Clinical Pharmacokinetics

, Volume 6, Issue 6, pp 429–453 | Cite as

Understanding the Dose-Effect Relationship

Clinical Application of Pharmacokinetic-Pharmacodynamic Models
  • Nicholas H. G. Holford
  • Lewis B. Sheiner
Article

Summary

It is a major goal of clinical pharmacology to understand the dose-effect relationship in therapeutics. Much progress towards this goal has been made in the last 2 decades through the development of pharmacokinetics as a discipline. The study of pharmacokinetics seeks to explain the time course of drug concentration in the body. Recognition of the crucial concepts of clearance and volume of distribution has provided an important link to the physiological determinants of drug disposition. Mathematical models of absorption, distribution, metabolism and elimination have been extensively applied, and generally their predictions agree remarkably well with actual observations. However, the time course of drug concentration cannot in itself predict the time course or magnitude of drug effect. When drug concentrations at the effect site have reached equilibrium and the response is constant, the concentration-effect relationship is known as pharmacodynamics. Mathematical models of pharmacodynamics have been used widely by pharmacologists to describe drug effects on isolated tissues. The crucial concepts of pharmacodynamics are potency — reflecting the sensitivity of the organ or tissue to a drug, and efficacy — describing the maximum response. These concepts have been embodied in a simple mathematical expression, the Emax model, which provides a practical tool for predicting drug response analogous to the compartmental model in pharmacokinetics for predicting drug concentration.

The application of pharmacodynamics to the study of drug action in vivo requires the linking of pharmacokinetics and pharmacodynamics to predict firstly the dose-concentration, and then the concentration-effect relationship. This may be done directly by equating the concentration predicted by a pharmacokinetic model to the effect site concentration, but this simplistic approach is often not appropriate for various reasons, including delay in drug equilibrium with the receptor site, use of indirect measures of drug action, the presence of active metabolites, or homeostatic responses, thus often necessitating the use of more complex models.

The relative pharmacodynamic bioavailability of different preparations of the same drug may be determined from the time course of a drug effect. Bioavailability determined in this way may differ markedly from bioavailability defined by measurements of drug concentration if active metabolites are formed or if effects are produced in the non-linear region of the concentration-effect relationship.

The influence of changes in the extent of plasma protein binding may be important in the interpretation of drug concentration measurements since it is generally held that only the unbound fraction is pharmacologically active. Clear examples of this phenomenon are few, but this reflects the general paucity of adequate observations rather than casting doubt on the usual assumption.

The design of rational dosing regimens for clinical therapeutics cannot be performed with a knowledge of pharmacokinelics alone. The time course of drug effect may be essentially independent of concentration when a dose produces near maximal effects throughout the dosing interval. If effects are between 20 and 80% of maximum, the response will decrease linearly even though concentrations are declining exponentially. Finally, at relatively small degrees of effect, the time course of drug effect and concentration will be in parallel. The usual ‘rule of thumb’ of dosing every half-life is a conservative strategy for limiting wide fluctuations in drug effect, but demands more from the patient in terms of dosing frequency than may be necessary to achieve consistent drug action. On the other hand, if therapeutic success is dependent more on cumulative response than moment to moment activity, the use of extended dosing intervals may markedly reduce the effectiveness of the same average dose. Considerations of these factors can be incorporated into a dosing scheme by combined application of the principles of pharmacokinelics and pharmacodynamics.

