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Bayesian Semiparametric Analysis of Developmental Toxicology Data

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  • Francesca Dominici
  • Giovanni Parmigiani

Abstract

Summary. Modeling of developmental toxicity studies often requires simple parametric analyses of the dose‐response relationship between exposure and probability of a birth defect but poses challenges because of nonstandard distributions of birth defects for a fixed level of exposure. This article is motivated by two such experiments in which the distribution of the outcome variable is challenging to both the standard logistic model with binomial response and its parametric multistage elaborations. We approach our analysis using a Bayesian semiparametric model that we tailored specifically to developmental toxicology studies. It combines parametric dose‐response relationships with a flexible nonparametric specification of the distribution of the response, obtained via a product of Dirichlet process mixtures approach (PDPM). Our formulation achieves three goals: (1) the distribution of the response is modeled in a general way, (2) the degree to which the distribution of the response adapts nonparametrically to the observations is driven by the data, and (3) the marginal posterior distribution of the parameters of interest is available in closed form. The logistic regression model, as well as many of its extensions such as the beta‐binomial model and finite mixture models, are special cases. In the context of the two motivating examples and a simulated example, we provide model comparisons, illustrate overdispersion diagnostics that can assist model specification, show how to derive posterior distributions of the effective dose parameters and predictive distributions of response, and discuss the sensitivity of the results to the choice of the prior distribution.

Suggested Citation

  • Francesca Dominici & Giovanni Parmigiani, 2001. "Bayesian Semiparametric Analysis of Developmental Toxicology Data," Biometrics, The International Biometric Society, vol. 57(1), pages 150-157, March.
  • Handle: RePEc:bla:biomet:v:57:y:2001:i:1:p:150-157
    DOI: 10.1111/j.0006-341X.2001.00150.x
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    References listed on IDEAS

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    1. Tom Leonard & Melvin R. Novick, 1986. "Bayesian Full Rank Marginalization for Two-Way Contingency Tables," Journal of Educational and Behavioral Statistics, , vol. 11(1), pages 33-56, March.
    2. D. A. Williams, 1982. "Extra‐Binomial Variation in Logistic Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(2), pages 144-148, June.
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    Cited by:

    1. 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.
    2. 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.
    3. Michael L. Pennell & David B. Dunson, 2006. "Bayesian Semiparametric Dynamic Frailty Models for Multiple Event Time Data," Biometrics, The International Biometric Society, vol. 62(4), pages 1044-1052, December.
    4. Kassandra Fronczyk & Athanasios Kottas, 2017. "Risk Assessment for Toxicity Experiments with Discrete and Continuous Outcomes: A Bayesian Nonparametric Approach," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(4), pages 585-601, December.

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