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A litter‐based approach to risk assessment in developmental toxicity studies via a power family of completely monotone functions

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  • Anthony Y. C. Kuk

Abstract

Summary. A new class of distributions for exchangeable binary data is proposed that originates from modelling the joint success probabilities of all orders by a power family of completely monotone functions. The distribution proposed allows flexible modelling of the dose–response relationship for both the marginal response probability and the pairwise odds ratio and is especially well suited for a litter‐based approach to risk assessment. Specifically, the risk of at least one adverse response within a litter takes on a simple form under the distribution proposed and can be reduced further to a generalized linear model if a complementary log–log‐link function is used. Existing distributions such as the beta–binomial or folded logistic functions have a tendency to assign too much probability to zero, leading to an underestimation of the risk that at least one foetus is affected and an overestimation of the safe dose. The distribution proposed does not suffer from this problem. With the aid of symbolic differentiation, the distribution proposed can be fitted easily and quickly via the method of scoring. The usefulness of the class of distributions proposed and its superiority over existing distributions are demonstrated in a series of examples involving developmental toxicology and teratology data.

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  • Anthony Y. C. Kuk, 2004. "A litter‐based approach to risk assessment in developmental toxicity studies via a power family of completely monotone functions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(2), pages 369-386, April.
    • Handle: RePEc:bla:jorssc:v:53:y:2004:i:2:p:369-386
    DOI: 10.1046/j.1467-9876.2003.05369.x
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    Cited by:

    1. Dette, Holger & Biedermann, Stefanie & Zhu, Wei, 2005. "Geometric construction of optimal designs for dose-responsemodels with two parameters," Technical Reports 2005,08, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Zhen Pang & Anthony Y. C. Kuk, 2005. "A Shared Response Model for Clustered Binary Data in Developmental Toxicity Studies," Biometrics, The International Biometric Society, vol. 61(4), pages 1076-1084, December.
    3. Kolossiatis, M. & Griffin, J.E. & Steel, M.F.J., 2011. "Modeling overdispersion with the normalized tempered stable distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2288-2301, July.
    4. Zhen Pang & Anthony Y. C. Kuk, 2007. "Test of Marginal Compatibility and Smoothing Methods for Exchangeable Binary Data with Unequal Cluster Sizes," Biometrics, The International Biometric Society, vol. 63(1), pages 218-227, March.
    5. Dale Bowman & E. Olusegun George, 2017. "Weighted least squares estimation for exchangeable binary data," Computational Statistics, Springer, vol. 32(4), pages 1747-1765, December.
    6. Hui-Xiu Zhao & Jin-Guan Lin, 2013. "An approximately optimal non-parametric procedure for analyzing exchangeable binary data with random cluster sizes," Computational Statistics, Springer, vol. 28(5), pages 2029-2047, October.
    7. Dette, Holger & Biedermann, Stefanie & Zhu, Wei, 2004. "Optimal designs for dose-response models with restricted design spaces," Technical Reports 2004,40, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    8. Yu, Chang & Zelterman, Daniel, 2008. "Sums of exchangeable Bernoulli random variables for family and litter frequency data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1636-1649, January.

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