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.

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This paper presents an approach for characterizing the probability of adverse effects occurring in a population exposed to dose rates in excess of the Reference Dose (RfD). The approach uses a linear threshold (hockey stick) model of response and is based on the current system of uncertainty factors used in setting RfDs. The approach requires generally available toxicological estimates such as No-Observed-Adverse-Effect Levels (NOAELs) or Benchmark Doses and doses at which adverse effects are observed in 50% of the test animals (ED50s). In this approach, Monte Carlo analysis is used to characterize the uncertainty in the dose response slope based on the range and magnitude of the key sources of uncertainty in setting protective doses. The method does not require information on the shape of the dose response curve for specific chemicals, but is amenable to the inclusion of such data. The approach is applied to four compounds to produce estimates of response rates for dose rates greater than the RfD.

In this commentary, we respond to the conclusions of recent publications by (7,8) * The authors used urinary arsenic concentrations from grab samples as the basis for evaluating methylating capacity. However, the proportion of inorganic arsenic excreted in the urine varies substantially over time; thus, an individual grab sample is not representative of the degree of methylation that is occurring. Studies by Buchet et al. (6) show that after ingestion of inorganic arsenic, the proportion of arsenic in the urine that is inorganic arsenic is high soon after exposure (0-12 hr), but much lower later on (>12 hr). The appropriate measurement with which to examine metabolism and elimination of arsenic is the total mass of inorganic arsenic and its metabolites eliminated over a 24-to 48-hr time period; using mass per time rather than concentration would control not only for variability in the proportions of the metabolites over the course of a day, but also for variability in urine volume. A recent 7-day diet study in Japan found that the intake and excretion of total arsenic were balanced when averaged over a week but not over 1 day (9). Smith et al. Currently, the CSF for ingested arsenic is based on the incidence of nonmelanoma skin cancers associated with exposure to high levels of arsenic in drinking water in Taiwan; however, Smith et al. have suggested that arsenic could be an important risk factor not only for skin cancer, but also for several internal cancers including lung, liver, bladder, and kidney. Smith et al. used the data from another epidemiological study in Taiwan (10) to examine