Hierarchical models for probabilistic dose-response assessment

Probabilistic risk assessment is gaining acceptance as the most appropriate way to characterize and communicate uncertainties in estimates of human health risk and/or reference levels of exposure such as benchmark doses. Although probabilistic techniques are well established in the exposure-assessment component of the National Research Council's risk-assessment paradigm, they are less well developed in the dose-response-assessment component. This paper proposes the use of hierarchical statistical models as tools for implementing probabilistic dose-response assessments, in that such models provide a natural connection between the pharmacokinetic (PK) and pharmacodynamic (PD) components of dose-response models. The results show that incorporating internal dose information into dose-response assessments via the coupling of PK and PD models in a hierarchical structure can reduce the uncertainty in the dose-response assessment of risk. However, information on the mean of the internal dose distribution is sufficient; having information on the variance of internal dose does not affect the uncertainty in the resulting estimates of excess risks or benchmark doses. In addition, the complexity of a PK model of internal dose does not affect how the variability in risk is measured via the ultimate endpoint.