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Fundamentals of Population Pharmacokinetic Modelling

Validation Methods

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Abstract

Population pharmacokinetic modelling is widely used within the field of clinical pharmacology as it helps to define the sources and correlates of pharmacokinetic variability in target patient populations and their impact upon drug disposition; and population pharmacokinetic modelling provides an estimation of drug pharmacokinetic parameters. This method’s defined outcome aims to understand how participants in population pharmacokinetic studies are representative of the population as opposed to the healthy volunteers or highly selected patients in traditional pharmacokinetic studies. This review focuses on the fundamentals of population pharmacokinetic modelling and how the results are evaluated and validated.

This review defines the common aspects of population pharmacokinetic modelling through a discussion of the literature describing the techniques and placing them in the appropriate context. The concept of validation, as applied to population pharmacokinetic models, is explored focusing on the lack of consensus regarding both terminology and the concept of validation itself.

Population pharmacokinetic modelling is a powerful approach where pharmacokinetic variability can be identified in a target patient population receiving a pharmacological agent. Given the lack of consensus on the best approaches in model building and validation, sound fundamentals are required to ensure the selected methodology is suitable for the particular data type and/or patient population. There is a need to further standardize and establish the best approaches in modelling so that any model created can be systematically evaluated and the results relied upon.

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References

  1. Ette EI, Williams PJ. Pharmacometrics: the science of quantitative pharmacology. Hoboken (NJ): John Wiley, 2007

    Book  Google Scholar 

  2. FDA. Guidance for industry: population pharmacokinetics. US Department of Health and Human Services; Food and Drug Administration; Centre for Drug Evaluation and Research & Centre for Biologics Evaluation and Research, 1999 Feb; CP 1 [online]. Available from URL: http://www.fda.gov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/UCM072137.pdf?utm_campaign=Google2&utm_source=fdaSearch&utm_medium=website&utm_term=Guidanceforindustrypopulationpharmacokinetics&utm_content=1 [Accessed 2011 Sep 1]

  3. EMA. Guideline on reporting the results of population pharmacokinetic analyses. European Medicines Agency 21 June 2007 (Doc. Ref. CHMP/EWP/185990/06) [online]. Available from URL: http://www.ema.europa.eu/docs/en_GB/document_library/Scientific_guideline/2009/09/WC500003067.pdf [Accessed 2011 Sep 2]

  4. Wade JR, Edholm M, Salmonson T. A guide for reporting the results of population pharmacokinetic analyses: a Swedish perspective. AAPS J 2005; 7:45

    Article  PubMed  Google Scholar 

  5. Hennig S, Wainwright CE, Bell SC, et al. Population pharmacokinetics of itraconazole and its active metabolite hydroxy-itraconazole in paediatric cystic fibrosis and bone marrow transplant patients. Clin Pharmacokinet 2006; 45: 1099–114

    Article  PubMed  CAS  Google Scholar 

  6. Falck P, Midtvedt K, Vân Lê TT, et al. A population pharmacokinetic model of ciclosporin applicable for assisting dose management of kidney transplant recipients. Clin Pharmacokinet 2009; 48: 615–23

    Article  PubMed  CAS  Google Scholar 

  7. Perez-Ruixo JJ, Zannikos P, Hirankarn S, et al. Population pharmacokinetic meta-analysis of trabectedin (ET-743, Yondelis) in cancer patients. Clin Pharmacokinet 2007; 46: 867–84

    Article  PubMed  CAS  Google Scholar 

  8. Musuamba FT, Rousseau A, Bosmans J-L, et al. Limited sampling models and Bayesian estimation for mycophenolic acid area under the curve prediction in stable renal transplant patients co-medicated with ciclosporin or sirolimus. Clin Pharmacokinet 2009; 48: 745–58

    Article  PubMed  CAS  Google Scholar 

  9. Lahu G, Hünnemeyer A, Diletti E, et al. Population pharmacokinetic modelling of roflumilast and roflumilast N-oxide by total phosphodiesterase-4 in-hibitory activity and development of a population pharmacodynamic-adverse event model. Clin Pharmacokinet 2010; 49: 589–606

