A Baseline Approach for Probabilistic Reference Doses. Jeff Swartout and Michael L. Dourson, U.S. Environmental Protection Agency, Environmental Criteria and Assessment Office, Cincinnati, OH
The U.S. EPA is currently involved in a joint research project with ChemRisk, Inc. to develop an approach for the probabilistic treatment of the Reference Dose (RfD), a standard method in the development of noncancer toxicity values. The intent of this paper is to present a "baseline" approach for the probabilistic expression of the RfD. This approach is based solely on the definition of the RfD rather than on specific data. The formula for the RfD is: NOAEL, (UF1 x UF2 x UF3 x UF4 x MF)--where NOAEL is the experimentally-derived no observed-adverse-effect level, each UFi, represents a specific area of uncertainty and MF is a modifying factor. The RfD is operationally defined as "an estimate (with uncertainty spanning perhaps an order of magnitude) of a daily exposure to the human population (including sensitive subgroups) that is likely to be without an appreciable risk of deleterious effects during a lifetime" (IRIS, 1994). The phrase, "uncertainty spanning perhaps an order of magnitude," sets the quantitative limits for a probabilistic framework. Whether the RfD is centered in, or at one of the extremes of, this order of magnitude range, is a matter of interpretation. However, if we adopt a probabilistic view of the uncertainty factors (UFs), it becomes clear that the RfD, as determined by the standard process, "migrates' towards the lower, more conservative, tail of the distribution of possible RfDs as each additional UF is applied. This conclusion arises from treating any single UF, with a value of 10, as an upper limit on that uncertainty. In this context, the standard approach to quantifying RfD uncertainty is equivalent to applying a geometric progression of 95th percentile UFs, with the resulting RfD point estimate acquiring a successively lower and lower probability. In essence, the probabilistic framework described here reverses the process; probability density functions (PDFs) for each area of uncertainty and the NOAEL are combined, generating a distribution for the RfD, from which the value at any given percentile can be estimated. This approach allows the comparison, or use of, RfDs of equivalent probability, given the assumptions and limitations of the probabilistic framework employed. With these considerations, and with specific assumptions about the underlying biological mechanisms, probability density functions are assigned to each area of uncertainty and to the NOAEL. Output distributions of hypothetical RfDs for different combination of UFs are generated using Monte Carlo simulation techniques. Selected percentiles of these distributions are compared to the point estimate values obtained directly from the standard RfD procedure. Results show that, within this baseline "reference" system, RfDs derived by the standard procedure correspond to percentiles ranging from 0.1 for one UF to 0.002 for three UFs. Correspondingly, the magnitude of total uncertainty required to obtain RfDs of equal probability (0.05) range from 13 for one UF to 180 for three UFs. The acquisition and analysis of data applicable for refinement of this approach is ongoing.