Statistical uncertainty in the no-observed-adverse-effect level.

The no-observed-adverse-effect level (NOAEL) is a dose value that U.S. EPA reduces by uncertainty factors (UF) and modifying factors (MF) to obtain a reference dose (RfD) for input to regulatory decision making. Whether the true added risk at the NOAEL is below an acceptable level, however, is a source of statistical uncertainty itself. As several authors have previously noted, the probability that added risk at the NOAEL is not negligibly small increases as sample sizes decrease. This is because the definition of the NOAEL statistically controls for the chance of a false-positive error, but not for a false-negative error. The false-positive rate is the test level set by the user in testing for a statistically significant dose effect, typically 0.05. When it is held fixed, the increase in statistical uncertainty as sample size decreases produces an increase in the false-negative rate. Hence, the fewer data available for statistical inference, the higher the expected value of the NOAEL and the less toxic an agent is likely to appear. The solution lies in calculating the probability that a statistical procedure used will detect the maximum added risk acceptable for health regulation (the "power" at that added risk). If the observed response in a dose group is not significantly elevated relative to the control group, and the power for detecting a difference is low as well, then the statistical evidence is inconclusive. In such a case, additional data or other sources of information are needed for evaluating added risk. These concepts are illustrated for examples from the literature with dichotomous (quantal response) data and categorical (severity) data, using a new statistical procedure.