Empirical Bayes calculations of concordance between endpoints in environmental toxicity experiments

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3 Scopus citations


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 languageEnglish (US)
Pages (from-to)153-162
Number of pages10
JournalEnvironmental and Ecological Statistics
Issue number2
StatePublished - Jun 1994


  • 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 and Probability
  • General Environmental Science
  • Statistics, Probability and Uncertainty


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