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References

  1. Ariens, E.J. and Simonis, A.M.: A molecular basis for drug action. Journal of Pharmacy and Pharmacology 27: 137–257 (1964a).CrossRefGoogle Scholar
  2. Ariens, E.J. and Simonis, A.M.: A molecular basis for drug action. The interaction of one or more drugs with different receptors. Journal of Pharmacy and Pharmacology 16: 289–312 (1964b).CrossRefGoogle Scholar
  3. Bean, B.L.; Bronn, J.J.; Casals-Stenzel, J.; Fraser, R.; Lerer, A.F.; Millar, J.A. and Norton, J.J.: The relation of arterial pressure and plasma angiotensin II concentration. Circulation Research 44: 452–458 (1979).PubMedCrossRefGoogle Scholar
  4. Beller, G.A.; Smith, T.W.; Abelman, W.H.; Haber, E. and Hood, W.B., Jr: Digitalis intoxication. A prospective clinical study with serum level correlations. New England Journal of Medicine 284: 989–997 (1971).PubMedCrossRefGoogle Scholar
  5. Bellville, J.R.; Cohen, E.N. and Hamilton, J.: The interaction of morphine and d-tubocurarine on respiration and grip strength in man. Clinical Pharmacology and Therapeutics 5: 35 (1964).PubMedGoogle Scholar
  6. Benet, L.Z.: General treatment of linear mammillary models with elimination from any compartment as used in pharmacokinetics. Journal of Pharmaceutical Sciences 61: 536–541 (1972).PubMedCrossRefGoogle Scholar
  7. Boudoulas, H.; Lewis, R.P.; Kates, R.E. and Dalamangas, G.: Hypersensitivity to adrenergic stimulation after propranolol withdrawal in normal subjects. Annals of Internal Medicine 87: 433–436 (1977).PubMedGoogle Scholar
  8. Box, G.E.P. and Lucas, H.L.: Design of experiments in non-linear situations. Biometrika 46: 77–90 (1959).Google Scholar
  9. Breckenridge, A.; Orme, M.; Wesseling, H.; Lewis, J.R. and Gibbons, R.: Pharmacokinetics and pharmacodynamics of the enantiomers of warfarin in man. Clinical Pharmacology and Therapeutics 15: 424–430 (1974).PubMedGoogle Scholar
  10. Burland, W.L.; Duncan, W.A.M.; Hesselbo, T.; Mills, J.G. and Sharpe, P.C.: Pharmacological evaluation of cimetidine, a new histamine H2-receptor antagonist in healthy man. British Journal of Clinical Pharmacology 2: 481–486 (1975).PubMedCrossRefGoogle Scholar
  11. Collste, P.; Haglund, K. and von Bahr, C.: Plasma levels and effects of metoprolol after single and multiple oral doses. Clinical Pharmacology and Therapeutics 27: 441–449 (1980).PubMedCrossRefGoogle Scholar
  12. Di Stefano, J.J.: Optimized blood sampling protocols and sequential design of kinetic experiments. American Journal of Physiology 240: R259–R265 (1981).Google Scholar
  13. Eichelbaum, M.; Birkel, P.; Grube, E.; Gutgemann, U. and Somogyi, A.: Effects of verapamil on P-R intervals in relation to verapamil plasma levels following single i.v. and oral administration and during chronic treatment. Klinische Wochenschrift 58: 919–925 (1980).PubMedCrossRefGoogle Scholar
  14. Elson, J.; Strong, J.M.; Lee, W.K. and Atkinson, A.J.: Antiarrhythmic potency of N-acetylprocainamide. Clinical Pharmacology and Therapeutics 17: 134–140 (1975).PubMedGoogle Scholar
  15. Esler, M.; Zweifer, A.; Randall, O. and DeQuattro, V.: Pathophysiologic and pharmacokinetic determinants of the antihypertensive response to propanolol. Clinical Pharmacology and Therapeutics 22: 299–308 (1977).PubMedGoogle Scholar
  16. Forrester, W.; Lewis, R.P.; Weissler, A.M. and Wilke, T.A.: The onset and magnitude of the contractile response to commonly used digitalis glycosides in normal subjects. Circulation 49: 517–521 (1974).CrossRefGoogle Scholar
  17. Galeazzi, R.L.; Benet, L.Z. and Sheiner, L.B.: Relationship between the pharmacokinetics and pharmacodynamics of procainamide. Clinical Pharmacology and Therapeutics 20: 278–289 (1976).PubMedGoogle Scholar
