Dose-response relationships confidence limits

Benchmark Dose (BMD)—Usually defined as the lower confidence limit on the dose that produces a specified magnitude of changes in a specified adverse response. For example, a BMDio would be the dose at the 95% lower confidence limit on a 10% response, and the benchmark response (BMR) would be 10%. The BMD is determined by modeling the dose response curve in the region of the dose response relationship where biologically observable data are feasible. 

The 95% confidence limits of the estimate of the linear component of the LMS model, /, can also be calculated. The 95% upper confidence limit is termed qi and is central to the US-EPA s use of the LMS model in quantitative risk assessment, as qi represents an upper bound or worst-case estimate of the dose-response relationship at low doses. It is considered a plausible upper bound, because it is unlikely that the tme dose-response relationship will have a slope higher than qi, and it is probably considerably lower and may even be zero (as would be the case if there was a threshold). Lfse of the qj as the default, therefore, may have considerable conservatism incorporated into it. The values of qi have been considered as estimates of carcinogenic potency and have been called the unit carcinogenic risk or the Carcinogen Potency Factor (CPF). 

Mathematical modelling of the dose-response relationship is an alternative approach to quantify the estimated response within the experimental range. This approach can be used to determine the BMD or benchmark concentration (BMC) for inhalation exposure, which can be used in place of the LOAEL or NOAEL (Crump, 1984). The BMD (used here for either BMD or BMC) is defined as the lower confidence limit on a dose that produces a particular level of response (e.g., 1%, 5%, 10%) and has several advantages over the LOAEL or NOAEL (Kimmel Gaylor, 1988 Kimmel, 1990 USEPA, 1995 IPCS, 1999). For example, (1) the BMD approach uses all of the data in fitting a model instead of only data indicating the LOAEL or NOAEL (2) by fitting all of the data, the BMD approach takes into account the slope of the dose-response curve (3) the BMD takes into account variability in the data and (4) the BMD is not limited to one experimental dose. Calculation and use of the BMD approach are described in a US EPA... 

First, the threshold for hazardous chemicals that cause deterministic effects is assumed for purposes of health protection to represent a lower confidence limit, taking into account uncertainties in the dose-response relationship (see Section 3.2.1.2.7). Depending, for example, on the slope of the dose-response relationship near the threshold, the chosen steps in the dosing regimen, and the magnitude of uncertainties in the data, the lower confidence limit of the assumed threshold can be substantially below MLE. In radiation protection, the estimated thresholds for deterministic effects are based on MLEs of dose-response relationships (ICRP, 1991). 

Kltzes and Ketchum (237) reported giving 39 volunteers Intramuscular EA 3443 at 1.0-2.7 pg/kg. These doses Induced no hallucinations or abnormal neurologic signs. Dry mouth, blurred vision, and drowsiness were the most common complaints, t drlasls occurred to a mild degree. There was no consistent dose-response relationship for the heart rate, but that rate may have been decreased, rather than Increased. The minimal effective dose for reducing performance in the Number Facility Test of half the subjects by at least 25Z (HED5Q) in this study was 1.21 pg/kg, with 95% confidence limits of 1.00 and 1.48 pg/kg. The time for onset of these minimal effects was about 8 h, and the duration of effects was about 4 h. 

FIGURE 5-2 Plots of the logit and hockey-stick dose-response analysis of the relationship between retarded walking and maternal-hair concentrations during gestation. The two dose-response curves are shown by solid lines. The shaded area represents the 95% confidence limits from kernel smoothing. Source Cox et al. 1989. Reprinted with permission from Environmental Research-, eopyright 1989, Academic Press. 

---