Bayesian Approach to Expressing Variability in Dose-Response Estimates. Vic Hasselblad, Center for Health Policy Research and Education, Duke University, Durham, NC 27705; and A. M. Jarabek, National Center for Environmental Assessment, U.S. EPA, Research Triangle Park, NC 27711
Uncertainty factors (UFs) have typically been applied to observed effect levels in order to derive a dose-response estimate for characterizing risk. Recent work on developing distributions for UFs promises a probabilistic approach to such derivations. However, expressing the dose-response estimate as a single point statistic, i.e., as an observed effect level, fails to adequately incorporate variability inherent in the dose-response estimate and diminishes the probabilistic nature that application of these UF distributions might impart. Mathematical modeling of the dose-response function, e.g., the benchmark dose (BMD) approach, offers the ability to account for variability in the initial estimate. A Bayesian approach offers additional advantages over the BMD approach because it can express dose-response estimates for various outcomes (categorical, count, continuous) as a probability density distribution that is readily amenable to integration with UF distributions. The Bayesian approach also provides for formal statistical combination of more than one data set to derive a dose-response estimate and can incorporate variability in the exposure measure directly. Visual display of the density distribution also provides much information about the usefulness of the data. Case studies of the Bayesian approach applied to assessment of noncancer and cancer toxicity are presented to illustrate these attributes.