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Dose‐Response Models for Correlated Multinomial Data from Developmental Toxicity Studies

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  • Y. Zhu
  • D. Krewski
  • W. H. Ross

Abstract

Developmental anomalies induced by toxic chemicals may be identified by using laboratory experiments with rats and mice. This paper examines dose‐response models for correlated multinomial data arising in studies of developmental toxicity. A hierarchical probability structure is used to unify and extend previous methods of modelling correlated binary data arising in such studies. Generalized estimating equations in conjunction with an extended Dirichlet‐multinomial covariance function are used to estimate jointly the regression parameters in Weibull dose‐response models for both embryolethality and fetal malformations. Quadratic estimating equations are used to estimate the overdispersion (correlation) parameters. Maximum likelihood estimates based on a Dirichlet‐multinomial distribution are also computed for comparison. The modelling procedures proposed are illustrated through the analysis of data from a recent large scale study of the developmental toxicity of the herbicide 2,4,5‐trichlorophenoxyacetic acid.

Suggested Citation

  • Y. Zhu & D. Krewski & W. H. Ross, 1994. "Dose‐Response Models for Correlated Multinomial Data from Developmental Toxicity Studies," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(4), pages 583-598, December.
    • Handle: RePEc:bla:jorssc:v:43:y:1994:i:4:p:583-598
    DOI: 10.2307/2986259
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    Cited by:

    1. Daniel Krewski & Robert Smythe & Karen Y. Fung, 2002. "Optimal Designs for Estimating the Effective Dose in Developmental Toxicity Experiments," Risk Analysis, John Wiley & Sons, vol. 22(6), pages 1195-1205, December.
    2. Dette, Holger & Pepelyshev, Andrey & Wong, Weng Kee, 2008. "Optimal designs for dose finding experiments in toxicity studies," Technical Reports 2008,09, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Karen Y. Fung & Leonora Marro & Daniel Krewski, 1998. "A Comparison of Methods for Estimating the Benchmark Dose Based on Overdispersed Data from Developmental Toxicity Studies," Risk Analysis, John Wiley & Sons, vol. 18(3), pages 329-342, June.
    4. Andrew S. Allen & Huiman X. Barnhart, 2002. "Joint Models for Toxicology Studies with Dose‐Dependent Number of Implantations," Risk Analysis, John Wiley & Sons, vol. 22(6), pages 1165-1173, December.
    5. Molenberghs, Geert & Declerck, Lieven & Aerts, Marc, 1998. "Misspecifying the likelihood for clustered binary data," Computational Statistics & Data Analysis, Elsevier, vol. 26(3), pages 327-349, January.
    6. Silvio S. Zocchi & Anthony C. Atkinson, 1999. "Optimum Experimental Designs for Multinomial Logistic Models," Biometrics, The International Biometric Society, vol. 55(2), pages 437-444, June.
    7. D. Krewski & Y. Zhu, 1995. "A Simple Data Transformation for Estimating Benchmark Doses in Developmental Toxicity Experiments," Risk Analysis, John Wiley & Sons, vol. 15(1), pages 29-39, February.

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