### Abstract

Methods are presented for modeling dose-related effects in proportion data when extra-binomial variability is a concern. Motivation is taken from experiments in developmental toxicology, where similarity among conceptuses within a litter leads to intralitter correlations and to overdispersion in the observed proportions. Appeal is made to the well-known beta-binomial distribution to represent the overdispersion. From this, an exponential function of the linear predictor is used to model the dose-response relationship. The specification was introduced previously for econometric applications by Heckman and Willis; it induces a form of logistic regression for the mean response, together with a reciprocal biexponential model for the intralitter correlation. Large-sample, likelihood-based methods for estimating and testing the joint proportion-correlation response are studied. A developmental toxicity data set illustrates the methods.

Original language | English (US) |
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Pages (from-to) | 125-133 |

Number of pages | 9 |

Journal | Biometrics |

Volume | 56 |

Issue number | 1 |

DOIs | |

State | Published - Mar 2000 |

Externally published | Yes |

### Keywords

- Beta-binomial distribution
- Correlated binary data
- Developmental toxicology
- Extra-binomial variability
- Hierarchical model
- Intralitter correlation
- Litter effect
- Logistic regression
- Overdispersion
- Teratology

### ASJC Scopus subject areas

- Statistics and Probability
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics

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## Cite this

*Biometrics*,

*56*(1), 125-133. https://doi.org/10.1111/j.0006-341X.2000.00125.x