  18. Gero, A.: Intimate study of drug action III: Mechanisms of molecular drug action; in DiPalma (Ed) Drill’s Pharmacology in Medicine, pp.67–98 (McGraw-Hill, New York 1971).Google Scholar
  19. Gibaldi, M. and Perrier, D.: Pharmacokinetics (Marcel Dekker, New York 1975).Google Scholar
  20. Guentert, T.W.; Holford, N.H.G.; Coates, P.C.; Upton, R.A. and Riegelman, S.: Quinidine pharmacokinetics in man: Choice of a disposition model and absolute bioavailability studies. Journal of Pharmacokinetics and Biopharmaceutics 7: 315–330 (1979).PubMedGoogle Scholar
  21. Hager, W.D.; Fenster, P.; Mayersohn, M.; Perrier, D.; Graves, P.; Marcus, F.I. and Goldman, S.: Digoxin-quinidine interaction. New England Journal of Medicine 302: 1238–1241 (1979).CrossRefGoogle Scholar
  22. Hannemann, R.E.; Randall, J.E.; Stoltman, W.P.; Bronsen, E.C.; Williams, E.J.; Long, R.A.; Hull, J.H. and Starbuck, R.R.: Digital plethysmography for assessing erythrityl tetranitrate bioavailability. Clinical Pharmacology and Therapeutics 29: 35–39 (1981).PubMedCrossRefGoogle Scholar
  23. Hill, A.V.: The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. Journal of Physiology 40: iv–vii (1910).Google Scholar
  24. Holford, N.H.G.; Coates, P.E.; Guentert, T.W.; Riegelman, S. and Sheiner, L.B.: The effect of quinidine and its metabolites on the electrocardiogram and systolic time intervals: Concentration-effect relationships. British Journal of Clinical Pharmacology 11: 187–195 (1981).PubMedCrossRefGoogle Scholar
  25. Holford, N.H.G. and Sheiner, L.B.: Pharmacokinetic and pharmacodynamic modelling in vivo. Critical Revues in Bioengineering. In press (1981a).Google Scholar
  26. Holford, N.H.G. and Sheiner, L.B.: Kinetics of pharmacologic response. Pharmacology and Therapeutics. In press (1981b).Google Scholar
  27. Hull, C.J.; van Beem, H.B.H.; McLeod, K.; Sibbals, A. and Watson, M.J.: A pharmacodynamic model for pancuronium. British Journal of Anaesthesia 50: 1113–1123 (1978).PubMedCrossRefGoogle Scholar
  28. Hunder, G.G.; Sheps, S.G.; Allen, G.L. and Joyce, J.W.: Daily and alternate-day corticosteroid regimens in treatment of giant cell arteritis. Annals of Internal Medicine 82: 613–618 (1975).PubMedGoogle Scholar
  29. Kaojarern, S.; Feldman, M.; Richardson, C.T. and Brater, D.C.: Tiotidine and cimetidine — kinetics and dynamics. Clinical Pharmacology and Therapeutics 29: 198–202 (1981).PubMedCrossRefGoogle Scholar
  30. Kelman, A.W. and Whiting, B.: Modelling of drug response in individual subjects. Journal of Pharmacokinetics and Biopharmaceutics 8: 115–130 (1980).PubMedGoogle Scholar
  31. Kramer, W.G.; Kolibash, A.J.; Lewis, R.P.; Bathala, M.S.; Visconti, J.A. and Reuning, R.H.: Pharmacokinetics of digoxin: Relationship between intensity and predicted compartmental drug levels in man. Journal of Pharmacokinetics and Biopharmaceutics 7: 47–61 (1979).PubMedGoogle Scholar
  32. Lertora, J.J.L.; Atkinson, A.J.; Kushner, W.; Nevin, M.J.; Lee, W.K.; Jones, C. and Schmid, F.R.: Long term antiarrhythmic therapy with N-acetylprocainamide. Clinical Pharmacology and Therapeutics 25: 273–282 (1979).PubMedGoogle Scholar
  33. Levy, G.: Relationship between rate of elimination of tubocurarine and rate of decline of its pharmacological activity. British Journal of Anaesthesia 36: 694–695 (1964).PubMedCrossRefGoogle Scholar
  34. Lewis, R.J.; Trager, W.F.; Chan, K.K.; Breckenridge, A.; Orme, M.; Roland, M. and Schary, W.: Warfarin-stereochemical aspects of its metabolism and the interaction with phenylbutazone. Journal of Clinical Investigation 53: 1607–1617 (1974).PubMedCrossRefGoogle Scholar
  35. Mayersohn, M. and Perrier, D.: Kinetics of pharmacologic response to cocaine. Research Communications in Chemical Pathology and Pharmacology 22: 465–474 (1978).PubMedGoogle Scholar