    Article  PubMed  CAS  Google Scholar 

  10. Kerbusch T, de Kraker J, Mathôt RAA, et al. Population pharmacokinetics of ifosfamide and its dechloroethylated and hydroxylated metabolites in chil-dren with malignant disease: a sparse sampling approach. Clin Pharmacokinet 2001; 40: 615–25

    Article  PubMed  CAS  Google Scholar 

  11. Djebli N, Rousseau A, Hoizey G, et al. Sirolimus population pharmacokinetic/pharmacogenetic analysis and Bayesian modelling in kidney transplant recipients. Clin Pharmacokinet 2006; 45: 1135–48

    Article  PubMed  CAS  Google Scholar 

  12. Sam WJ, Tham LS, Holmes MJ, et al. Population pharmacokinetics of tacrolimus in whole blood and plasma in Asian liver transplant patients. Clin Pharmacokinet 2006; 45: 59–75

    Article  PubMed  CAS  Google Scholar 

  13. Lehr T, Staab A, Tillmann C, et al. A quantitative enterohepatic circulation model: development and evaluation with tesofensine and meloxicam. Clin Pharmacokinet 2009; 48: 529–42

    Article  PubMed  CAS  Google Scholar 

  14. Nielsen EI, Sandström M, Honoré PH, et al. Developmental pharmacokinetics of gentamicin in preterm and term neonates: population modelling of a prospective study. Clin Pharmacokinet 2009; 48: 253–63

    Article  PubMed  CAS  Google Scholar 

  15. Pilla Reddy V, Kozielska M, Johnson M, et al. Structural models describing placebo treatment effects in schizophrenia and other neuropsychiatric disorders. Clin Pharmacokinet 2011; 50: 429–50

    Article  Google Scholar 

  16. Krekels EH, DeJongh J, van Lingen RA, et al. Predictive performance of a recently developed population pharmacokinetic model for morphine and its metabolites in new datasets of (preterm) neonates, infants and children. Clin Pharmacokinet 2011; 50: 51–63

    Article  PubMed  CAS  Google Scholar 

  17. Han K, Bies R, Johnson H, et al. Population pharmacokinetic evaluation with external validation and bayesian estimator of voriconazole in liver transplant recipients. Clin Pharmacokinet 2011; 50: 201–14

    Article  PubMed  CAS  Google Scholar 

  18. Beal SL. Validation of a population model. NONMEM users group (NMusers), 1994 Feb 1 [online]. Available from URL: http://www.cognigencorp.com/nonmem/nmo/topic006.html [Accessed 2011 Sep 2]

  19. International Programme on Chemical Safety (IPCS). Characterization and application of physiologically based pharmacokinetic models in risk assessment. Geneva: WHO, 2010 [online]. Available from URL: http://www.inchem.org/documents/harmproj/harmproj/harmproj9.pdf [Accessed 2012 May 28]

    Google Scholar 

  20. Barton HA, Chiu WA, Woodrow Setzer R, et al. Characterizing uncertainty and variability in physiologically based pharmacokinetic models: state of the science and needs for research and implementation. Toxicol Sci 2007; 99: 395–402

    Article  PubMed  CAS  Google Scholar 

  21. Babuska I. Verification and validation in computational engineering and science: basic concepts. Comput Methods Appl Mech Eng 2004; 193:4057–66

    Article  Google Scholar 

  22. Sun H, Fadiran EO, Jones CD, et al. Population pharmacokinetics: a regulatory perspective. Clin Pharmacokinet 1999; 37: 41–58

    Article  PubMed  CAS  Google Scholar 

  23. Mesnil F, Mentre F, Dubruc C, et al. Population pharmacokinetic analysis of mizolastine and validation from sparse data on patients using the nonparametric maximum likelihood method. J Pharmacokinet Biopharm 1998; 26: 133–61

    Article  PubMed  CAS  Google Scholar 

  24. Williams PJ, Ette EI. The role of population pharmacokinetics in drug development in light of the Food and Drug Administration’s ‘Guidance for Industry: population pharmacokinetic’. Clin Pharmacokinet 2000; 39: 385–95

    Article  PubMed  CAS  Google Scholar 

  25. Ette EI, Ludden TM. Population pharmacokinetic modeling: the importance of informative graphics. Pharm Res 1995; 12: 1845–55

