### Abstract

Hierarchical models are considered for estimating the probability of agreement between two outcomes or endpoints from an environmental toxicity experiment. Emphasis is placed on generalized regression models, under which the prior mean is related to a linear combination of explanatory variables via a monotone function. This function defines the scale over which the systematic effects are modelled as additive. Specific illustration is provided for the logistic link function. The hierarchical model employs a conjugate beta prior that leads to parametric empirical Bayes estimators of the individual agreement parameters. An example from environmental carcinogenesis illustrates the methods, with motivation derived from estimation of the concordance between two species carcinogenicity outcomes. Based on a large database of carcinogenicity studies, the inter-species concordance is seen to be reasonably informative, i.e. in the range 67–84%. Stratification into pertinent potency-related sub-groups via the logistic model is seen to improve concordance estimation: for environmental stimuli at the extremes of the potency spectrum, concordance can reach well above 90%.

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

Pages (from-to) | 153-162 |

Number of pages | 10 |

Journal | Environmental and Ecological Statistics |

Volume | 1 |

Issue number | 2 |

DOIs | |

State | Published - 1994 |

Externally published | Yes |

### Fingerprint

### Keywords

- agreement
- confidence intervals
- dichotomous data
- environmental carcinogenesis
- generalized linear models
- hierarchical models
- logistic regression
- parametric empirical Bayes methods
- potency
- shrinkage estimator

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Environmental Science(all)
- Statistics and Probability

### Cite this

**Empirical Bayes calculations of concordance between endpoints in environmental toxicity experiments.** / Piegorsch, Walter W.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Empirical Bayes calculations of concordance between endpoints in environmental toxicity experiments

AU - Piegorsch, Walter W

PY - 1994

Y1 - 1994

N2 - Hierarchical models are considered for estimating the probability of agreement between two outcomes or endpoints from an environmental toxicity experiment. Emphasis is placed on generalized regression models, under which the prior mean is related to a linear combination of explanatory variables via a monotone function. This function defines the scale over which the systematic effects are modelled as additive. Specific illustration is provided for the logistic link function. The hierarchical model employs a conjugate beta prior that leads to parametric empirical Bayes estimators of the individual agreement parameters. An example from environmental carcinogenesis illustrates the methods, with motivation derived from estimation of the concordance between two species carcinogenicity outcomes. Based on a large database of carcinogenicity studies, the inter-species concordance is seen to be reasonably informative, i.e. in the range 67–84%. Stratification into pertinent potency-related sub-groups via the logistic model is seen to improve concordance estimation: for environmental stimuli at the extremes of the potency spectrum, concordance can reach well above 90%.

AB - Hierarchical models are considered for estimating the probability of agreement between two outcomes or endpoints from an environmental toxicity experiment. Emphasis is placed on generalized regression models, under which the prior mean is related to a linear combination of explanatory variables via a monotone function. This function defines the scale over which the systematic effects are modelled as additive. Specific illustration is provided for the logistic link function. The hierarchical model employs a conjugate beta prior that leads to parametric empirical Bayes estimators of the individual agreement parameters. An example from environmental carcinogenesis illustrates the methods, with motivation derived from estimation of the concordance between two species carcinogenicity outcomes. Based on a large database of carcinogenicity studies, the inter-species concordance is seen to be reasonably informative, i.e. in the range 67–84%. Stratification into pertinent potency-related sub-groups via the logistic model is seen to improve concordance estimation: for environmental stimuli at the extremes of the potency spectrum, concordance can reach well above 90%.

KW - agreement

KW - confidence intervals

KW - dichotomous data

KW - environmental carcinogenesis

KW - generalized linear models

KW - hierarchical models

KW - logistic regression

KW - parametric empirical Bayes methods

KW - potency

KW - shrinkage estimator

UR - http://www.scopus.com/inward/record.url?scp=4243114456&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243114456&partnerID=8YFLogxK

U2 - 10.1007/BF02426659

DO - 10.1007/BF02426659

M3 - Article

AN - SCOPUS:4243114456

VL - 1

SP - 153

EP - 162

JO - Environmental and Ecological Statistics

JF - Environmental and Ecological Statistics

SN - 1352-8505

IS - 2

ER -