Precision of benchmark dose estimates for continuous (nonquantal) measurements of toxic effects

The benchmark dose (BMD) corresponding to a low level of the risk of induced disease, e.g., 1 to 10%, has been proposed by various authors as a replacement for the no observed adverse effect level for noncancer endpoints in the regulation of the conditions of exposure to chemicals. This paper focuses on the variability of estimates of the BMD for nonquantal (continuous measurements) of biological endpoints such as are encountered for hematological data, clinical chemistry, and studies of neurotoxic effects. For biological endpoints that can be described by a normal distribution, estimates of the mean and standard deviation are required to calculate the BMD. Estimates of the standard deviation generally are quite variable, particularly for small sample sizes. The purpose of this paper is to examine the precision of the estimates of risk and of the BMD resulting from the inherent variability of the estimates of the standard deviations particularly for bioassays that employ a small number of animals. When the standard deviation is underestimated, the BMD and the regulatory "safe" dose are underestimated. Conversely, when the standard deviation is overestimated, the BMD and safe dose are overestimated. Overestimation of the BMD can be reduced or eliminated by using a lower confidence limit. The worst cases arise where only a few animals are used per dose and the dose response is supralinear (changes rapidly at low doses and levels off at higher doses). If the standard deviation is constant across doses (for lognormally distributed data if the coefficient of variation is constant), a pooled estimate across doses of the standard deviation can be used. In this case, for bioassays employing a total of 40 to 50 animals, the calculation of the BMD will generally be within a factor of 2 of the true value. When the standard deviation is not constant across dose groups, it is desirable to have more than 10 animals per dose group.