Skip to main content
Top
Published in: Clinical Pharmacokinetics 12/2017

01-12-2017 | Original Research Article

A Joint Model for Vitamin K-Dependent Clotting Factors and Anticoagulation Proteins

Authors: Qing Xi Ooi, Daniel F. B. Wright, R. Campbell Tait, Geoffrey K. Isbister, Stephen B. Duffull

Published in: Clinical Pharmacokinetics | Issue 12/2017

Login to get access

Abstract

Background

Warfarin acts by inhibiting the reduction of vitamin K (VK) to its active form, thereby decreasing the production of VK-dependent coagulation proteins. The aim of this research is to develop a joint model for the VK-dependent clotting factors II, VII, IX and X, and the anticoagulation proteins, proteins C and S, during warfarin initiation.

Methods

Data from 18 patients with atrial fibrillation who had warfarin therapy initiated were available for analysis. Nine blood samples were collected from each subject at baseline, and at 1–5, 8, 15 and 29 days after warfarin initiation and assayed for factors II, VII, IX and X, and proteins C and S. Warfarin concentration–time data were not available. The coagulation proteins data were modelled in a stepwise manner using NONMEM® Version 7.2. In the first stage, each of the coagulation proteins was modelled independently using a kinetic-pharmacodynamic model. In the subsequent step, the six kinetic-pharmacodynamic models were combined into a single joint model.

Results

One patient was administered VK and was excluded from the analysis. Each kinetic-pharmacodynamic model consisted of two parts: (1) a common one-compartment pharmacokinetic model with first-order absorption and elimination for warfarin; and (2) an inhibitory E max model linked to a turnover model for coagulation proteins. In the joint model, an unexpected pharmacodynamic lag was identified and the estimated degradation half-life of VK-dependent coagulation proteins were in agreement with previously published values. The model provided an adequate fit to the observed data.

