Skip to main content
SpringerLink
Log in

Competitive Antagonism in Pharmacology: A Proposed Single Step Evaluation

  • Published:
Drug information journal : DIJ / Drug Information Association Aims and scope Submit manuscript

Abstract

The inhibitory capacity of a competitive antagonist is measured using the pA2 (the negative logarithm of the antagonist dissociation constant). The conventional two-step procedure, based on Schild’s regression, neglects a portion of the errors. New single step methods are proposed based on nonlinear regression on dose-effect. Whereas verification of the competition hypothesis often interferes with pA2 estimation, the development of improved nonlinear models could explain and partially incorporate the reasons for noncompetition. The improvements are of two kinds: 1. Pharmacological, based on the inclusion of suspected pharmacological mechanisms such as spare receptors or transduction into a nonlinear fixed-effects model (with examples from the literature); and 2. Experimental, incorporating biovariability as a random effect into a mixed-effects model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Schild HO. pA, a new scale for the measurement of drug antagonism. Br J Pharmacol. 1947;2:189–206.

    CAS  Google Scholar 

  2. MacKay D. How should values of pA2 and affinity constants for pharmacological competitive antagonists be estimated? J Pharm Pharmacol. 1978;30:312–313.

    Article  CAS  Google Scholar 

  3. Jenkinson DH, Barnard EA, Hoyer D, Humphrey PPA, Leff P, Shankley NP. International Union of Pharmacology Committee on Receptor Nomenclature and Drug Classification. IX. Recommendations on terms and symbols in quantitative pharmacology. Pharmacol Rev. 1995;47(2):255–266.

    CAS  PubMed  Google Scholar 

  4. Tallarida JR, Cowan A, Adler MW. pA2 and receptor differenciation: a statistical analysis of competitive antagonism. Life Sci. 1979;25:637–654.

    Article  CAS  Google Scholar 

  5. Carter EM, Hubert JJ. A growth-curve model approach to multivariate quantal bioassay. Biometrics. 1984;40:699–706.

    Article  Google Scholar 

  6. Ariëns EJ. ed. Molecular Pharmacology: The Mode of Action of Biologically Active Compounds. Vol 1. New York and London: Academic Press; 1964.

    Google Scholar 

  7. Waud DR, Parker RB. Pharmacological estimation of drug-receptor dissociation constants. Statistical evaluation. II. Competitive antagonists. J Pharmacol Exp Ther. 1971;177(1):13–24.

    CAS  PubMed  Google Scholar 

  8. Stephenson RP. A modification of receptor theory. Br J Pharmacol. 1956;178:379–393.

    Google Scholar 

  9. Black JW, Leff P. Operational models of pharmacological agonism. Proc R Soc Lond. 1983; B220:141–162.

    Google Scholar 

  10. Grizzle JE, Allen DM. Analysis of growth and dose response curves. Biometrics. 1969;25:357–381.

    Article  CAS  Google Scholar 

  11. Volund A. Multivariate bioassay. Biometrics. 1980;36:225–236.

    Article  CAS  Google Scholar 

  12. Laird NM, Ware JH. Random-effects models for longitudinal data. Biometrics. 1982;38:963–974.

    Article  CAS  Google Scholar 

  13. Jennrich RI, Schluchter MD. Unbalanced repeated-measures models with structured covariance matrices. Biometrics. 1986;42:805–820.

    Article  CAS  Google Scholar 

  14. Vonesh EF, Carter RL. Efficient inference for random-coefficient growth curve models with unbalanced data. Biometrics. 1987;43:617–628.

    Article  CAS  Google Scholar 

  15. Elston RC, Grizzle JE. Estimation of time-response curves and their confidence bands. Biometrics. 1962;20:148–159.

    Article  Google Scholar 

  16. Lindstrom MJ, Bates DM. Nonlinear mixed effects models for repeated measures data. Biometrics. 1990;46:673–687.

    Article  CAS  Google Scholar 

  17. Sheiner LB, Beal SL. Evaluation of methods for estimating population pharmacokinetic parameters. J Pharmacokinet Biopharm. 1980;8:553–571.

    Article  CAS  Google Scholar 

  18. Vonesh EF, Carter RL. Mixed-effects nonlinear regression for unbalanced repeated mesures. Biometrics. 1992;48:1–17.

    Article  CAS  Google Scholar 

  19. Laird NM, Lange N, Stram D. Maximum likelihood computations with repeated measures: application to the E. algorithm. J Am Stat Assoc. 1987; 82:97–105.

    Article  Google Scholar 

  20. Lindstrom MJ, Bates DM. Newton-Raphson and E. algorithm for linear mixed-effects models for repeated measures data. J Am Stat Assoc. 1987;82:97–105.

    Article  Google Scholar 

  21. Davidian M, Giltninan DM. Some general estimation methods for nonlinear mixed-effects models. J Biopharm Stat. 1993;3:23–55.

    Article  CAS  Google Scholar 

  22. Schluchter MD. Analysis of incomplete multivariate data using linear models with structured covariance matrices. Stat Med. 1988;7:317–324.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Statistical Department, Servier Research Institute, 11 rue des Moulineaux, 92150, Suresnes, France

    Lisa Maïofiss & Corinne Thomas-Haimez

  2. Inserm U 169, Villejuif Cedex, France

    Jean Maccario

Authors
  1. Lisa Maïofiss
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Corinne Thomas-Haimez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jean Maccario
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Based on a presentation made at the DIA Workshop “Statistical Methodology in Non-clinical and Toxicological Studies,” March 25–27, 1996, Bruges, Belgium. The article presented was called “The pA2 in pharmacology: a need for a new way of estimation.”

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maïofiss, L., Thomas-Haimez, C. & Maccario, J. Competitive Antagonism in Pharmacology: A Proposed Single Step Evaluation. Ther Innov Regul Sci 31, 563–572 (1997). https://doi.org/10.1177/009286159703100224

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1177/009286159703100224

Key Words

Search

Navigation