  36. Meffin, P.J.; Winkle, R.A.; Blaschke, T.F.; Fitzgerald, J. and Harrison, D.C.: Response optimization of drug dosage: Antiarrhythmic studies with tocainide. Clinical Pharmacology and Therapeutics 22: 42–57 (1977).PubMedGoogle Scholar
  37. Mitenko, P.A. and Ogilvie, R.I.: Rational intravenous doses of theophylline. New England Journal of Medicine 289: 600–603 (1973).PubMedCrossRefGoogle Scholar
  38. Murphy, J.; Casey, W. and Lasagna, L.: The effect of dosage regimes on the diuretic efficacy of chlorothiazide in human subjects. Journal of Pharmacology and Experimental Therapeutics 134: 286–290 (1961).PubMedGoogle Scholar
  39. Nagashima, R.; O’Reilly, R.A. and Levy, G.: Kinetics of pharmacologie effects in man: The anticoagulant action of warfarin. Clinical Pharmacology and Therapeutics 10: 22–35 (1969).PubMedGoogle Scholar
  40. O’Reilly, R.A.: Studies on the optical enantiomorphs of warfarin in man. Clinical Pharmacology and Therapeutics 16: 348–354 (1974).PubMedGoogle Scholar
  41. O’Reilly, R.A.; Trager, W.F.; Motley, C.H. and Howald, W.: Stereoselective interaction of phenylbutazone with [12C/13C] warfarin pseudoracemates in man. Journal of Clinical Investigation 65: 746–753 (1980).PubMedCrossRefGoogle Scholar
  42. Powell, R.; Fenster, P.; Wandell, M.; Hager, D.; Graves, P.; Conrad, K. and Goldman, S.: Quinidine-digoxin interaction: Multiple-dose pharmacokinetics. Clinical Pharmacology and Therapeutics 27: 279 (1980).Google Scholar
  43. Powers, W.F.; Abbrecht, P.J. and Covell, D.G.: Systems and microcomputer approach to anticoagulant therapy. IEEE Transactions on Bio-Medical Engineering. BME-27: 520–523 (1980).CrossRefGoogle Scholar
  44. Reidenberg, M.; Odar-Cederlof, I.; Bahr, von C.; Borga, O. and Sjoqvist, F.: Protein binding of diphenylhydantoin and dismethylimipramine in plasma from patients with poor renal function. New England Journal of Medicine 285: 264–267 (1971).PubMedCrossRefGoogle Scholar
  45. Reiner, N.E.; Bioxham, D.D. and Thompson, W.L.: Nephrotoxicity of gentamicin and tobramycin given once daily or continuously in dogs. Journal of Antimicrobial Chemotherapy 4: 85–101 (1978).PubMedCrossRefGoogle Scholar
  46. Routledge, P.A.; Chapman, P.H.; Davies, D.M. and Rawlins, M.D.: Pharmacokinetics and pharmacodynamics of warfarin at steady state. British Journal of Clinical Pharmacology 8: 243–247 (1979).PubMedCrossRefGoogle Scholar
  47. St John, R.C. and Draper, N.R.: D-optimality for regression designs — a review. Technometrics 17: 15–23 (1975).CrossRefGoogle Scholar
  48. Schroeder, P.; Klitgaard, N.A. and Simensen, E.: Significance of the acetylation phenotype and the therapeutic effect of procainamide. European Journal of Clinical Pharmacology 15: 63–68 (1979).CrossRefGoogle Scholar
  49. Shapiro, W.; Narhara, K. and Taubert, K.: Relationship of sma digoxin and digoxin to cardiac response following intravenous digitization in man. Circulation 42: 1065–1072 (1970).PubMedCrossRefGoogle Scholar
  50. Sheiner, L.B.: Computer-aided long-term anticoagulation therapy. Computers and Biomedical Research 2: 307–318 (1969).CrossRefGoogle Scholar
  51. Sheiner, L.B.; Stanski, D.R.; Vozeh, S.; Miller, R.D. and Ham, J.: Simultaneous modelling of pharmacokinetics and pharmacodynamics: Application to d-tubocurarine. Clinical Pharmacology and Therapeutics 25: 358–371 (1979).PubMedGoogle Scholar
  52. Shepherd, A.M.M.; Wilson, M. and Stevenson, I.H.: Warfarin sensitivity in the elderly; in Crooks and Stevenson (Eds) Drugs and the Elderly, pp.199–209 (University Park Press, Baltimore 1979).Google Scholar
  53. Singh, B.N.; Williams, F.M.; Whitlock, R.M.; Collett, J. and Chew, C.: Plasma timolol levels and systolic time intervals. Clinical Pharmacology and Therapeutics 27: 159–166 (1980).Google Scholar
  54. Snyder, S.H.: Receptors, neurotransmitters and drug responses. New England Journal of Medicine 300: 465–472 (1979).PubMedCrossRefGoogle Scholar