    Article  PubMed  CAS  Google Scholar 

  26. Box GEP, Draper NR. Empirical model-building and response surfaces. New York: John Wiley & Sons, 1987

    Google Scholar 

  27. Karlsson MO, Savic RM. Diagnosing model diagnostics. Clin Pharmacol Ther 2007; 82: 17–20

    Article  PubMed  CAS  Google Scholar 

  28. Ette EI. Stability and performance of a population pharmacokinetic model. J Clin Pharmacol 1997; 37: 486–95

    Article  PubMed  CAS  Google Scholar 

  29. Vilicich M. Validation Strategy for NONMEM. NONMEM users group (NMusers) 2008 Oct 17 [online]. Available from URL: http://www.cognigencorp.com/nonmem/current/2008-October/1214.html [Accessed 2011 Sep 2]

  30. Brendel K, Dartois C, Comets E, et al. Are population pharmacokinetic and/or pharmacodynamic models adequately evaluated? A survey of the literature from 2002 to 2004. Clin Pharmacokinet 2007; 46: 221–34

    Article  PubMed  Google Scholar 

  31. Frame B, Koup J, Miller R, et al. Population pharmacokinetics of clinafloxacin in healthy volunteers and patients with infections: experience with hetero-geneous pharmacokinetic data. Clin Pharmacokinet 2001; 40: 307–15

    Article  PubMed  CAS  Google Scholar 

  32. Feillet F, Clarke L, Meli C, et al. Pharmacokinetics of sapropterin in patients with phenylketonuria. Clin Pharmacokinet 2008; 47: 817–25

    Article  PubMed  CAS  Google Scholar 

  33. Sugiyama E, Kaniwa N, Kim S-R, et al. Population pharmacokinetics of gemcitabine and its metabolite in Japanese cancer patients: impact of genetic polymorphisms. Clin Pharmacokinet 2010; 49: 549–58

    Article  PubMed  CAS  Google Scholar 

  34. Parke J, Holford NH, Charles BG. A procedure for generating bootstrap samples for the validation of nonlinear mixed-effects population models. Comput Methods Programs Biomed 1999; 59: 19–29

    Article  PubMed  CAS  Google Scholar 

  35. Benkali K, Prémaud A, Picard N, et al. Tacrolimus population pharmaco-kinetic-pharmacogenetic analysis and Bayesian estimation in renal transplant recipients. Clin Pharmacokinet 2009; 48: 805–16

    Article  PubMed  CAS  Google Scholar 

  36. Moltó J, Barbanoj MJ, Miranda C, et al. Simultaneous population pharmacokinetic model for lopinavir and ritonavir in HIV-infected adults. Clin Pharmacokinet 2008; 47: 681–92

    Article  PubMed  Google Scholar 

  37. Saint-Marcoux F, Royer B, Debord J, et al. Pharmacokinetic modelling and development of Bayesian estimators for therapeutic drug monitoring of mycophenolate mofetil in reduced-intensity haematopoietic stem cell transplantation. Clin Pharmacokinet 2009; 48: 667–75

    Article  PubMed  CAS  Google Scholar 

  38. Efron B. The jackknife, the bootstrap, and other resampling plans. Philadelphia (PA): Society for Industrial and Applied Mathematics, 1982

    Book  Google Scholar 

  39. Zahr N, Amoura Z, Debord J, et al. Pharmacokinetic study of mycophenolate mofetil in patients with systemic lupus erythematosus and design of Bayesian estimator using limited sampling strategies. Clin Pharmacokinet 2008; 47:277–84

    Article  PubMed  CAS  Google Scholar 

  40. Coulter CV, Isbister GK, Duffull SB. The pharmacokinetics of methanol in the presence of ethanol: a case study. Clin Pharmacokinet 2011; 50: 245–51

    Article  PubMed  CAS  Google Scholar 

  41. Stockis A, Toublanc N, Sargentini-Maier ML, et al. Retrospective population pharmacokinetic analysis of levetiracetam in children and adolescents with epilepsy: dosing recommendations. Clin Pharmacokinet 2008; 47: 333–41

    Article  PubMed  Google Scholar 

  42. Wilde S, Jetter A, Rietbrock S, et al. Population pharmacokinetics of the BEACOPP polychemotherapy regimen in Hodgkin’s lymphoma and its effect on myelotoxicity. Clin Pharmacokinet 2007; 46: 319–33

