Percentiles of the product of uncertainty factors for establishing probabilistic reference doses

Exposure guidelines for potentially toxic substances are often based on a r eference dose (RfD) that is determined by dividing a no-observed-adverse-ef fect-level (NOAEL), lowest-observed-adverse-effect-level (LOAEL), or benchm ark dose (BD) corresponding to a low level of risk, by a product of uncerta inty factors. The uncertainty factors for animal to human extrapolation, va riable sensitivities among humans, extrapolation from measured subchronic e ffects to unknown results for chronic exposures, and extrapolation from a L OAEL to a NOAEL can be thought of as random variables that vary from chemic al to chemical. Selected databases are examined that provide distributions across chemicals of inter- and intraspecies effects, ratios of LOAELs to NO AELs, and differences in acute and chronic effects, to illustrate the deter mination of percentiles for uncertainty factors. The distributions of uncer tainty factors tend to be approximately lognormally distributed. The logari thm of the product of independent uncertainty factors is approximately dist ributed as the sum of normally distributed variables, making it possible to estimate percentiles for the product. Hence, the size of the products of u ncertainty factors can be selected to provide adequate safety for a large p ercentage (e.g., approximately 95%) of RfDs. For the databases used to desc ribe the distributions of uncertainty factors, using values of 10 appear to be reasonable and conservative. For the databases examined the following s imple "Rule of 3s" is suggested that exceeds the estimated 95th percentile of the product of uncertainty factors: If only a single uncertainty factor is required use 33, for any two uncertainty Factors use 3 x 33 approximate to 100, for any three uncertainty factors use a combined factor of 3 x 100 = 300, and if all four uncertainty factors are needed use a total factor of 3 x 300 = 900. If near the 99th percentile is desired use another factor o f 3. An additional factor may be needed for inadequate data or a modifying factor for other uncertainties (e.g., different routes of exposure) not cov ered above.