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Nonlinear Modeling of Dose-Response Data

  • Roel Straetemans
Chapter
Part of the Use R! book series (USE R)

Abstract

In contrast with Chaps. 2 and 3 in which we discussed the LRT for an order-restricted ANOVA model, Chap. 3 is focused on parametric dose-response modeling of a continuous response variable. The main model of interest will be the four-parameter logistic (4PL) model. Interpretation of the model parameters as well as practical implementation using the R function gnls() is given in Sect.4.2. In Sect. 4.3, we discuss several alternatives for the 4PL model such as the 3PL and 5PL models, the Emax model and growth models such as the Gompertz function and Richards function.

Keywords

Gompertz Model Emax Model Gompertz Function Gompertz Curve Continuous Response Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. Petrov, & B. Csaki (Eds.), Second international symposium on information theory (pp. 267–281). Budapest: Academiai Kiado.Google Scholar
  2. Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London, 115, 513–585.Google Scholar
  3. Gottschalk, P. G., & Dunn, J. R. (2005). The five-parameter logistic: A characterization and comparison with the four-parameter logistic. Analytical Biochemistry, 343, 54–65.Google Scholar
  4. Lindsey, J. (2001). Nonlinear Models in Medical Statistics. Oxford, Oxford University Press.Google Scholar
  5. Narinc, D., Karaman, E., Firat, M. Z. F., & Aksoy, T. (2010). Comparison of non-linear growth models to describe the growth in Japanese Quail. Journal of Animal and Veterinary Advances, 9(14), 1961–1966.Google Scholar
  6. Pinheiro, J. C., & Bates, D. M. (2000). Mixed-effects models in S and S-Plus. New York: Springer.Google Scholar
  7. Plikaytis, B. D., Turner, S. H., Gheesling, L. L., & Carlone, G. M. (1991). Comparisons of standard curve-fitting methods to quantitate Neisseria meningitides group a polysaccharide antibody levels by enzyme-linked immunosorbent assay. Journal of Clinical Microbiology, 29(7), 1439–1446.Google Scholar
  8. Richards, F. J. A. (1959). Flexible growth function for empirical use. Journal of Experimental Botany, 10(29), 290–300.Google Scholar
  9. Straetemans, R., & Bijnens, L. (2010). Application of the separate ray model to investigate interaction effects. Frontiers in Bioscience, E2, 266–278.Google Scholar
  10. Tanila, H., Kauppila, T., & Tana, T. (1993). Inhibition of intestinal motility and reversal of postlaparotomy ileus by selective 2-adrenergic drugs in the rat. Gastroenterology, 104, 819–824.Google Scholar
  11. Ting, N. (Ed.). (2006). Dose finding in drug development. New York: Springer.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Ablynx NVZwijnaardeBelgium

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