Identification of a critical dose level for risk assessment: Developments in benchmark dose analysis of continuous endpoints

The benchmark dose (BMD) method has been recommended to replace the no-observed-adverse-effect-level (NOAEL) approach in health risk assessment of chemical substances. In the present article, developments in BMD analysis from continuous experimental data are proposed. The suggested approach defines the BMD as the dose at which the slope of the S-shaped dose-response relationship changes the most in the low-dose region. This dose resides in a region where the sensitivity to chemical exposure may start to change noticeably. It is shown that the response (defined as a percent change relative to the magnitude, or size, of response) corresponding to the dose where the slope changes the most depends on the geometrical shape of the dose-response curve; the response becomes lower as the curve becomes more asymmetrical and threshold-like in the low-dose region. Given a symmetrical case, described by the Hill function, the response associated with the critical dose level becomes 21% (defined as a percent change relative to the magnitude, or size, of response). According to a limiting case of asymmetry and threshold-like characteristics, reflected by a Gompertz curve, the response corresponding to the dose of interest becomes as low as 7.3% (defined as a percent change relative to the magnitude, or size, of response). Use of a response in the range of 5-10% when estimating the BMD conservatively accounts for uncertainties associated with the proposed strategy, and may be appropriate in a risk assessment point of view. The present investigation also indicated that a BMD defined according to the suggested procedure may be estimated more precisely relative to BMDs defined under other approaches for continuous data.