Pharmacodynamic models: Parameterizing the hill equation, michaelis-menten, the logistic curve, and relationships among these models

Journal of Biopharmaceutical Statistics

Volumn 23, Issue 3, 2013, Pages 648-661

  Reeve, Russell ^a   Turner, J Rick ^a  

^a IQVIA   (United States)

Author keywords

Curvature; Hill model; Logistic model; Michaelis Menten model; Multicollinearity; Nonlinear regression; Optimal parameterization

Indexed keywords

PLACEBO;

ALGORITHM; ARTICLE; HILL EQUATION; LOGISTIC CURVE; MATHEMATICAL MODEL; MICHAELIS MENTEN; PHARMACODYNAMICS; PRIORITY JOURNAL; STATISTICAL CONCEPTS; STATISTICAL MODEL;

ALGORITHMS; ANIMALS; AREA UNDER CURVE; DATA INTERPRETATION, STATISTICAL; DOSE-RESPONSE RELATIONSHIP, DRUG; ENZYME INDUCTION; HEPATOMEGALY; HYPOLIPIDEMIC AGENTS; LINEAR MODELS; LIPOPROTEINS, LDL; LOGISTIC MODELS; MODELS, STATISTICAL; NONLINEAR DYNAMICS; PHARMACOKINETICS; RATS; SILOXANES;

EID: 84877121034     PISSN: 10543406     EISSN: 15205711     Source Type: Journal    
DOI: 10.1080/10543406.2012.756496     Document Type: Article

References (29)

1. Aiken, L. S., West, S. G. (1991). Multiple Regression: Testing and Interpreting Interactions. Newbury Park, CA: Sage.
2. Derendorf, H., Meibohm, B. (1999). Modeling of pharmacokinetic/ pharmacodynamic (PK/PD) relationships: Concepts and perspectives. Pharmaceutical Research 16:176-185.
3. Dowd, J., Riggs, D. (1965). A comparison of estimates of Michaelis-Menten kinetic constants under various linear transformations. Journal of Biological Chemistry 240:863-869.
4. Draper, N., Smith, H. Jr, (1981). Applied Regression Analysis. 2nd ed. New York, NY: John Wiley & Sons.
5. El-Kareh, A., Secomb, T. (2005). Two-mechanism peak concentration model for cellular pharmacodynamics of doxorubicin. Neoplasia 7:705-713.
6. Farenc, C., Lefrant, J-Y., Audran, M., Bressolle, F. (2001). Pharmacokineticpharmacodynamic modeling of atracurium in intensive care patients. Journal of Clinical Pharmacology 41:44-50.
7. Food and Drug Administration. (2006). Critical path opportunities list, topic 3. http://www. fda.gov/downloads/ScienceResearch/SpecialTopics/ CriticalPathInitiative/CriticalPath OpportunitiesReports/UCM077258.pdf, accessed April 22, 2010.
8. Gabrielsson, J., Weiner, D. (2000). Pharmacokinetic and Pharmacodynamic Data Analysis. 3rd ed. Stockholm, Sweden: Swedish Pharmaceutical Press.
9. Goutelle, S., Maurin, M., Rougier, F., Barbaut, X., Bourguignon, L., Ducher, M., Maire, P. (2008). The Hill equation: A review of its capabilities in pharmacological modeling. Fundamental & Clinical Pharmacology 22:633-648.
10. Henri, V. (1903). Lois Générales de l'Action des Diastases. Paris, France: Hermann.
11. Hill, A. V. (1910). The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. Journal of Physiology 40:iv- vii.
12. Houston, J. B., Kenworthy, K. (2000). In vivo-in vitro scaling for CYP kinetic data not consistent with the classical Michaelis-Menten model. Drug Metabolism and Disposition 28:246-254.
13. Liao, C-M., Chen, B-C., Lin, M-C., Chiu, H-M., Chou, Y-H. (2002). Coupling toxokinetics and pharmacodynamics for predicting survival of abalone (Haliotis diversicolor supertexta) exposed to waterborne zinc. Environmental Toxicology and Water Quality 17:478-486.
14. MacDougal, J. (2006). Analysis of dose-response studies - Emax model. In: Ting, N., ed., Dose Finding in Drug Development. New York, NY: Springer, pp. 127-145.
15. Marquardt, D. W. (1980). You should standardize the predictor variables in your regression models. Journal of the American Statistical Association 75:87-91.
16. McKay, I., Voss, L., Sleigh, J., Barnard, J., Johannsen, E. (2006). Pharmacokineticpharmacodynamic modeling the hypnotic effect of sevoflurane using the spectral entropy of the electroencelphalogram. Anesthesia & Analgesia 102:91-97.
17. Meyers, R. (1990). Classical and Modern Regression with Applications. Belmont, CA: Duxbury Press.
18. Michaelis, L., Menten, M. L. (1913). The kinetics of invertase activity. [Die Kinetik der Invertinwerkung]. Biochemische Zeitschrift 49:333.
19. Moosbrugger, H., Schermelleh-Engel, K., Kelava, A., Klein, A. G. (2009). Testing multiple nonlinear effects in structural equation modeling: A comparison of alternative estimation approaches. In: Teo, T., Khine, M. S., eds., Structural Equation Modelling in Educational Research: Concepts and Applications, Rotterdam, NL: Sense Publishers, pp. 103-136.
20. Mouton, J. W., Dudley, M. N., Cars, O., Derendorf, H., Drusano, G. L. (2005). Standardization of pharmacokinetic/pharmacodynamic (PK/PD) terminology for anti-infective drugs: An update. Journal of Antimicrobial Chemotherapy, advance access, published March 16.
21. Mouton, J. W., Vinks, A. A. (2005). Pharmacokinetic/pharmacodynamic modelling of antibacterials in vitro and in vivo using bacterial growth and kill kinetics: The minimum inhibitory concentration versus stationary concentration. Clinical Pharmacokinetics 44:201.
22. Raaijmakers, J. (1987). Statistical analysis of Michaelis-Menten equation. Biometrics 43: 793-803.
23. Riviere, J. (1999). Comparative Pharmacokinetics. Ames: Iowa State Press.
24. Sarangapani, R., Teeguarden, J., Plotzke, K. P., McKim, J. M. Jr., Anderson, M. E. (2002 Dose-response modeling of cytochrome P450 induction in rats by octamethylcyclotetrasiloxane. Toxicological Sciences 67:159-172.
25. Seber, G. A. F., Wild, C. J. (1989). Nonlinear Regression. New York, NY: John Wiley & Sons.
26. Shoemaker, R., van Gerven, J. M. A., Adam, F., Cohen, A. F. (1998). Estimating potency for the Emax-model without attaining maximum effects. Journal of Pharmacokinetics and Biopharmaceutics 26:581-593.
27. Thomas, J., Forrest, A., Bhavnani, S., Hyatt, J., Cheng, A., Ballow, C., Schentag, J. (1998). Pharmacodynamic evaluation of factors associated with the development of bacterial resistance in acutely ill patients during therapy. Antimicrobial Agents and Chemotherapy 42:521-527.
28. Trombeta, A. (2009). Henri-Michaelis-Menten equation. http://www.whonamedit.com/synd. cfm/3464.html, viewed October 16, 2009.
29. Volund, A. (1978). Application of the four-parameter logistic model to bioassay: Comparison with slope ratio and parallel line models. Biometrics 34:357-365.