Dose-response threshold from A-bomb survivor data

[Bernard L Cohen <blc+@pitt.edu>]

	Roger Clark, in a talk at Harvard, stated that the A-bomb survivor
data shows that, if there is a threshold for radiation induced cancer, it
is below 5 rem. He quoted a paper by Pierce et al in Radiation Research
(1996). In case others are also deceived by that paper, I am sending the
following Letter-to-the-Editor.

THE CANCER RISK FROM LOW LEVEL RADIATION

	Your article by Pierce, Shimizu, Preston, Vaeth, and Mabuchi on
"Studies of the Mortality of Atomic Bomb Survivors........ "(1) contains
the statement "We have considered the question of determination of the
minimum dose dm for which there is a statistically significant dose
response when the analysis is restricted to the range [0,dm].......this is
dm = 0.05 (P=0.02, two-sided test)". This statement seems to imply that
even if we ignore the high dose data, the low dose data standing alone
indicate with 98% confidence, that any dose above 0.05 Sv increases the
risk of cancer. This has been widely interpreted as meaning that if there
is a threshold for radiation induced cancer, that threshold must be below
0.05 Sv (5 cSv or 5 rem) with 98% confidence. Our purpose here is to show
that such a conclusion is not supported by their data, and to calculate
what conclusion their data does support.
	 Let x=mean dose in cSv, Y=excess cancer deaths, SD=one standard
deviation for Y, calculated as the square root of the number of deaths.
Their data for doses up to 0.2 Sv, given in their paper, are as follows:           
		x = 0    Y = -42   SD = 55
		x = 5    Y =  85    SD = 53
		x = 15  Y =  18    SD = 22
This means, for example, that for x = 5, the cancer risk, y, is given by a
gausian distribution centered at y = 85 and with a gaussian width of 53.
Utilizing these data, we calculate the probability for various slopes of a
regression of y on x for these three data points, as follows. For each x
value, we select a y-value randomly from a gaussian distribution centered
at the above-listed Y-value and with a gaussian width equal to SD, and we
calculate the slope of the line of regression through the three resulting
data points. This process of random selection was repeated 100 times. The
distribution of slopes of the line of regression of y on x were:
	-- 25% negative
	-- 8%   negative by more than one standard deviation
	-- 64% positive by less than one standard deviation
	-- 11% positive by more than one standard deviation

	The obvious conclusion from these results is that there is no
statistically meaningful evidence for any dependence of risk on dose in
this region. Since the next data point covers the range 20-50 cSv and is
not highly statistically significant, it is reasonable to say that this
region extends at least up to 25 cSv.  
	This means that the statement by Pierce et al (1996) should be
modified to read dm = 0.25 Sv, and even then, the statistical significance
should be greatly reduced from their stated value. Actually their
statement was based on the assumption of a linear dependence (although
this was not stated) and it is therefore inappropriate to cite it as
evidence in support of a linear theory down to very low dose, a practice
that has been widely used by supporters of the linear-no threshold theory.
	
Reference:

1. D.A. Pierce, Y. Shimizu, D.L. Preston, M. Vaeth, and K. Mabuchi.
Studies of the mortality of atomic bomb survivors, Report 12, Part 1.
Cancer: 1950 1990, Radiation Research 146: 1-27 (1996)



Bernard L. Cohen
Physics Dept.
University of Pittsburgh
Pittsburgh, PA 15260
Tel: (412)624-9245
Fax: (412)624-9163
e-mail: blc+@pitt.edu