Confidence Associated with Multiple Safety Factors: Probabilistic Values for Acceptable Daily Intakes
Ralph L. Kodell, National Center for Toxicological Research, Food and Drug Administration, Jefferson, AR 72079
Acceptable daily intakes (ADIs) of potentially toxic substances are often derived by reducing experimental no-observed-adverse-effect levels (NOAELs), lowest-observed-adverse-effect levels (LOAELs), or benchmark doses (BMDs) by a product of uncertainty factors. These factors are presumed to ensure safety by accounting for uncertainty in dose extrapolation, uncertainty in duration extrapolation, differential sensitivity between humans and animals, and differential sensitivity among humans. The common default value for each uncertainty factor is 10, but the degree of safety provided by factors of 10 has not been quantified satisfactorily. In order to provide a stronger scientific basis for selecting uncertainty factors, researchers have compiled databases reflecting chemical-to-chemical variability with respect to each of these sources of uncertainty. These databases indicate that such variability may be characterized by distributions of lognormal random variables. This presentation describes a statistical procedure for using estimates of means and standard deviations of these individual distributions to estimate percentiles of the distribution of the product of uncertainty factors. An upper percentile of the distribution of this product can be chosen to ensure a high degree of safety (say, 95% or 99%) for ADIs with respect to these combined sources of uncertainty. Based on the databases examined here, a simple "rule of 3's" is suggested as a short-cut procedure for choosing a combined uncertainty factor that exceeds the estimated 95th percentile of the distribution of the product of uncertainty factors. With this rule, if only a single uncertainty factor is required, it should be 33. For any two sources of uncertainty, a factor of 3x33 ≈ 100 should be used. Any three sources of uncertainty would require a combined factor of 3x100=300, and any four sources a combined factor of 3x300=900. For 99% assurance of safety, an additional factor of 3 should be used.