  28. 28.
    Bertsekas D. Dynamic programming: deterministic and stochastic models. Suboptimal and adaptive control: section 4.1: certainty equivalent control. Englewood Cliffs (NJ): Prentice-Hall, 1987: 144–6Google Scholar
  29. 29.
    Taright N, Mentre F, Mallet A, et al. Nonparametric estimation of population characteristics of the kinetics of lithium from observational and experimental data: individualization of chronic dosing regimen using a new bayesian approach. Ther Drug Monit 1994; 16: 258–69PubMedCrossRefGoogle Scholar
  30. 30.
    Bayard D, Jelliffe R, Schumitzky A, et al. Precision drug dosage regimens using multiple model adaptive control: theory and application to simulated vancomycin therapy. In: Sridhar R, Rao K, Lakshminarayanan V, editors. Selected topics in mathematical physics. Professor R. Vasudevan memorial volume. Madras: Allied Publishers Inc., 1995: 407–26Google Scholar
  31. 31.
    Jerling M. Population kinetics of antidepressant and neuroleptic drugs: studies of therapeutic drug monitoring data to evaluate kinetic variability, drug interactions, nonlinear kinetics, and the influence of genetic factors [PhD thesis]. Stockholm: Division of Clinical Pharmacology, Department of Medical Laboratory Sciences and Technology, Karolinska Institute at Huddinge University Hospital, 1995: 28–9Google Scholar
  32. 32.
    Jelliffe R, Schumitzky A, Bayard D, et al. Model-based, goal-oriented, individualised drug therapy: linkage of population modelling, new ‘multiple model’ dosage design, bayesian feedback and individualised target goals. Clin Pharmacokinet 1998; 34: 57–77PubMedCrossRefGoogle Scholar
  33. 33.
    Bayard D, Milman M, Schumitzky A. Design of dosage regimens: a multiple model stochastic approach. Int J Biomed Comput 1994; 36: 103–15PubMedCrossRefGoogle Scholar

Copyright information

© Adis Data Information BV 2006

Authors and Affiliations

  • Aida Bustad
    • 1
  • Dimiter Terziivanov
    • 2
  • Robert Leary
    • 3
  • Ruediger Port
    • 4
  • Alan Schumitzky
    • 1
  • Roger Jelliffe
    • 1
    Email author
  1. 1.Laboratory of Applied PharmacokineticsUSC Keck School of MedicineLos AngelesUSA
  2. 2.Clinic of Clinical Pharmacology and PharmacokineticsUniversity Hospital ‘St I. Rilsky’SofiaBulgaria
  3. 3.Pharsight CorporationCaryUSA
  4. 4.German Cancer Research CenterHeidelbergGermany

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