FIGURE 10B-1 Risks of lung cancer versus dose from experiments in which doses were administered fractionally or chronically. Each plotted point corresponds to an estimated risk from one experiment. The plotting symbol shows the number of fractions (number of separate acute exposures) or “C” if the administration was chronic. The curves show an estimated LQ model for risk from dose D administered in K fractions, αD + βD2 / K, for five different values of K (where K is taken to be infinity for chronic exposure).

dotted lines tend to intersect most of the error bars—the evidence for different curvatures is not as extreme as it might appear from simple visual inspection.

By acting as if there is a single value of θ, the evidence for it is summarized by the likelihood function labeled “Animal Experiments” in Figure 10B-4. This is a scaled profile likelihood function for θ from a model in which the risk estimates of Figure 10B-2 are normally distributed with variances that are proportional to the reciprocal of the squared standard errors. The means are modeled to depend on the particular condition—corresponding to each of the 11 graphs in Figure 10B-2—with linear-in-dose coefficients that depend on the particular condition and with a quadratic coefficient that is θ divided by the linear coefficient. Thus, the different conditions have different linear and quadratic terms, but the ratio of the quadratic to linear term is held constant.

The “life-shortening” data used here are the mean survival times of mice exposed acutely and chronically to γ-rays at various doses (Storer and others 1979). Indications of a dose-rate effect from these data stem from the observation that the mean survival times are longer for chronically exposed mice than for acutely exposed mice given the same total dose. However, to extract specific information about curvature, it is necessary to understand the connection between age-specific failure rate and survival time. The human risk models estimated with the LSS data are for age-specific failure rates, also known as hazard functions. Interest here therefore concerns LQ models for hazard functions. Data on mouse survival times may, in principle, be used directly to estimate the hazard function, by employing standard statistical tools of survival analysis, but the unavailability of the raw data precluded this approach by the committee. If the survival times are assumed to follow an exponential probability distribution, then the hazard function is the reciprocal of the mean survival time. By using this exponential assumption (which is probably incorrect but useful nonetheless for extracting information about curvature, at least roughly), the



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