Modelling Response Time Profiles in the Absence of Drug Concentrations: Definition and Performance Evaluation of the K–PD Model
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The plasma concentration–time profile of a drug is essential to explain the relationship between the administered dose and the kinetics of drug action. However, in some cases such as in pre-clinical pharmacology or phase-III clinical studies where it is not always possible to collect all the required PK information, this relationship can be difficult to establish. In these circumstances several authors have proposed simple models that can analyse and simulate the kinetics of the drug action in the absence of PK data. The present work further develops and evaluates the performance of such an approach. A virtual compartment representing the biophase in which the concentration is in equilibrium with the observed effect is used to extract the (pharmaco)kinetic component from the pharmacodynamic data alone. Parameters of this model are the elimination rate constant from the virtual compartment (KDE), which describes the equilibrium between the rate of dose administration and the observed effect, and the second parameter, named EDK50 which is the apparent in vivo potency of the drug at steady state, analogous to the product of EC50, the pharmacodynamic potency, and clearance, the PK “potency” at steady state. Using population simulation and subsequent (blinded) analysis to evaluate this approach, it is demonstrated that the proposed model usually performs well and can be used for predictive simulations in drug development. However, there are several important limitations to this approach. For example, the investigated doses should extend from those producing responses well below the EC50 to those producing ones close to the maximum response, optimally reach steady state response and followed until the response returns to baseline. It is shown that large inter-individual variability on PK–PD parameters will produce biases as well as large imprecision on parameter estimates. It is also clear that extrapolations to dosage routes or schedules other than those used to estimate the parameters should be undertaken with great caution (e.g., in case of non-linearity or complex drug distribution). Consequently, it is advised to apply this approach only when the underlying structural PD and PK are well understood. In any case, K–PD model should definitively not be substituted for the gold standard PK–PD model when correct full model can and should be identified.
Keywordspopulation pharmacokinetic–phamacodynamic simulation kinetics of drug action dose-response-time-model K–PD model
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- 1.Holford N.H., Sheiner L.B. (1982) Kinetics of pharmacologic response. Pharmac. Ther. 16:143–166CrossRef
- 2.Sheiner L.B., Stanski D.R., Vozeh S., Miller R.D., Ham J. (1979) Simultaneous modeling of pharmacokinetics and pharmacodynamics: application to d-tubocurarine. Clin. Pharmacol. Ther. 29:358–371
- 3.Jusko W.J., Ko H.C. (1994) Physiologic indirect response models characterize diverse types of pharmacodynamic effects. Clin. Pharmacol. Ther. 56:406–419CrossRef
- 4.Verotta D., Sheiner L.B. (1995) A general conceptual model for non-steady state pharmacokinetic/pharmacodynamic data [see comments]. J. Pharmacokinet. Biopharm. 23:1–4CrossRef
- 5.Wade J.R., Kelman A.W., Howie C.A., Whiting B. (1993) Effect of misspecification of the absorption process on subsequent parameter estimation in population analysis. J. Pharmacokinet. Biopharm. 21:209–222CrossRef
- 6.Wade J.R., Beal S.L., Sambol N.C. (1994) Interaction between structural, statistical, and covariate models in population pharmacokinetic analysis. J. Pharmacokinet. Biopharm. 22: 165–177CrossRef
- 7.Pillai G., Gieschke R., Goggin T., Jacqmin P., Schimmer R.C., Steimer J.L. (2004) A semimechanistic and mechanistic population PK–PD model for biomarker response to ibandronate, a new bisphosphonate for the treatment of osteoporosis. Br. J. Clin. Pharmacol. 58:618–631CrossRef
- 8.Derks M.G., van den Berg B.T., van der Zee J.S., Braat M.C., van Boxtel C.J. (1997) Biphasic effect–time courses in man after formoterol inhalation: eosinopenic and hypokalemic effects and inhibition of allergic skin reactions. J. Pharmacol. Exp. Ther. 283:824–832