    Article  PubMed  CAS  Google Scholar 

  43. Ette EI, Williams PJ, Kim YH, et al. Model appropriateness and population pharmacokinetic modeling. J Clin Pharmacol 2003; 43: 610–23

    PubMed  CAS  Google Scholar 

  44. Mentre F, Ebelin M. Validation of population pharmacokinetic/pharmacodynamic analyses: review of proposed approaches. In: Balant L, Aarons L, editors. The population approach: measuring and managing variability in response, concentration and dose. Brussels: Commission of the European Communities, 1997: 147–60

    Google Scholar 

  45. Wahlby U, Jonsson EN, Karlsson MO. Assessment of actual significance levels for covariate effects in NONMEM. J Pharmacokinet Pharmacodyn 2001; 28: 231–52

    Article  PubMed  CAS  Google Scholar 

  46. Montgomery D, Peck E. Introduction to linear regression analysis. New York: Wiley, 1982

    Google Scholar 

  47. Bachman W. Model diagnostics. Nmusers; 2003 [online]. Available from URL: http://www.cognigencorp.com/nonmem/nm/99may012003.html [Accessed 2006 Jan 12]

  48. Yamaoka K, Nakagawa T, Uno T. Application of Akaike’s information criterion (AIC) in the evaluation of linear pharmacokinetic equations. J Pharmacokinet Biopharm 1978; 6: 165–75

    Article  PubMed  CAS  Google Scholar 

  49. Ludden TM, Beal SL, Sheiner LB. Comparison of the Akaike information criterion, the Schwarz criterion and the F test as guides to model selection. J Pharmacokinet Biopharm 1994; 22: 431–45

    Article  PubMed  CAS  Google Scholar 

  50. Sheiner LB, Beal SL. Some suggestions for measuring predictive performance. J Pharmacokinet Biopharm 1981; 9: 503–12

    Article  PubMed  CAS  Google Scholar 

  51. Hooker AC, Staatz CE, Karlsson MO. Conditional weighted residuals (CWRES): a model diagnostic for the FOCE method. Pharm Res 2007; 24: 2187–97

    Article  PubMed  CAS  Google Scholar 

  52. Pérez-Ruixo JJ, Krzyzanski W, Bouman-Thio E, et al. Pharmacokinetics and pharmacodynamics of the erythropoietin Mimetibody™ construct CNTO 528 in healthy subjects. Clin Pharmacokinet 2009; 48: 601–13

    Article  PubMed  Google Scholar 

  53. Yano Y, Beal SL, Sheiner LB. Evaluating pharmacokinetic/pharmacodynamic models using the posterior predictive check. J Pharmacokinet Pharmacodyn 2001; 28: 171–92

    Article  PubMed  CAS  Google Scholar 

  54. Mentre F, Escolano S. Prediction discrepancies for the evaluation of nonlinear mixed-effects models. J Pharmacokinet Pharmacodyn 2006; 33: 345–67

    Article  PubMed  Google Scholar 

  55. Wiczling P, Lowe P, Pigeolet E, et al. Population pharmacokinetic modelling of filgrastim in healthy adults following intravenous and subcutaneous admin-istrations. Clin Pharmacokinet 2009; 48: 817–26

    Article  PubMed  CAS  Google Scholar 

  56. Mueck W, Frey R. Population pharmacokinetics and pharmacodynamics of cinaciguat, a soluble guanylate cyclase activator, in patients with acute decompensated heart failure. Clin Pharmacokinet 2010; 49: 119–29

    Article  PubMed  CAS  Google Scholar 

  57. Lindauer A, Siepmann T, Oertel R, et al. Pharmacokinetic/pharmacodynamic modelling of venlafaxine: pupillary light reflex as a test system for noradrenergic effects. Clin Pharmacokinet 2008; 47: 721–31

    Article  PubMed  CAS  Google Scholar 

  58. Retlich S, Duval V, Ring A, et al. Pharmacokinetics and pharmacodynamics of single rising intravenous doses (0.5 mg–10mg) and determination of absolute bioavailability of the dipeptidyl peptidase-4 inhibitor linagliptin (BI 1356) in healthy male subjects. Clin Pharmacokinet 2010; 49: 829–40

