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Risk Assessment for Toxicity Experiments with Discrete and Continuous Outcomes: A Bayesian Nonparametric Approach

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  • Kassandra Fronczyk

    (Lawrence Livermore National Laboratory)

  • Athanasios Kottas

    (University of California)

Abstract

We present a Bayesian nonparametric modeling approach to inference and risk assessment for developmental toxicity studies. The primary objective of these studies is to determine the relationship between the level of exposure to a toxic chemical and the probability of a physiological or biochemical response. We consider a general data setting involving clustered categorical responses on the number of prenatal deaths, the number of live pups, and the number of live malformed pups from each laboratory animal, as well as continuous outcomes (e.g., body weight) on each of the live pups. We utilize mixture modeling to provide flexibility in the functional form of both the multivariate response distribution and the various dose–response curves of interest. The nonparametric model is built from a structured mixture kernel and a dose-dependent Dirichlet process prior for the mixing distribution. The modeling framework enables general inference for the implied dose–response relationships and for dose-dependent correlations between the different endpoints, features which provide practical advances relative to traditional parametric models for developmental toxicology. We use data from a toxicity experiment that investigated the toxic effects of an organic solvent (diethylene glycol dimethyl ether) to demonstrate the range of inferences obtained from the nonparametric mixture model, including comparison with a parametric hierarchical model. Supplementary materials accompanying this paper appear on-line.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jagbes:v:22:y:2017:i:4:d:10.1007_s13253-017-0293-6
    DOI: 10.1007/s13253-017-0293-6
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    References listed on IDEAS

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    1. De Iorio, Maria & Muller, Peter & Rosner, Gary L. & MacEachern, Steven N., 2004. "An ANOVA Model for Dependent Random Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 205-215, January.
    2. Maria De Iorio & Wesley O. Johnson & Peter Müller & Gary L. Rosner, 2009. "Bayesian Nonparametric Nonproportional Hazards Survival Modeling," Biometrics, The International Biometric Society, vol. 65(3), pages 762-771, September.
    3. Gelfand, Alan E. & Kottas, Athanasios & MacEachern, Steven N., 2005. "Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1021-1035, September.
    4. Faes, Christel & Geys, Helena & Aerts, Marc & Molenberghs, Geert, 2006. "A hierarchical modeling approach for risk assessment in developmental toxicity studies," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1848-1861, December.
    5. Lelys Bravo Guenni & Susan J. Simmons & Athanasios Kottas & Ziwei Wang & Abel Rodríguez, 2012. "Spatial modeling for risk assessment of extreme values from environmental time series: a Bayesian nonparametric approach," Environmetrics, John Wiley & Sons, Ltd., vol. 23(8), pages 649-662, December.
    6. Athanasios Kottas & Milovan Krnjajić, 2009. "Bayesian Semiparametric Modelling in Quantile Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 297-319, June.
    7. Meredith M. Regan & Paul J. Catalano, 1999. "Likelihood Models for Clustered Binary and Continuous Out comes: Application to Developmental Toxicology," Biometrics, The International Biometric Society, vol. 55(3), pages 760-768, September.
    8. Francesca Dominici & Giovanni Parmigiani, 2001. "Bayesian Semiparametric Analysis of Developmental Toxicology Data," Biometrics, The International Biometric Society, vol. 57(1), pages 150-157, March.
    9. Michele Guindani & Alan E. Gelfand, 2006. "Smoothness Properties and Gradient Analysis Under Spatial Dirichlet Process Models," Methodology and Computing in Applied Probability, Springer, vol. 8(2), pages 159-189, June.
    10. Kassandra Fronczyk & Athanasios Kottas, 2014. "A Bayesian Nonparametric Modeling Framework for Developmental Toxicity Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 873-888, September.
    11. David B. Dunson & Zhen Chen & Jean Harry, 2003. "A Bayesian Approach for Joint Modeling of Cluster Size and Subunit-Specific Outcomes," Biometrics, The International Biometric Society, vol. 59(3), pages 521-530, September.
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