Dose-Response Models linear quadratic

The BEIR III risk estimates formulated under several dose-response models demonstrate that the choice of the model can affect the estimated excess more than can the choice of the data to which the model is applied. BEIR III estimates of lifetime excess cancer deaths among a million males exposed to 0.1 Gy (10 rad) of low-LET radiation, derived with the three dose-response functions employed in that report, vary by a factor of 15, as shown in Ikble 6.1 (NAS/NRC, 1980). In animal experiments with high-LET radiation, the most appropriate dose-response function for carcinogenesis is often found to be linear at least in the low to intermediate dose range (e.g., Ullrich and Storer, 1978), but the data on bone sarcomas among radium dial workers are not well fitted by either a linear or a quadratic form. A good fit for these data is obtained only with a quadratic to which a negative exponential term has been added (Rowland et al., 1978). 

The nominal probability coefficient for radionuclides normally used in radiation protection is derived mainly from maximum likelihood estimates (MLEs) of observed responses in the Japanese atomic-bomb survivors. A linear or linear-quadratic dose-response model, which is linear at low doses, is used universally to extrapolate the observed responses at high doses and dose rates to the low doses of concern in radiation protection. The probability coefficient at low doses also includes a small adjustment that takes into account an assumed decrease in the response per unit dose at low doses and dose rates compared with the observed responses at high doses and dose rates. 

For radionuclides, NCRP reaffirms use of a best estimate (MLE) of the response probability obtained from a linear or linear-quadratic model as derived from data in humans, principally the Japanese atomic-bomb survivors. This model essentially is linear at the low doses of concern to waste classification. Specifically, for purposes of health protection of the public, NCRP reaffirms use of a probability coefficient for fatal cancers (probability per unit effective dose) of 0.05 Sv 1 (ICRP, 1991 NCRP, 1993a). Although this probability coefficient is less rigorous for intakes of some long-lived radionuclides that are tenaciously retained in the body than for other exposure situations, such as external exposure or intakes of short-lived radionuclides (Eckerman et al., 1999), it is adequate for the purpose of generally classifying waste, especially when the lack of data on cancer risks in humans for most chemicals is considered. 

There is considerable controversy over the shape of the dose-response curve at the chronic low dose levels important for environmental contamination. Proposed models include linear models, nonlinear (quadratic) models, and threshold models. Because risks at low dose must be extrapolated from available data at high doses, the shape of the dose-response curve has important implications for the environmental regulations used to protect the general public. Detailed description of dosimetry models can be found in Cember (1996), BEIR IV (1988), and Harley (2001). 

Since the linear model consistently predicts the highest response frequency per unit dose in very low dose range, it is usually the most conservative or least likely to underestimate human health risk. It is often recommended by regulating agencies to determine the risk of known or suspected human carcinogens. For non-carcinogens, the quadratic model that predicts a threshold dose at which there is no effect is often used. 

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