### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 150-157 |

Number of pages | 8 |

Journal | Biometrics |

Volume | 57 |

Issue number | 1 |

State | Published - 2001 |

### Fingerprint

### Keywords

- Bayesian semiparametric
- Beta-binomial distribution
- Dirichlet distribution
- Overdispersion
- Toxicology data

### ASJC Scopus subject areas

- Agricultural and Biological Sciences(all)
- Public Health, Environmental and Occupational Health
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics
- Statistics and Probability

### Cite this

*Biometrics*,

*57*(1), 150-157.

**Bayesian semiparametric analysis of developmental toxicology data.** / Dominici, Francesca; Parmigiani, Giovanni.

Research output: Contribution to journal › Article

*Biometrics*, vol. 57, no. 1, pp. 150-157.

}

TY - JOUR

T1 - Bayesian semiparametric analysis of developmental toxicology data

AU - Dominici, Francesca

AU - Parmigiani, Giovanni

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

KW - Bayesian semiparametric

KW - Beta-binomial distribution

KW - Dirichlet distribution

KW - Overdispersion

KW - Toxicology data

UR - http://www.scopus.com/inward/record.url?scp=0035106735&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035106735&partnerID=8YFLogxK

M3 - Article

C2 - 11252591

AN - SCOPUS:0035106735

VL - 57

SP - 150

EP - 157

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 1

ER -