Advertisement

Environmental and Ecological Statistics

, Volume 1, Issue 4, pp 303–314 | Cite as

Statistical analysis of bioassays, based on hazard modelling

  • J. J. M. Bedaux
  • S. A. L. M. Kooijman
Article

Abstract

A stochastic model is proposed to describe time-dependent lethal effects of toxic compounds. It is based on simple mechanistic assumptions and provides a measure for the toxicity of a chemical compound, the so-called killing rate. The killing rate seems a promising alternative for the LC50. The model also provides the no-effect level and the LC50, both as a function of exposure time. The model is applied to real data and to simulated data.

Keywords

killing rate LC50 maximum likelihood no-effect level one-compartment model quantal assay data time dependent toxicity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bedaux, J.J.M. and Kooijman, S.A.L.M. (1994) Stochasticity in deterministic models. In Handbook of Statistics, volume 12: Environmental Statistics, G.P. Patil and C.R. Rao, eds., North Holland, pp. 561-81.Google Scholar
  2. Carter, E.M. and Hubert, J.J. (1984) A growth-curve model approach to multivariate quantal bioassay. Biometrics 40, 699–706.Google Scholar
  3. Cox, C. (1987) Threshold dose-response models in toxicology. Biometrics 43, 511–23.Google Scholar
  4. Diggle, P.J. and Gratton, R.J. (1984) Monte Carlo methods of inference for implicit statistical models. Journal of the Royal Statistical Society B 46, 193–227.Google Scholar
  5. Hoekstra J.A. (1991). Estimation of the LC50, A Review. Environmetrics 2, 139–52.Google Scholar
  6. Jacquez, J.A. (1985). Compartmental Analysis in Biology and Medicine. Elsevier Amsterdam.Google Scholar
  7. Janssen, M.P.M., Bruins, A., De Vries, T.H. and Van Straalen, N.M. (1991) Comparison of cadmium kinetics in four soil arthropods species. Archives of Environmental Contamination and Toxicology 20, 305–12.Google Scholar
  8. Kooijman, S.A.L.M. (1981) Parametric analyses of mortality rates in bioassays. Water Research 15, 107–19.Google Scholar
  9. Kooijman, S.A.L.M. (1993) Dynamic Energy Budgets in Biological Systems. Theory and Applications in Ecotoxicology. Cambridge University Press.Google Scholar
  10. McCullagh, P. and Nelder, J.A. (1989) Generalized Linear Models. Chapman and Hall, London.Google Scholar
  11. Laurence, A.F. and Morgan, B.J.T. (1989) Observations on a stochastic model for quantal assay data. Biometrics 45, 733–44.Google Scholar
  12. Morgan, B.J.T. (1988) Extended models for quantal response data. Statistica Neerlandica 42, 253–72.Google Scholar
  13. Morgan, B.J.T. (1992). Analysis of Quantal Response Data. Chapman and Hall, London.Google Scholar
  14. Puri, P.S. and Senturia, J. (1972) On a mathematical theory of quantal response data. Proceedings of the 6th Berkeley Symposium on Mathematical Statistics, 4, 231–47.Google Scholar
  15. Van Ryzin, J. and Rai, K. (1987) A dose-response model incorporating nonlinear kinetics. Biometrics 43, 95–105.Google Scholar

Copyright information

© Chapman & Hall 1994

Authors and Affiliations

  • J. J. M. Bedaux
    • 1
  • S. A. L. M. Kooijman
    • 1
  1. 1.Department of Theoretical BiologyVrije Universiteit AmsterdamHV AmsterdamThe Netherlands

Personalised recommendations