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

  • Kassandra Fronczyk
  • Athanasios Kottas
Article

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.

Keywords

Dependent Dirichlet process Developmental toxicology data dose–response relationship Gaussian process Nonparametric mixture modeling 

Notes

Acknowledgements

The work of the second author was supported in part by the National Science Foundation under award DMS 1310438. The authors wish to thank an Associate Editor and two reviewers for useful feedback and for comments that improved the presentation of the material in the paper.

Supplementary material

13253_2017_293_MOESM1_ESM.pdf (142 kb)
Supplementary material 1 (pdf 141 KB)

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Copyright information

© International Biometric Society 2017

Authors and Affiliations

  1. 1.Applied Statistics GroupLawrence Livermore National LaboratoryLivermoreUSA
  2. 2.Department of Applied Mathematics and StatisticsUniversity of CaliforniaSanta CruzUSA

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