    Article  PubMed  CAS  Google Scholar 

  59. Samtani MN, Vermeulen A, Stuyckens K. Population pharmacokinetics of intramuscular paliperidone palmitate in patients with schizophrenia: a novel once-monthly, long-acting formulation of an atypical antipsychotic. Clin Pharmacokinet 2009; 48: 585–600

    Article  PubMed  CAS  Google Scholar 

  60. Mukonzo JK, Nanzigu S, Rekic D, et al. HIV/AIDS patients display lower relative bioavailability of efavirenz than healthy subjects. Clin Pharmacokinet 2011; 50: 531–40

    Article  PubMed  Google Scholar 

  61. Jauregizar N, de la Fuente L, Lucero ML, et al. Pharmacokinetic-pharmacodynamic modelling of the antihistaminic (H1) effect of bilastine. Clin Pharmacokinet 2009; 48: 543–54

    Article  PubMed  CAS  Google Scholar 

  62. Mueck W, Lensing AWA, Agnelli G, et al. Rivaroxaban: population pharmacokinetic analyses in patients treated for acute deep-vein thrombosis and exposure simulations in patients with atrial fibrillation treated for stroke prevention. Clin Pharmacokinet 2011; 50: 675–86

    Article  PubMed  CAS  Google Scholar 

  63. Wang DD, Zhang S. Standardized visual predictive check — how and when to used it in model evaluation [abstract no. 1501]. PAGE. Abstracts of the 18th Annual Meeting of the Population Approach Group in Europe; 2009 Jun 23–26; St Petersburg [online]. Available from URL: http://www.page-meeting.org/?abstract=1501 [Accessed 2012 May 28]

    Google Scholar 

  64. Karlsson MO, Holford NH. A tutorial on visual predictive checks [abstract no. 1434]. PAGE. Abstracts of the 17th Annual Meeting of the Population Approach Group in Europe; 2008 Jun 18–20; Marseille [online]. Available from URL: http://www.page-meeting.org/?abstract=1434 [Accessed 2012 May 28]

    Google Scholar 

  65. Bergstrand M, Hooker AC, Wallin JE, et al. Prediction-corrected visual predictive checks for diagnosing nonlinear mixed-effects models. AAPS J 2011; 13: 143–51

    Article  PubMed  Google Scholar 

  66. Brendel K, Comets E, Laffont C, et al. Metrics for external model evaluation with an application to the population pharmacokinetics of gliclazide. Pharm Res 2006; 23: 2036–49

    Article  PubMed  CAS  Google Scholar 

  67. Brendel K, Comets E, Laffont C, et al. Evaluation of different tests based on observations for external model evaluation of population analyses. J Phar-macokinet Pharmacodyn 2010; 37: 49–65

    Article  Google Scholar 

  68. Mandema JW, Verotta D, Sheiner LB. Building population pharmacokinetic-pharmacodynamic models: I. Models for covariate effects. J Pharmacokinet Biopharm 1992; 20: 511–28

    Article  PubMed  CAS  Google Scholar 

  69. Sheiner LB. Analysis of pharmacokinetic data using parametric models: III. Hypothesis tests and confidence intervals. J Pharmacokinet Biopharm 1986; 14: 539–55

    Article  PubMed  CAS  Google Scholar 

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Acknowledgements

No funding was provided to assist in the preparation of this review. The authors have no potential conflicts of interest that are directly relevant to the content of this review to declare.

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Authors and Affiliations

  1. Division of Clinical Pharmacology & Clinical Trials Office, Department of Pediatrics, University of Utah School of Medicine, Salt Lake City, Utah, USA

    Catherine M. T. Sherwin & Michael G. Spigarelli

  2. Faculty of Pharmaceutical Sciences, The University of British Columbia, Vancouver, British Columbia, Canada

    Tony K. L. Kiang &  Mary H. H. Ensom

  3. Department of Pharmacy, Children’s and Women’s Health Centre of British Columbia, Vancouver, British Columbia, Canada

    Mary H. H. Ensom

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  1. Catherine M. T. Sherwin
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  2. Tony K. L. Kiang
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Correspondence to Mary H. H. Ensom.

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Sherwin, C.M.T., Kiang, T.K.L., Spigarelli, M.G. et al. Fundamentals of Population Pharmacokinetic Modelling. Clin Pharmacokinet 51, 573–590 (2012). https://doi.org/10.1007/BF03261932

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