Abstract
This article presents the theoretical and practical aspects involved in the design and analysis of pharmacokinetic-pharmacodynamic modelling studies. The main features of the protocol of pharmacokinetic-pharmacodynamic studies are discussed with special focus on experimental designs in relation to individual and population approaches. Some basic pharmacodynamic models (such as linear, log-linear, hyperbolic and sigmoid models) are presented as well as more complex time-dependent models (effect compartment and physiological indirect response, tolerance models) which are required when the concentration-effect relationship shows a hysteresis loop. The methods of estimation, with special focus on the individual and populations approaches, are covered, along with the way pharmacodynamic models and methods of estimation can be applied to real data and the information required to criticise the results of modelling. We also present some real problems frequently encountered when performing pharmacokinetic-pharmacodynamic modelling and give some potential solutions (problems with hysteresis loops, lack of convergence, problems with residuals). The last section discusses the significance of pharmacodynamic parameters.
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References
Grevel J. Kinetic-effect models and their applications. Pharm Res 1987; 4: 86–91.
Kroboth PD, Schmith VD, Smith RB. Pharmacodynamic modelling: application to new drag development. Clin Pharmacokinet 1991; 20: 91–8.
Peck CC, Barr WH, Benet LZ, et al. Opportunities for integration of pharmacokinetics, pharmacodynamics, and toxicokinetics in rational drug development. Clin Pharmacol Ther 1992; 51: 465–73.
Berman M. The formulation and testing of models. Ann NY Acad Sci 1963; 108: 182–94.
Benet LZ. General treatment of linear mamillary models with elimination from any compartment as used in pharmacokinetics. J Pharm Sciences 1972; 61: 536–41.
Gibaldi M, Perrier D, editors. Pharmacokinetics. New York: Marcel Dekker, 1982.
Rowland M, Tozer TN. Clinical pharmacokinetics: concepts and applications. Philadelphia: Lea & Febiger, 1989.
Wagner JG. Kinetics of pharmacologic response: I. Proposed relationships between response and drug concentration in the intact animal and man. J Theoret Biol 1968; 20: 173–201.
Holford NHG. Concepts and usefulness of pharmacokineticpharmacodynamic modelling. Fundam Clin Pharmacol 1990; 4 Suppl. 2: 93S–101S.
Bellissant E, Chau NP, Giudicelli JF. Pharmacokinetic-pharmacodynamic model relating lisinopril plasma concentrations to regional hemodynamic effects in healthy volunteers. J Cardiovasc Pharmacol 1996; 28: 470–8.
Bellissant E, Giudicelli JF. Pharmacokinetic-pharmacodynamic model relating zabiciprilat plasma concentrations to brachial and femoral hemodynamic effects in normotensive volunteers. Br J Clin Pharmacol 1998. In press.
Sheiner LB. Population approach in drug development: rationale and basic concepts. In: Rowland M, Aarons L, editors. New strategies in drug development and clinical evaluation: the population approach. Brussels: Commission of the European Communities, 1992: 13–29.
Holford NHG, Peck CC. Population pharmacodynamics and drug development. In: Van Boxtel CJ, Holford NHG, Danhof M, editors. The in vivo study of drug action. Amsterdam: Elsevier, 1992: 401–13.
Steimer JL, Ebelin ME, Van Bree J. Pharmacokinetic and pharmacodynamic data and models in clinical trials. Eur J Drug Metab Pharmacokinet 1993; 18: 61–76.
Girard P, Nony P, Boissel JP. Can we model dose-response in real prescription environment? In: Aarons L, Balant LP, Danhof M, et al., editors. The population approach: measuring and managing variability in response, concentration and dose. Luxembourg: Office for Official Publications of the European Communities, 1997: 57–66.
Meineke I, Gundert-Remy U. Managing pharmacodynamic variability: cardiovascular disorders. In: Aarons L, Balant LP, Danhof M, et al., editors. The population approach: measuring and managing variability in response, concentration and dose. Luxembourg: Office for Official Publications of the European Communities, 1997: 67–71.
Holford NHG. Population models for Alzheimer’s and Parkinson’s disease. In: Aarons L, Balant LP, Danhof M, et al., editors. The population approach: measuring and managing variability in response, concentration and dose. Luxembourg: Office for Official Publications of the European Communities, 1997: 95–104.
Galeazzi RL. Simultaneous modeling of pharmacodynamics and pharmacokinetics. J Pharmacol 1986; 17 Suppl. I: 63–70.
Paintaud G, Alván G, Berninger E, et al. The concentration-effect relationships of quinine induced hearing impairment. Clin Pharmacol Ther 1994; 55: 317–23.
Mould DR, DeFeo TM, Reele S, et al. Simultaneous modeling of the pharmacokinetics and pharmacodynamics of midazolam and diazepam. Clin Pharmacol Ther 1995; 58: 35–43.
Holford NHG, Sheiner LB. Pharmacokinetic and pharmacodynamic modeling in vivo. CRC CritRevBioeng 1981; 5: 273–322.
Holford NHG, Sheiner LB. Understanding the dose-effect relationship: clinical application of pharmacokinetic-pharmacodynamic models. Clin Pharmacokinet 1981; 6: 429–53.
Holford NHG, Sheiner LB. Kinetics of pharmacologic response. Pharmacol Ther 1982; 16: 143–66.
