Estimation of Relative Potency with the Parallel-Line Model

  • Received : 2012.04.16
  • Accepted : 2012.06.25
  • Published : 2012.08.31


Biological methods are described for the assay of certain substances and preparations whose potency cannot be adequately assured by chemical or physical analysis. The principle applied through these assays is of a comparison with a standard preparation to determine how much of the examined substance produces the same biological effects as a given quantity (the Unit) of the standard preparation. In these dilution assays, to estimate the relative potencies of the unknown preparations to the standard preparations, it is necessary to compare dose-response relationships of standard and unknown preparations. The dose-response relationship in the dilution assay is non-linear and sigmoid when a wide range of doses is applied. The parallel line model (applied to the dose region with the steepest slope) is used to estimate the relative potency. In this paper, the statistical theory in the parallel line model is explained with an application to a dilution assay data. The parallel line method is implemented in a SAS program and is available at the author's homepage(


Relative potency;dilution assay;parallel line model;SAS program


  1. Korea Food and Drug Administration (2009). 2009 Korean National Biological Reference Standards Annual Report, Osong.
  2. Lee, T. (2011). 2011 Stability Analysis of Potency for Korean National Biological Reference Materials, Osong.
  3. European Directorate for the Quality of Medicines (2007). European Pharmacopoeia, 6th Edition, Strasbourg.
  4. Fieller, E. C. (1944). A fundamental formula in statistics of biological assay, and some applications, Quarterly Journal of Pharmacy and Pharmacology, 17, 117-123.
  5. Finney, D. J. (1978). Statistical Methods in Biological Assays. 3rd Edition, Charles Griffin, London.
  6. Volund, A. (1978). Application of the four-parameter logistic model to bioassay: Comparison with sloperatio and parallel-line models, Biometrics, 34, 357-365.


Supported by : National Research Foundation of Korea (NRF)