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.