Dw. Gaylor et Jj. Chen, PRECISION OF BENCHMARK DOSE ESTIMATES FOR CONTINUOUS (NONQUANTAL) MEASUREMENTS OF TOXIC EFFECTS, Regulatory toxicology and pharmacology, 24(1), 1996, pp. 19-23
The benchmark dose (BMD) corresponding to a low level of the risk of i
nduced disease, e.g., 1 to 10%, has been proposed by various authors a
s a replacement for the no observed adverse effect level for noncancer
endpoints in the regulation of the conditions of exposure to chemical
s. This paper focuses on the variability of estimates of the BMD for n
onquantal (continuous measurements) of biological endpoints such as ar
e 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 deviatio
n generally are quite variable, particularly for small sample sizes. T
he 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 e
mploy a small number of animals. When the standard deviation is undere
stimated, 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 aris
e 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 dos
es). If the standard deviation is constant across doses (for lognormal
ly distributed data if the coefficient of variation is constant), a po
oled estimate across doses of the standard deviation can be used. In t
his case, for bioassays employing a total of 40 to 50 animals, the cal
culation 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. (C) 199
6 Academic Press, Inc.