  55. Somogyi, A.; Rohner, H.G. and Gugler, R.: Pharmacokinetics and bioavailability of cimetidine in gastric and duodenal ulcer patients. Clinical Pharmacokinetics 5: 84–94 (1980).PubMedCrossRefGoogle Scholar
  56. Steiness, E.; Waldorff, S.; Hansen, P.B.; Kjaergård, H.; Buch, J. and Egeblad, H.: Reduction of digoxin-induced inotropism during quinidine administration. Clinical Pharmacology and Therapeutics 27: 791–795 (1980).PubMedCrossRefGoogle Scholar
  57. Van Dyke, C.; Jatlow, P.; Ungerer, J.; Barash, P.G. and Byck, R.: Oral cocaine; plasma concentration and central effects. Science 200: 211–213 (1978).PubMedCrossRefGoogle Scholar
  58. Vaughan, D.P. and Trainor, A.: Derivation of general equations for linear mammillary models when the drug is administered by different routes. Journal of Pharmacokinetics and Biopharmaceutics 3: 203–218 (1975).PubMedGoogle Scholar
  59. Veng Pedersen, P.: Model-independent method of analyzing input in linear pharmacokinetic systems having polyexponential impulse response. I: Theoretical analysis. Journal of Pharmaceutical Sciences 69: 298–305 (1980).CrossRefGoogle Scholar
  60. Wagner, J.G.; Agahajanian, G.K. and Bing, O.H.: Correlation of performance test scores with ‘tissue concentration’ of lysergic acid diethylamide in human subjects. Clinical Pharmacology and Therapeutics 9: 635–638 (1968).PubMedGoogle Scholar
  61. Wagner, J.G.: Kinetics of pharmacologie response. I: Proposed relationships between response and drug concentration in the intact animal and man. Journal of Theoretical Biology 20: 171–201 (1968).CrossRefGoogle Scholar
  62. Wagner, J.G.: Fundamentals of Clinical Pharmacokinetics (Drug Intelligence, Hamilton 1975).Google Scholar
  63. Whelton, A.; Carter, G.G.; Craig, T.J.; Bryant, H.H.; Herbst, D.V. and Walker, W.G.: Comparison of the intrarenal disposition of tobramycin and gentamicin: Therapeutic and toxicologic answers. Journal of Antimicrobial Chemotherapy 4: 13–22 (1978).PubMedCrossRefGoogle Scholar
  64. Whitfield, L.R. and Levy, G.: Relationship between concentration and anticoagulant effect of heparin in plasma of normal subjects: Magnitude and predictability of interindividual differences. Clinical Pharmacology and Therapeutics 28: 509–516 (1980).PubMedCrossRefGoogle Scholar
  65. Whiting, B.; Holford, N.H.G. and Sheiner, L.B.: Quantitative analysis of the disopyramide concentration-response relationship. British Journal of Clinical Pharmacology 9: 67–75 (1980).PubMedCrossRefGoogle Scholar
  66. Whitlon, D.S.; Sadowski, J.A. and Suttie, J.W.: Mechanism of coumarin action: Significance of vitamin K epoxide reductase inhibition. Biochemistry 17: 1371–1377 (1978).PubMedCrossRefGoogle Scholar
  67. Winkle, R.A.; Meffïn, P.J.; Fitzgerald, J.W. and Harrison, D.C.: Clinical efficacy and pharmacokinetics of a new orally effective antiarrhythmic tocainide. Circulation 54: 884–889 (1976).CrossRefGoogle Scholar
  68. Yacobi, A.; Chii-Ming, L. and Levy, G.: Comparative pharmacokinetics of coumarin anticoagulants. LXV: Pharmacokinetic and pharmacodynamic studies of acute interaction between warfarin and phenylbutazone in rats. Journal of Pharmaceutical Sciences 69: 14–20 (1980).PubMedCrossRefGoogle Scholar

Copyright information

© ADIS Press Australasia Pty Ltd. 1981

Authors and Affiliations

  • Nicholas H. G. Holford
    • 1
    • 2
  • Lewis B. Sheiner
    • 1
    • 2
  1. 1.Division of Clinical Pharmacology, Departments of Medicine and PharmacySchools of Medicine and PharmacyUSA
  2. 2.Department of Laboratory Medicine, School of MedicineUniversity of CaliforniaSan FranciscoUSA
  3. 3.Division of Clinical Pharmacology, 926 ScienceUniversity of California Medical CenterSan FranciscoUSA

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