Response to Comments on “An Approach for Modeling Noncancer Dose Responses with an Emphasis on Uncertainty” and “A Probabilistic Framework for the Reference Dose (Probabilistic RfD)”

Determining the probabilistic limits for the uncertainty factors used in the derivation of the Reference Dose (RfD) is an important step toward the goal of characterizing the risk of noncarcinogenic effects from exposure to environmental pollutants. If uncertainty factors are seen, individually, as "upper bounds" on the dose-scaling factor for sources of uncertainty, then determining comparable upper bounds for combinations of uncertainty factors can be accomplished by treating uncertainty factors as distributions, which can be combined by probabilistic techniques. This paper presents a conceptual approach to probabilistic uncertainty factors based on the definition and use of RfDs by the U.S. EPA. The approach does not attempt to distinguish one uncertainty factor from another based on empirical data or biological mechanisms but rather uses a simple displaced lognormal distribution as a generic representation of all uncertainty factors. Monte Carlo analyses show that the upper bounds for combinations of this distribution can vary by factors of two to four when compared to the fixed-value uncertainty factor approach. The probabilistic approach is demonstrated in the comparison of Hazard Quotients based on RfDs with differing number of uncertainty factors.