Conclusion

The joint model represents the first work to quantify the influence of warfarin on all six VK-dependent coagulation proteins simultaneously. Future work will expand the model to predict the influence of exogenously administered VK on the time course of clotting factor concentrations after warfarin overdose and during perioperative warfarin reversal procedures.
Appendix
Available only for authorised users
Literature
3.
go back to reference Hamberg AK, Wadelius M, Lindh JD, et al. A pharmacometric model describing the relationship between warfarin dose and INR response with respect to variations in CYP2C9, VKORC1, and age. Clin Pharmacol Ther. 2010;87(6):727–34. doi:10.1038/clpt.2010.37.CrossRefPubMed Hamberg AK, Wadelius M, Lindh JD, et al. A pharmacometric model describing the relationship between warfarin dose and INR response with respect to variations in CYP2C9, VKORC1, and age. Clin Pharmacol Ther. 2010;87(6):727–34. doi:10.​1038/​clpt.​2010.​37.CrossRefPubMed
5.
go back to reference Sasaki T, Tabuchi H, Higuchi S, Ieiri I. Warfarin-dosing algorithm based on a population pharmacokinetic/pharmacodynamic model combined with Bayesian forecasting. Pharmacogenomics. 2009;10(8):1257–66. doi:10.2217/pgs.09.65.CrossRefPubMed Sasaki T, Tabuchi H, Higuchi S, Ieiri I. Warfarin-dosing algorithm based on a population pharmacokinetic/pharmacodynamic model combined with Bayesian forecasting. Pharmacogenomics. 2009;10(8):1257–66. doi:10.​2217/​pgs.​09.​65.CrossRefPubMed
8.
go back to reference Xue L, Holford NH, Miao L (eds). Warfarin PKPD: theory, body composition and genotype. In: Annual Meeting of the Population Approach Group in Europe. Lisbon; 2016 (7–10 June). Xue L, Holford NH, Miao L (eds). Warfarin PKPD: theory, body composition and genotype. In: Annual Meeting of the Population Approach Group in Europe. Lisbon; 2016 (7–10 June).
9.
go back to reference McCollum D, Tait RC, Conkie J, et al. The effect of initiation of oral anticoagulation on protein Z and coagulation activation. Br J Haematol. 2004;125(Suppl. 1):1. McCollum D, Tait RC, Conkie J, et al. The effect of initiation of oral anticoagulation on protein Z and coagulation activation. Br J Haematol. 2004;125(Suppl. 1):1.
10.
go back to reference Tait RC, Sefcick A. A warfarin induction regimen for out-patient anticoagulation in patients with atrial fibrillation. Br J Haematol. 1998;101(3):450–4.CrossRefPubMed Tait RC, Sefcick A. A warfarin induction regimen for out-patient anticoagulation in patients with atrial fibrillation. Br J Haematol. 1998;101(3):450–4.CrossRefPubMed
12.
go back to reference O’Reilly RA, Aggeler PM, Leong LS. Studies on the coumarin anticoagulant drugs: the pharmacodynamics of warfarin in man. J Clin Invest. 1963;42(10):1542–51.CrossRefPubMedPubMedCentral O’Reilly RA, Aggeler PM, Leong LS. Studies on the coumarin anticoagulant drugs: the pharmacodynamics of warfarin in man. J Clin Invest. 1963;42(10):1542–51.CrossRefPubMedPubMedCentral
14.
go back to reference Pitsiu M, Parker EM, Aarons L, Rowland M. A Bayesian method based on clotting factor activity for the prediction of maintenance warfarin dosage regimens. Ther Drug Monit. 2003;25(1):36–40.CrossRefPubMed Pitsiu M, Parker EM, Aarons L, Rowland M. A Bayesian method based on clotting factor activity for the prediction of maintenance warfarin dosage regimens. Ther Drug Monit. 2003;25(1):36–40.CrossRefPubMed
16.
go back to reference Shivva V, Korell J, Tucker IG, Duffull SB. An approach for identifiability of population pharmacokinetic-pharmacodynamic models. CPT Pharmacomet Syst Pharmacol. 2013;2(6):e49. doi:10.1038/psp.2013.25.CrossRef Shivva V, Korell J, Tucker IG, Duffull SB. An approach for identifiability of population pharmacokinetic-pharmacodynamic models. CPT Pharmacomet Syst Pharmacol. 2013;2(6):e49. doi:10.​1038/​psp.​2013.​25.CrossRef
18.
