TABLE 1.

Lung cancer incidence among Wistar rats that inhaled Pu-239 + Yb-169 and associated expected (assuming no protection) and observed RR and related gamma-ray associated protection factor against cancer based on data from Sanders (2007)

Average Alpha Radiation Dose (mGy)	Average Gamma Radiation Dose (mGy)	Number of Animals	Lung Cancer Incidence	Expected Relative Risk Based on LNTa	Observed Relative Risk	PROFAC
0	0	1052	0.00095 ± 0.00095	1	1
56 ± 20	1	1389	0 (0.00072)b	20	0 [1]c	1.0 [0.95]d
190 ± 90	2	343	0 (0.0029)b	67	0 [1]c	1.0 [0.985]d
620 ± 160	1	145	0 (0.0069)b	216	0 [1]c	1.0 [0.995]d

^aBased on rats not exposed to gamma rays from a Yb-169 label and Equation 2 (filled circles in Figure 2) with RR evaluated based on B = 0.00095 rather than the value of 0.00150 reported by Sanders (2007) for rats exposed only to ²³⁹Pu alpha radiation; the calculated value for K_α is 3.3 × 10⁻⁴ mGy⁻¹.

^b

Binomial-distribution-associated standard error (SE) for frequency (Fleiss 1981) had exactly one rat developed lung cancer, given that no cancers were observed:

$$\text{SE}={[f(1-f)/N]}^{1/2}, \text{with} f=1/N, \text{where} N= \text{the number of animals exposed.}$$

^cSubjective upper bound (RR = 1).

^dSubjective lower bound on PROFAC based on a subjective upper bound of 1 for the observed RR; calculated using the expected RR (column 5) as a reference, i.e., PROFAC = 1 − (1/Expected RR). This equation is based on Equation 1.