Dose-response extrapolation curves

To.xicity values for carcinogenic effects can be e.xprcsscd in several ways. The slope factor is usually, but not always, the upper 95th percent confidence limit of the slope of the dose-response curve and is e.xprcsscd as (mg/kg-day). If the extrapolation model selected is the linearized multistage model, this value is also known as the ql. That is ... 

Zero-Threshold Linear Hypothesis—The assumption that a dose-response curve derived from data in the high dose and high dose-rate ranges may be extrapolated through the low dose and low dose range to zero, implying that, theoretically, any amount of radiation will cause some damage. 

Conversion of experimental dose/response data into a form suitable for extrapolation of human risk using least squares or, more usually, maximum likelihood curve fits. 

Brown, J.M., The Shape of the Dose-Response Curve for Radiation Carcinogenesis Extrapolation to Low Doses, Radiation Research 71 34-50 (1977). 

In animal experiments exposures can be carefully controlled, and dose-response curves can be formally estimated. Extrapolating such information to the human situation is often done for regulatory purposes. There are several models for estimating a lifetime cancer risk in humans based on extrapolation from animal data. These models, however, are premised on empirically unverified assumptions that limit their usefulness for quantitative purposes. While quantitative cancer risk assessment is widely used, it is by no means universally accepted. Using different models, one can arrive at estimates of potential cancer incidence in humans that vary by several orders of magnitude for a given level of exposure. Such variations make it rather difficult to place confidence intervals around benefits estimations for regulatory purposes. Furthermore, low dose risk estimation methods have not been developed for chronic health effects other than cancer. The... 

Figure 8.1 Dose-response curves for carcinogens and illustration of low-dose extrapolation using linear, no-threshold model. Benchmark dose (BMD) is also illustrated.

Values obtained from dose response curves, with the exception of Compounds 9 and 10, which were extrapolated from a single 10 pM dose in duplicate (Included with permission from SAGE publications. [10])... 

Compared with aquatic exposure, many more uncertainties surround the potential for outcomes from human exposure. Given the sparse research performed on ultra-low-dose studies, and the complexity introduced by mixed-mode (nonmonotonic) dose-response curves (which effectively prevent extrapolations to lower doses), it... 

DOSE-RESPONSE CURVE (LOAEL-TO-NOAEL EXTRAPOLATION)... 

ECETOC (2003) recommended that if an appropriate NOAEL is available, then no extrapolation and hence, no assessment factor is necessary. Where it is considered more appropriate to use the LOAEL, a default assessment factor of 3 was recommended however, the factor may need to be adjusted depending on the effects observed at the LOAEL and the slope of the dose-response curve. The BMD could be an alternative approach for defining or confirming a NOAEL depending on the data quality and dose spacing. 

In relation to the dose-response curve, KEMI (2003) stated that the slope always has to be considered. A moderate assessment factor (not further specified) may provide an adequate MOS if the dose-response relationship is relatively steep, but may not be sufficiently conservative if the dose-response curve is relatively shallow, see Figure 5.6. In relation to extrapolation from LOAEL to NOAEL, KEMI considered that analysis of several databases does support the statement that a... 

KEMI recommended that extrapolation using the historical LOAEL/NOAEL ratio should not be undertaken in order to arrive at the dose without adverse effects from the LOAEL. The BMD approach should be used if data are adequate. If it is not possible to use the BMD approach, or to set a NOAEL, an extrapolation factor of 3-10, depending on the shape of the curve, is suggested for extrapolation from LOAEL to NOAEL. A LOAEL should preferably only be used in the case of a steep dose-response curve, and there is no guarantee that extrapolation of a LOAEL with any factor will yield an estimate of the NOAEL. 

Dose-Response Curve (LOAEL-to-NOAEL Extrapolation) Summary AND Recommendations... 

The NOAEL is not very accurate with respect to the degree to which it corresponds with the (unknown) tme NAEL. One of the most evident limitations in the NOAEL setting is that it does not take into account the shape of the dose-response curve, including its slope, for the effect as the NOAEL by definition is one of the doses tested in the specific experimental study, and all other data points are ignored. In case a NOAEL cannot be set for the critical effect, a LOAEL is then set and extrapolated to a NOAEL this extrapolation can also be regarded as part of the dose-response analysis. 

Quantitative extrapolation by mathematical modeling of the dose-response curve to estimate the risk at likely human exposures, i.e., low-dose risk extrapolation... 