go back to reference Holford NH, Kirkpatrick C, Duffull SB (eds). NONMEM termination status is not an important indicator of the quality of bootstrap parameter estimates. In: Annual Meeting of the Population Approach Group in Europe. Brugge; 2006. Holford NH, Kirkpatrick C, Duffull SB (eds). NONMEM termination status is not an important indicator of the quality of bootstrap parameter estimates. In: Annual Meeting of the Population Approach Group in Europe. Brugge; 2006.
21.
go back to reference Jacqmin P, Snoeck E, van Schaick EA, et al. Modelling response time profiles in the absence of drug concentrations: definition and performance evaluation of the K-PD model. J Pharmacokinet Pharmacodyn. 2007;34(1):57–85. doi:10.1007/s10928-006-9035-z.CrossRefPubMed Jacqmin P, Snoeck E, van Schaick EA, et al. Modelling response time profiles in the absence of drug concentrations: definition and performance evaluation of the K-PD model. J Pharmacokinet Pharmacodyn. 2007;34(1):57–85. doi:10.​1007/​s10928-006-9035-z.CrossRefPubMed
23.
go back to reference Chan E, McLachlan AJ, Pegg M, et al. Disposition of warfarin enantiomers and metabolites in patients during multiple dosing with rac-warfarin. Br J Clin Pharmacol. 1994;37(6):563–9.CrossRefPubMedPubMedCentral Chan E, McLachlan AJ, Pegg M, et al. Disposition of warfarin enantiomers and metabolites in patients during multiple dosing with rac-warfarin. Br J Clin Pharmacol. 1994;37(6):563–9.CrossRefPubMedPubMedCentral
24.
go back to reference D’Angelo A, Della Valle P, Crippa L, et al. Relationship between international normalized ratio values, vitamin K-dependent clotting factor levels and in vivo prothrombin activation during the early and steady phases of oral anticoagulant treatment. Haematologica. 2002;87(10):1074–80.PubMed D’Angelo A, Della Valle P, Crippa L, et al. Relationship between international normalized ratio values, vitamin K-dependent clotting factor levels and in vivo prothrombin activation during the early and steady phases of oral anticoagulant treatment. Haematologica. 2002;87(10):1074–80.PubMed
25.
go back to reference O’Reilly RA, Aggeler PM. Studies on coumarin anticoagulant drugs: initiation of warfarin therapy without a loading dose. Circulation. 1968;38(1):169–77.CrossRefPubMed O’Reilly RA, Aggeler PM. Studies on coumarin anticoagulant drugs: initiation of warfarin therapy without a loading dose. Circulation. 1968;38(1):169–77.CrossRefPubMed
26.
go back to reference Bowie EJ, Thompson JH Jr, Didisheim P, Owen CA Jr. Disappearance rates of coagulation factors: transfusion studies in factor-deficient patients. Transfusion. 1967;7(3):174–84.CrossRefPubMed Bowie EJ, Thompson JH Jr, Didisheim P, Owen CA Jr. Disappearance rates of coagulation factors: transfusion studies in factor-deficient patients. Transfusion. 1967;7(3):174–84.CrossRefPubMed
27.
go back to reference Pitsiu M, Parker EM, Aarons L, Rowland M. Population pharmacokinetics and pharmacodynamics of warfarin in healthy young adults. Eur J Pharm Sci. 1993;1(3):151–7.CrossRef Pitsiu M, Parker EM, Aarons L, Rowland M. Population pharmacokinetics and pharmacodynamics of warfarin in healthy young adults. Eur J Pharm Sci. 1993;1(3):151–7.CrossRef
28.
go back to reference Hjort PF, Egeberg O, Mikkelsen S. Turnover of prothrombin, factor VII and factor IX in a patient with hemophilia A. Scand J Clin Lab Invest. 1961;13(4):668–72.CrossRefPubMed Hjort PF, Egeberg O, Mikkelsen S. Turnover of prothrombin, factor VII and factor IX in a patient with hemophilia A. Scand J Clin Lab Invest. 1961;13(4):668–72.CrossRefPubMed
30.
go back to reference D’Angelo A, Vigano-D’Angelo S, Esmon CT, Comp PC. Acquired deficiencies of protein S: protein S activity during oral anticoagulation, in liver disease, and in disseminated intravascular coagulation. J Clin Invest. 1988;81(5):1445–54.CrossRefPubMedPubMedCentral D’Angelo A, Vigano-D’Angelo S, Esmon CT, Comp PC. Acquired deficiencies of protein S: protein S activity during oral anticoagulation, in liver disease, and in disseminated intravascular coagulation. J Clin Invest. 1988;81(5):1445–54.CrossRefPubMedPubMedCentral
31.
