Using Copulas to Introduce Dependence in Dose-Response Modeling of Multiple Binary Endpoints



We propose a method for introducing dependence in the dose-response modeling of multiple dichotomous endpoints. The method uses a copula to define a joint multivariate distribution that is consistent with predetermined marginal distributions representing the individual dose-response functions for each endpoint. Use of copulas allows the marginal dose-response functions for each dose-endpoint combination to be unrestricted in form. An application of particular relevance to risk assessment is the dose-response modeling of multiple types of tumors in test animals exposed to a carcinogen, allowing for tumors at different sites in the same animal to be statistically dependent. In addition, the method can be used to address the possibility that different tissues/organs are subject to different internal doses and possibly different active moieties. These applications are illustrated with rodent cancer bioassay data from two example compounds.

Key Words

Dependent binary response Dependent tumor response Multivariate normal distribution Physiologically based pharmacokinetic model Quantitative risk assessment 


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Copyright information

© International Biometric Society 2011

Authors and Affiliations

  1. 1.National Center for Environmental Assessment, Office of Research and DevelopmentUnited States Environmental Protection AgencyWashingtonUSA
  2. 2.Department of Mathematics and StatisticsLouisiana Tech UniversityRustonUSA

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