Environmental and Ecological Statistics

, Volume 7, Issue 1, pp 57–76 | Cite as

Litter-based methods in developmental toxicity risk assessment

  • Lieven Declerck
  • Geert Molenberghs
  • Marc Aerts
  • Louise Ryan


Developmental toxicity experiments are designed to assess potential adverse effects of drugs and other exposures on developing fetuses from pregnant dams. Extrapolation to humans is a very difficult problem. An important issue here is whether risk assessment should be based on the fetus or the litter level. In this paper, fetus and litter-based risks that properly account for cluster size are defined and compared for the beta-binomial model and a conditional model for clustered binary data. It is shown how the hierarchical structure of non-viable implants and viable but malformed offspring can be incorporated. Risks based on a joint model for death/resorption and malformation are contrasted with risks based on an adverse event defined as either death/resorption or malformation. The estimation of safe exposure levels for all risk types is discussed and it is shown how estimation of the cluster size distribution affects variance estimation. The methods are applied to data collected under the National Toxicology Program and in large sample simulations.

beta-binomial clustered data likelihood estimation safe dose teratology 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aerts, M., Declerck, L., and Molenberghs, G. (1997) Likelihood misspecification and safe dose determination for clustered binary data. Environmetrics, 8, 613-27.Google Scholar
  2. Altham, P.M.E. (1978) Two generalizations of the binomial distribution. Applied Statistics, 27, 162-7.Google Scholar
  3. Bahadur, R.R. (1961) A representation of the joint distribution of responses to n dichotomous items. In Studies in Item Analysis and Prediction, H. Solomon (ed.), Stanford Mathematical Studies in the Social Sciences VI. Stanford, California: Stanford University Press.Google Scholar
  4. Catalano, P.J. and Ryan, L.M. (1992) Bivariate latent variable models for clustered discrete and continuous outcomes. Journal of the American Statistical Association, 87, 651-8.Google Scholar
  5. Catalano, P.J., Scharfstein, D.O., Ryan, L.M., Kimmel, C.A., and Kimmel, G.L. (1993) Statistical model for fetal death, fetal weight and malformation in developmental toxicity studies. Teratology, 47, 281-90.Google Scholar
  6. Chen, J.J., Kodell, R.L., Howe, R.B., and Gaylor, D.W. (1991) Analysis of trinomial responses from reproductive and developmental toxicity experiments. Biometrics, 47, 1049-58.Google Scholar
  7. Crump, K.S. (1984) A new method for determining allowable daily intakes. Fundamental and Applied Toxicology, 4, 854-71.Google Scholar
  8. Efron, B. (1986) Double exponential families and their use in generalized linear regression. Journal of the American Statistical Association, 81, 709-21.Google Scholar
  9. Gart, J.J., Krewski, D., Lee, P.N., Tarone, R.E., and Wahrendorf, J. (1986) Statistical Methods in Cancer Research, Volume III: The Design and Analysis of Long-Term Animal Experiments, International Agency for Research on Cancer, Lyon.Google Scholar
  10. George, E.O. and Bowman, D. (1995) A full likelihood procedure for analyzing exchangeable binary data. Biometrics, 51, 512-23.Google Scholar
  11. George, J.D., Price, C.J., Kimmel, C.A., and Marr, M.C. (1987) The developmental toxicity of triethylene glycol dimethyl ether in mice. Fundamental and Applied Toxicology, 9, 173-81.Google Scholar
  12. Kleinman, J.C. (1973) Proportions with extraneous variance: single and independent samples. Journal of the American Statistical Association, 68, 46-54.Google Scholar
  13. Krewski, D. and Zhu, Y. (1994) Applications of multinomial dose-response models in developmental toxicity risk assessment. Risk Analysis, 14, 613-28.Google Scholar
  14. Krewski, D. and Zhu, Y. (1995) A simple data transformation for estimating benchmark doses in developmental toxicity experiments. Risk Analysis, 15, 29-40.Google Scholar
  15. Lindström, P., Morrissey, R.E., George, J.D., Price, C.J., Marr, M.C., Kimmel, C.A., and Schwetz, B.A. (1990) The developmental toxicity of orally administered theophylline in rats and mice. Fundamental and Applied Toxicology, 14, 167-78.Google Scholar
  16. Lipsitz, S.R., Laird, N.M., and Harrington, D.P. (1991) Generalized estimating equations for correlated binary data: Using the odds ratio as a measure of association. Biometrika, 78, 153-60.Google Scholar
  17. Molenberghs, G. and Lesaffre, E. (1994) Marginal modeling of correlated ordinal data using a multivariate Plackett distribution. Journal of the American Statistical Association, 89, 633-44.Google Scholar
  18. Molenberghs, G. and Ryan, L.M. (1999) Likelihood inference for clustered multivariate binary data. Environmetrics, 10, 279-300.Google Scholar
  19. Pendergast, J.F., Gange, S.J., Newton, M.A., Lindstrom, M.J., Palta, M., and Fisher, M.R. (1996) A survey of methods for analyzing clustered binary response data. International Statistical Review, 64, 89-118.Google Scholar
  20. Price, C.J., Kimmel, C.A., George, J.D., and Marr, M.C. (1987) The developmental toxicity of diethylene glycol dimethyl ether in mice. Fundamental and Applied Toxicology, 8, 115-26.Google Scholar
  21. Price, C.J., Kimmel, C.A., Tyl, R.W., and Marr, M.C. (1985) The developmental toxicity of ethylene glycol in rats and mice. Toxicology and Applied Pharmacology, 81, 113-27.Google Scholar
  22. Rai, K. and Van Ryzin, J. (1985) A dose-response model for teratological experiments involving quantal responses. Biometrics, 47, 825-39.Google Scholar
  23. Rotnitzky, A. and Wypij, D. (1994) A note on the bias of estimators with missing data. Biometrics, 50, 1163-70.Google Scholar
  24. Ryan, L. (1992) Quantitative risk assessment for developmental toxicity. Biometrics, 48, 163-74.Google Scholar
  25. Santner, T.J. and Duffy, D.E. (1989) The Statistical Analysis of Discrete Data, Springer-Verlag, New York.Google Scholar
  26. Skellam, J.G. (1948) A probability distribution derived from the binomial distribution by regarding the probability of success as variable between the sets of trials. Journal of the Royal Statistical Society, Series B, 10, 257-61.Google Scholar
  27. Tyl, R.W., Price, C.J., Marr, M.C., and Kimmel, C.A. (1988) Developmental toxicity evaluation of dietary di(2-ethylhexyl)phthalate in Fischer 344 rats and CD-1 mice. Fundamental and Applied Toxicology, 10, 395-412.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Lieven Declerck
    • 1
  • Geert Molenberghs
    • 2
  • Marc Aerts
    • 2
  • Louise Ryan
    • 1
  1. 1.BiostatisticsHarvard School of Public Health and Dana-Farber Cancer InstituteBostonUSA
  2. 2.Biostatistics, Center for StatisticsLimburgs Universitair CentrumDiepenbeekBelgium

Personalised recommendations