go back to reference Riess H, Binsack T, Hiller E. Protein C antigen in prothrombin complex concentrates: content, recovery and half life. Blut. 1985;50(5):303–6.CrossRefPubMed Riess H, Binsack T, Hiller E. Protein C antigen in prothrombin complex concentrates: content, recovery and half life. Blut. 1985;50(5):303–6.CrossRefPubMed
32.
go back to reference Bertola JP, Mazoyer E, Bergmann JF, et al. Early prediction of the sensitivity of warfarin in elderly patients by the fall in factor VIIc and protein C at the induction of treatment. Thromb Res. 2003;109(5–6):287–91.CrossRefPubMed Bertola JP, Mazoyer E, Bergmann JF, et al. Early prediction of the sensitivity of warfarin in elderly patients by the fall in factor VIIc and protein C at the induction of treatment. Thromb Res. 2003;109(5–6):287–91.CrossRefPubMed
33.
go back to reference Vainieri H, Wingard LB Jr. Effect of warfarin on the kinetics of the vitamin K-dependent clotting factors in rats. J Pharmacol Exp Ther. 1977;201(2):507–17.PubMed Vainieri H, Wingard LB Jr. Effect of warfarin on the kinetics of the vitamin K-dependent clotting factors in rats. J Pharmacol Exp Ther. 1977;201(2):507–17.PubMed
34.
go back to reference Chan E, McLachlan A, O’Reilly R, Rowland M. Stereochemical aspects of warfarin drug interactions: use of a combined pharmacokinetic-pharmacodynamic model. Clin Pharmacol Ther. 1994;56(3):286–94.CrossRefPubMed Chan E, McLachlan A, O’Reilly R, Rowland M. Stereochemical aspects of warfarin drug interactions: use of a combined pharmacokinetic-pharmacodynamic model. Clin Pharmacol Ther. 1994;56(3):286–94.CrossRefPubMed
35.
go back to reference Hirsh J, Dalen J, Anderson DR, et al. Oral anticoagulants: mechanism of action, clinical effectiveness, and optimal therapeutic range. Chest. 2001;119(1 Suppl.):8S–21S.CrossRefPubMed Hirsh J, Dalen J, Anderson DR, et al. Oral anticoagulants: mechanism of action, clinical effectiveness, and optimal therapeutic range. Chest. 2001;119(1 Suppl.):8S–21S.CrossRefPubMed
36.
go back to reference Choonara IA, Malia RG, Haynes BP, et al. The relationship between inhibition of vitamin K1 2,3-epoxide reductase and reduction of clotting factor activity with warfarin. Br J Clin Pharmacol. 1988;25(1):1–7.CrossRefPubMedPubMedCentral Choonara IA, Malia RG, Haynes BP, et al. The relationship between inhibition of vitamin K1 2,3-epoxide reductase and reduction of clotting factor activity with warfarin. Br J Clin Pharmacol. 1988;25(1):1–7.CrossRefPubMedPubMedCentral
38.
go back to reference Bose A, Chatterjee S. Comparison of bootstrap and jackknife variance estimators in linear regression: second order results. Stat Sin. 2002;12(2):575–98. Bose A, Chatterjee S. Comparison of bootstrap and jackknife variance estimators in linear regression: second order results. Stat Sin. 2002;12(2):575–98.
39.
go back to reference Efron B, Gong G. A leisurely look at the bootstrap, the jackknife, and cross-validation. Am Stat. 1983;37(1):36–48. doi:10.2307/2685844. Efron B, Gong G. A leisurely look at the bootstrap, the jackknife, and cross-validation. Am Stat. 1983;37(1):36–48. doi:10.​2307/​2685844.
40.
go back to reference Bonate PL, Steimer JL. Pharmacokinetic-pharmacodynamic modeling and simulation. New York: Springer; 2006. Bonate PL, Steimer JL. Pharmacokinetic-pharmacodynamic modeling and simulation. New York: Springer; 2006.
41.
go back to reference Wright DF. Model-based drug dosing. Dunedin: University of Otago; 2013. Wright DF. Model-based drug dosing. Dunedin: University of Otago; 2013.
Metadata
Title
A Joint Model for Vitamin K-Dependent Clotting Factors and Anticoagulation Proteins
Authors
Qing Xi Ooi
Daniel F. B. Wright
R. Campbell Tait
Geoffrey K. Isbister
Stephen B. Duffull
Publication date
01-12-2017
Publisher
Springer International Publishing
Published in
Clinical Pharmacokinetics / Issue 12/2017
Print ISSN: 0312-5963
Electronic ISSN: 1179-1926
DOI
https://doi.org/10.1007/s40262-017-0541-5

Other articles of this Issue 12/2017

Clinical Pharmacokinetics 12/2017 Go to the issue

Acknowledgement to Referees

Acknowledgement to Referees