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.