The first step of the dose-response assessment is the evaluation of the data within the range of observation. If there are sufficient quantitative data and adequate understanding of the carcinogenic process, a biologically based model may be developed to relate dose and response data. Otherwise, as a default procedure, a standard model can be used to curve-fit the data. For each mmor response, a POD from the observed data is estimated to mark the beginning of extrapolation to lower doses. The POD is an estimated dose (expressed in human-equivalent terms) near the lower end of the observed range, without significant extrapolation to lower doses. 

When mmor data are used, a POD is obtained from the modeled mmor incidences. Response levels at or below 10% can often be used as the POD. The POD alone, being a single-point estimate of a single dose-response curve, does not convey all the critical information present in the data from which it is derived. To convey a measure of uncertainty, the POD should be presented as a central estimate with upper and lower bounds. The POD for extrapolating the relationship to environmental exposure levels of interest, when the latter are outside the range of observed data. 

The second step of the dose-response assessment is an extrapolation to lower dose levels, i.e., below the observable range. The purpose of low-dose extrapolation is to provide as much information as possible about risk in the range of doses below the observed data. The most versatile forms of low-dose extrapolation are dose-response models that characterize risk as a probability over a range of environmental exposure levels. Otherwise, default approaches for extrapolation below the observed data range should take into account considerations about the agent s mode of action at each tumor site. Mode-of-action information can suggest the likely shape of the dose-response curve at these lower doses. Both linear and nonlinear approaches are available. 

The linear approach should be used in two distinct circumstances (1) When there are mode-of-action data to indicate that the dose-response curve is expected to have a linear component below the POD. Agents that are generally considered to be linear in this region include agents that are DNA-reactive and have direct mutagenic activity. (2) As a default when the weight of evidence evaluation of all available data is insufficient to establish the mode of action for a tumor site, because linear extrapolation generally is considered to be a health-protective approach. 

For linear extrapolation, a line is drawn from the POD (from observed data), generally as a default, a LED (the 95% lower conhdence limit on a dose associated with an extra tumor risk) chosen to be representative of the lower end of the observed range, to the origin (zero dose/zero response), corrected for background incidences. This implies a proportional (linear) relationship between risk and dose at low doses (note that the dose-response curve generally is not linear at higher doses). The slope of this line, known as the slope factor, is an upper-bound estimate of risk per increment of dose that can be used to estimate risk probabihties for different exposure levels. The slope factor is equal to O.OI/LEDqi if the LEDqi is used as the POD. 

There are of course many mathematically complex ways to perform a risk assessment, but first key questions about the biological data must be resolved. The most sensitive endpoint must be defined along with relevant toxicity and dose-response data. A standard risk assessment approach that is often used is the so-called divide by 10 rule . Dividing the dose by 10 applies a safety factor to ensure that even the most sensitive individuals are protected. Animal studies are typically used to establish a dose-response curve and the most sensitive endpoint. From the dose-response curve a NOAEL dose or no observed adverse effect level is derived. This is the dose at which there appears to be no adverse effects in the animal studies at a particular endpoint, which could be cancer, liver damage, or a neuro-behavioral effect. This dose is then divided by 10 if the animal data are in any way thought to be inadequate. For example, there may be a great deal of variability, or there were adverse effects at the lowest dose, or there were only tests of short-term exposure to the chemical. An additional factor of 10 is used when extrapolating from animals to humans. Last, a factor of 10 is used to account for variability in the human population or to account for sensitive individuals such as children or the elderly. The final number is the reference dose (RfD) or acceptable daily intake (ADI). This process is summarized below. 

Data on drug abusers do not permit the construction of a dose-response curve. However, blood and urine concentrations of SNA after emergency hospitalization may permit some extrapolation to the quantities consumed. ... 

The existence of "no-effect doses" for toxic compounds is a controversial point, but it is clear that to measure the exposure sufficiently accurately and to detect the response reliably are major problems (see below for further discussion). Suffice it to say that certain carcinogens are carcinogenic after exposure to concentrations measured in parts per million, and the dose-response curves for some nitrosamines and for ionizing radiation appear to pass through zero when the linear portion is extrapolated. At present, therefore, in some cases no-effect levels cannot be demonstrated for certain types of toxic effect. 

Linear, No-Threshold Model. This simplest model is based on the assumption that risk is directly proportional to the dose P(d) = ad. When it is assumed that the true dose-response curve is convex, linear extrapolation in the low-dose region may overestimate the true risk. However, it is not known if the experimental dose is in the convex region of the curve. 

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