Linear model, risk calculation

Oncogenic Risk Calculations. On the basis of the expos ire analysis and potential oncogenic risk (oncogenic potency might be more descriptive), a risk analysis will be performed according to statistical methods like linear extrapolation (one-hit model) or multistage estimation (9.). 

If the exposure had been much smaller, the risk calculation would have been less direct and less certain. For purposes of risk reduction in public health, we may choose to err on the pessimistic side in risk estimations. For purposes of attribution, however, we want to make best estimates. Most of the numbers in Ikble 8.4 are overestimates of the risks. For radiation-induced leukemia, as described in Section 6.1.2, the best dose-incidence model might be lineai>quadratic and not linear. Thus, someone exposed to 50 mSv (5 rem) might be considered, on a linear extrapolation basis, to have a radiation related lifetime risk of cancer mortality of 10 (2 x 10 Sv 2 x 10 rem ), or a lifetime risk of mortality from leukemia of approximately 1.5 x 10 (0.3 x 10" Sv 0.3 X 10 rem ). The natural lifetime risk of mortality from leukemia other than chronic lymphocytic leukemia is approximately 56 x 10 . Therefore, the percent attribution to radiation according to the linear model would be ... 

ADI-type calculations were performed for noncarcinogens. For potential carcinogenic risk calculations, a linearized multistage model or a one-hit model was employed and water concentrations equivalent to calculated risks of 10"5, 10 6, and 10r were reported. No selection was made as the specific criterion however, 10-5 was suggested as a reasonable value. 

In the proposed criteria, the linear model was used to calculate the concentrations associated with incremental lifetime risks of 10-5. However, in response to public comment, the USEPA ultimately decided to adopt the linearized multistage model to make full use of all available data. Comparison of the values reported in the box indicates that, for most cases, the concentrations calculated by either model for a given nominal risk are very close. 

This means that extrapolating from a high dose of a chemical to a very low dose to determine a threshold and calculate risk may not be appropriate (see Chapter 12), especially if a linear model is used which implies there is no safe dose (for example, for a carcinogen). If true this has profound implications for risk assessment, suggesting that we may sometimes have been more cautious than necessary Thus attempting to reduce exposure levels for chemicals excessively may be unnecessary and, worse, a waste of effort and money. 

A few court decisions, however, have been more skeptical of the linear model. Eor example, the U.S. EPA s use of the linear, no-threshold model in its risk assessment for drinking water chlorinated byproducts was rejected by the court because it was contrary to evidence suggesting a nonlinear model that had been accepted by both the U.S. EPA and its Science Advisory Board (CCC 2000). On the other hand, the U.S. OSHA s departure from the linear, no-threshold model in its formaldehyde risk assessment was likewise rejected by the court (lU 1989). The court held that the U.S. OSHAhad improperly used the maximum likelihood estimate (MLE) rather than the upper confidence limit (UCL) to calculate risk, and the UCL but not the MLE model was consistent with a linear dose-response assumption. The court held that the U.S. OSHA had failed to justify its departure from its traditional linear, no-threshold dose-response assumption. 

Radioactive slope factors calculated by EPA s Office of Radiation and Indoor Air (ORIA). Slope factors are central estimates in a linear model of the age-averaged, lifetime attributable radiation cancer incidence (fatal and nonfatal cancer) risk per unit of activity ingested, expressed as risk per picocurie (pCi). 

In view of the considerable uncertainties in the extrapolation of results over several orders of magnitude, specification of risks in terms of predicted incidence or numbers of excess cancers per unit of the population implies a degree of precision that is considered misleading by some. Larsen (2006), e.g., noted that the model most often used in low-dose extrapolation is a linear extrapolation from the observable range, and the apparent precision of the calculations does not reflect the uncertainty in the risk estimate the results are therefore open to misinterpretation because the numerical estimates may be regarded as quantification of the actual risk. 

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). 

By using a modified linear multistage model, the NAS (1977) concluded that the nominal lifetime incremental risk of cancer falls between 1.5 and 3 X 10-7 per microgram per liter per day. The range of values obtained is the result of calculations made from several data sets. 

U.S. regulations for environmental contaminants have generally fallen in the 10-4 to 10-6 lifetime risk range, as calculated from a relatively worst-case linear multistage model. Most of those decisions incorporated consideration of costs and feasibility. 

The three sets of risk values listed were calculated by two versions of the linear multistage model generally from the same data, except for vinyl chloride for which CAG 1984 calculation used a different animal... 

Concentration values in micrograms per liter are provided in the box on page 728 for 40 substances at the calculated 10-5 risk level at the upper bound. Both a linearized multistage model and the one-hit model (in parentheses) were used (45). Many of these values are now being updated. 

The effects of genotoxic compounds are considered non-threshold. Thus, risk assessment for a given exposure is usually performed by a linear or sub-linear extrapolation from the high dose effects observed in animals to the lower human exposure. Since the outcome of the extrapolation depends on the model applied and extrapolation over different orders of magnitude is error prone, the European Food and Safety Authority (EFSA 2005) recommended to avoid this extrapolation and proposed the MOE approach. This approach uses the benchmark dose, or the T25 calculated from a carcinogenicity study and compares this with human exposure. A MOE of 10,000 and more is considered to be of minor concern. The advantage is that neither a debatable extrapolation from high to low doses needs to be performed nor are hypothetical cancer cases calculated. For details of the different approaches see, SCHER, SCCP, SCENIHR (2008). 

The decision to use an amortized exposure value or a peak exposure value has a profound Impact on the outcome of the quantitative risk assessment. To Illustrate this point, data from an actual field exposure study were used. The average dally dermal exposure level as measured by the patch technique was used to calculate the amortized exposure level and the peak exposure level (Table VIII). Estimates of risk at low doses were obtained using linear extrapolation from the 11 excess risk point based on a fitted Welbull model (32) and the Armltage-Doll multi-stage model (33). While both models gave similar results, the effect of the exposure estimates had a dramatic effect on the risk estloiates. The amortized exposure estloiates lowered the estloiates of risk substantially. 

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