Ariëns EJ, Simonis AM. A molecular basis for drug action. J Pharm Pharmacol 1964; 16: 137–57.
Ariëns EJ, Simonis AM. Amolecular basis for drug action: the interaction of one or more drugs with different receptors. J Pharm Pharmacol 1964; 16: 289–312.
Hill AV. The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J Physiol 1910; 40: iv–vii.
Girard P, Boissel JP. Clockwise hysteresis or proteresis. J Pharmacokinet Biopharm 1989; 17: 401–2.
Sheiner LB, Stanski DR, Vozeh S, et al. Simultaneous modeling of pharmacokinetics and pharmacodynamics: application to d-tubocurarine. Clin Pharmacol Ther 1979; 25: 358–71.
Colburn WA. Simultaneous pharmacokinetic and pharmacodynamic modeling. J Pharmacokinet Biopharm 1981; 9: 367–88.
Fuseau E, Sheiner LB. Simultaneous modeling of pharmacokinetics and pharmacodynamics with a nonparametric pharmacodynamic model. Clin Pharmacol Ther 1984; 35: 733–41.
Unadkat JD, Bartha F, Sheiner LB. Simultaneous modeling of pharmacokinetics and pharmacodynamics with nonparametric kinetic and dynamic models. Clin Pharmacol Ther 1986; 40: 86–93.
Dayneka NL, Garg V, Jusko WJ. Comparison of four basic models of indirect pharmacodynamic responses. J Pharmacokinet Biopharm 1993; 21: 457–78.
Jusko WJ, Ko HC. Physiologic indirect response models characterize diverse types of pharmacodynamic effects. Clin Pharmacol Ther 1994; 56: 406–19.
Wakelkamp M, Alvan G, Paintaud G. The time of maximum effect for model selection in pharmacokinetic-pharmacodynamic analysis applied to frusemide. Br J Clin Pharmacol 1998; 45: 63–70.
Hammarlund MM, Odlind B, Paalzow LK. Acute tolerance to furosemide diuresis in humans. Pharmacokinetic-pharmacodynamic modeling. J Pharmacol Exp Ther 1985; 233: 447–53.
Porchet HC, Benowitz NL, Sheiner LB. Pharmacodynamic model of tolerance: application to nicotine. J Pharmacol Exp Ther 1988; 244: 231–6.
Fung HL. PK/PD models of pharmacologie tolerance: application to nitrates. Therapie 1994; 49: 292.
Wakelkamp M, Alvan G, Gabrielsson J, et al. Pharmacodynamic modeling of furosemide tolerance after multiple intravenous administration. Clin Pharmacol Ther 1996; 60: 75–88.
Sheiner LB. The population approach to pharmacokinetic data analysis: rationale and standard data analysis method. Drug Metab Rev 1984; 15: 153–71.
Draper NR, Smith H. Applied regression analysis. 2nd ed. New York: Wiley, 1981.
Seber GAF, Wild CJ. Nonlinear regression. New York: Wiley, 1989.
Sheiner LB, Rosenberg B, Marathe VV. Estimation of population characteristics of pharmacokinetic parameters from routine clinical data. J Pharmacokinet Biopharm 1977; 5: 445–79.
Cox DR, Hinkley DV. Theoretical statistics. London: Chapman & Hall, 1974.
Beal SL, Sheiner LB. NONMEMUsers Guides. SanFrancisco: NONMEM Project Group, University of California, 1989.
Dempster AP, Laird NM, Rubin DB. Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B 1977; 39: 1–38.
Gabrielsson J, Weiner D. Pharmacokinetic-pharmacodynamic data analysis: concepts and applications. Stockholm: Swedish Pharmaceutical Press, 1994.
Peck CC, Beal SL, Sheiner LB, et al. Extended least square nonlinear regression: a possible solution to the ‘choice of weights’ problem in analysis of individual pharmacokinetic data. J Pharmacokinet Biopharm 1984; 12: 545–58.
Metzler CM. Extended least squares (ELS) for pharmacokinetic models. J Pharm Sci 1987; 76: 565–71.
Johnson LE. Computers, models, and optimization in physiological kinetics. CRC Crit Rev Bioeng 1974; 2: 1–37.
Boxenbaum HG, Riegelman S, Elashoff RM. Statistical estimations in pharmacokinetics. J Pharmacokinet Biopharm 1974; 2: 123–48.
Yamaoka K, Nakagawa T, Uno T. Application of Akaike’s information criterion (AIC) in the evaluation of linear pharmacoki-netic equations. J Pharmacokinet Biopharm 1978; 6: 165–75.
Bellissant E, Chau NP, Thuillez C, et al. Pharmacokinetic-pharmacodynamic model relating spiraprilat plasma concentrations to systemic and regional hemodynamic effects in congestive heart failure. J Cardiovasc Pharmacol 1997; 30: 253–60.
Ludden TM, Beal SL, Sheiner LB. Comparison of the Akaike information criterion, the Schwartz criterion and the F test as guides to model selection. J Pharmacokinet Biopharm 1994; 22: 431–45.
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Bellissant, E., Sébille, V. & Paintaud, G. Methodological Issues in Pharmacokinetic-Pharmacodynamic Modelling. Clin Pharmacokinet 35, 151–166 (1998). https://doi.org/10.2165/00003088-199835020-00004
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DOI: https://doi.org/10.2165/00003088-199835020-00004