Application of Akaike's information criterion (AIC) in the evaluation of linear pharmacokinetic equations

  • Kiyoshi Yamaoka
  • Terumichi Nakagawa
  • Toyozo Uno


According to linear pharmacokinetics, the time course of plasma concentration of a drug, Cp,is expressed by a sum of exponential functions, Cp i=1 n ai\(C_p = \sum\nolimits_{i = 1}^n {a_i e^{ - b_i t} } \).This article describes a statistical technique to estimate the number of exponential terms, n,for the time course of drug by the application of Akaike's information criterion (AIC). Plasma concentrations of ethoxybenzamide, sulfisoxazole, bishydroxycoumarin, and diazepam measured following bolus intravenous injection were used as clinical examples for this method. Selection of models is compared between the AIC method and an Ftest method at significance levels of 5% and 1%.

Key words

linear pharmacokinetic equations number of exponential terms amount of information in the time course Akaike's information criterion (AIC) F test ethoxybenzamide sulfisoxazole bishydroxycoumarin diazepam 


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  1. 1.
    H. G. Boxenbaum, S. Riegelman, and R. M. Elashoff. Statistical estimation in pharmacokinetics.J. Pharmacokin. Biopharm. 2:123–148 (1974).CrossRefGoogle Scholar
  2. 2.
    H. Akaike. Information theory and an extension of maximum likelihood principle. In B. N. Petrov and F. Csaki (eds),Second International Symposium on Information Theory, Akademiai Kiado, Budapest, 1973, pp. 267–281.Google Scholar
  3. 3.
    H. Akaike. A new look at the statistical model identification.IEEE Trans. Automat. Contr. 19:716–723 (1973).CrossRefGoogle Scholar
  4. 4.
    H. Akaike. An information criterion (AIC).Math. Sci. 14(153):5–9 (1976).Google Scholar
  5. 5.
    K. Tanabe. Treatment of errors in statistical data.BIT 7:1383–1395 (1975).Google Scholar
  6. 6.
    K. Tanabe. Statistical approach for the unsuitable problem.Math. Sci. 14(153):60–64 (1976).Google Scholar
  7. 7.
    S. A. Kaplan, R. E. Weinfeld, C. W. Abruzzo, and M. Lewis. Pharmacokinetic profile of sulfisoxazole following intravenous, intramuscular, and oral administration to man.J. Pharm. Sci. 61:773–778 (1972).PubMedCrossRefGoogle Scholar
  8. 8.
    R. Nagashima, G. Levy, and R. A. O'Reilly. Comparative pharmacokinetics of coumarin anticoagulant IV.J. Pharm. Sci. 57:1888–1895 (1968).PubMedCrossRefGoogle Scholar
  9. 9.
    H. Nogami, M. Hanano, S. Awazu, and H. H. Noon. Pharmacokinetic analysis on the disappearance of ethoxybenzamide from plasma. Statistical treatment of data of two compartment model by digital computer.Chem. Pharm. Bull. 17:2097–2104 (1969).PubMedCrossRefGoogle Scholar
  10. 10.
    S. A. Kaplan, M. L. Jack, K. Alexander, and R. E. Weinfeld. Pharmacokinetic profile of diazepam in man following single intravenous and oral and chronic oral administration.J. Pharm. Sci. 62: 1789–1796 (1969).CrossRefGoogle Scholar
  11. 11.
    J. G. Wagner. Linear pharmacokinetic model and vanishing exponential terms: Implication in pharmacokinetics.J. Pharmacokin. Biopharm. 4:395–425 (1976).CrossRefGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • Kiyoshi Yamaoka
    • 1
  • Terumichi Nakagawa
    • 1
  • Toyozo Uno
    • 1
  1. 1.Faculty of Pharmaceutical SciencesKyoto UniversityKyotoJapan

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