- 9.Duffull S.B., Chabaud S., Nony P., Laveille C., Girard P., Aarons L. (2000) A pharmacokinetic simulation model for ivabradine in healthy volunteers. Eur. J. Pharm. Sci. 10:285–294CrossRef
- 10.Chabaud S., Girard P., Nony P., Boissel J.P. (2002) Clinical trial simulation using therapeutic effect modeling: application to ivabradine efficacy in patients with angina pectoris. J. Pharmacokinet. Pharmacodyn. 29:339–363CrossRef
- 11.Johnson T.N., Rostami-Hodjegan A. Goddard J.M., Tanner M.S., Tucker G.T. (2002) Contribution of midazolam and its 1-hydroxy metabolite to preoperative sedation in children: a pharmacokinetic–pharmacodynamic analysis. Br. J. Anaesth. 89:428–437CrossRef
- 12.Snoeck E., Jacqmin P., Van P.A., Danhof M. (1999) A combined specific target site binding and pharmacokinetic model to explore the non-linear disposition of draflazine. J. Pharmacokinet. Biopharm. 27:257–281CrossRef
- 13.Levy G. (1964) Relationship between rate of elimination of tubocurarine and rate of decline of its pharmacological activity. Br. J. Anaesth. 36:694–5CrossRef
- 14.Levy G. (1967) Kinetics of pharmacologic activity of succinylcholine in man. J. Pharm. Sci. 56:1657–1688
- 15.Gibaldi M., Levy G. (1972) Dose-dependent decline of pharmacologic effects of drugs with linear pharmacokinetic characteristics. J. Pharm. Sci. 61:567–9CrossRef
- 16.Van Rossum J.M. (1977) Kinetics of Drug Action. Springer Verlag, Berlin, Heidelberg, New York
- 17.Rowland M., Tozer T.N. (1980) Clinical Pharmacokinetics: Concepts and Applications, 1st edn. Lea & Febiger, Philadelphia
- 18.Verotta D., Sheiner L.B. (1991) Semiparametric analysis of non-steady-state pharmacodynamics. J. Pharmacokinet. Biopharm. 19:691–712CrossRef
- 19.Gabrielsson J., Jusko W.J., Alari L. (2000) Modeling of dose-response-time data: four examples of estimating the turnover parameters and generating kinetic functions from response profiles. Biopharm. Drug. Dispos. 21:41–52CrossRef
- 20.Bragg P., Fisher D.M., Shi J., Donati F., Meistelman C., Lau M., Sheiner L.B. (1994) Comparison of twitch depression of the adductor pollicis and the respiratory muscles. Pharmacodynamic modeling without plasma concentrations. Anesthesiology. 80:310–319
- 21.Fisher D.M., Wright P.M. (1997) Are plasma concentration values necessary for pharmacodynamic modeling of muscle relaxants?. Anesthesiology 86:567–575CrossRef
- 22.Lalonde R.L., Gaudreault J., Karhu D.A., Marriott T.B. (1999) Mixed-effects modeling of the pharmacodynamic response to the calcimimetic agent R-568. Clin. Pharmacol. Ther. 65:40–49CrossRef
- 23.J. Gabrielsson and D. Weiner. Pharmacokinetic and Pharmacodynamic Data Analysis: Concepts & Applications. Swedish Pharmaceutical Press, 2000.
- 24.Beal S.L., Sheiner L.B. (1992) NONMEM User’s Guide, Part I. University of California at San Francisco, San Francisco
- 25.P. Girard and F. Mentré. A comparison of estimation methods in non-linear mixed effects models using a blind analysis. PAGE 14 (2005) Abstr 834 [www.page-meeting.org/?abstract=834].
- 26.van Schaick E.A., de Greef H.J., Langemeijer M.W., Sheehan M.J., IJzerman A.P., Danhof M. (1997) Pharmacokinetic–pharmacodynamic modelling of the anti-lipolytic and anti-ketotic effects of the adenosine A1-receptor agonist N 6-(p-sulfophenyl) adenosine in rats. Br. J. Pharmacol. 122: 525–533CrossRef
- 27.P. Jacqmin. Modelling of kinetics of drug action without plasma concentrations, when and how? In M. Danhof, M. Karlsson, and R. J. Powell (eds.) Measurements and Kinetics of in vivo Drug Effects. LACDR, Leiden; 2002.
- 28.T. Goggin, P. Jacqmin, R. Gieschke, G. Pillai, E. Snoeck, P. Girard, and J. L. Steimer. Population PD(-PK) modeling and clinical trial simulation, characterizing schedule dependence of hematotoxicity and other Phase II trial design features for a new oral anticancer drug. PAGE 10 (2001) Abstr 180 [www.page-meeting.org/?abstract=180].
- 29.Romberg R., Olofsen E., Sarton E., Teppema L., Dahan A. (2003) Pharmacodynamic effect of morphine-6-glucuronide versus morphine on hypoxic and hypercapnic breathing in healthy volunteers. Anesthesiology 99:788–798CrossRef
- 30.Jordan P., Gieschke R. (2005) Explicit solutions for a class of indirect pharmacodynamic response models. Comput. Methods Programs Biomed. 77:91–97CrossRef