Letter to Editor

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

	Since I posted a preliminary version of this Letter to the Editor
of Radiation Research and there have been several changes, I post the
final form here;

THE CANCER RISK FROM LOW LEVEL RADIATION

	Bernard L. Cohen
	University of Pittsburgh
	Pittsburgh, PA 15260

Dear Sir:
	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 unqualified statement in an
early section on results 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. It has also been  interpreted by many, including
the Chairman of ICRP (2) and the Chairman of the ICRP Committee  on
Analysis of Health Effects Studies (3), as supporting the linear-no
threshold theory of radiation carcinogenesis at least down to that low
dose. Our purpose here is to show that such a conclusion is not supported
by the data in Ref. (1), and to calculate what conclusion their data does
support.
	 Let x = mean dose in cSv, Y = excess cancer deaths per 1000
expected (to normalize for number of subjects exposed to each dose), SD =
one standard deviation for Y, calculated by taking the standard deviation
of the number of cancer deaths as the square root of that number. The data
in Ref. (1) for doses up to 0.2 Sv, are as follows:           
		x = 0    Y = -13.7   SD = 18.0
		x = 5    Y =  31.4    SD = 19.5
		x = 15  Y =  37.0    SD = 46.1
This means, for example, that for x = 5, the estimated cancer risk, y, has
a probability distribution given by a gausian distribution centered at y=
31.4 (in relative units) and with a gaussian width of 19.5. Utilizing
these data, we calculate the probability for various slopes of a
regression of y on x (which is the slope of the dose-response
relationship) 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 200 times. For
41 of these 200 cases, the slope of the line of regression of y on x was
negative. Thus, based on the data as presented, there is about a 20.5%
probability that the slope of the dose resonse relationship in this dose
region is negative. 
	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 up to about 25 cSv. In this region, the data are not
inconsistent with a zero slope, or even with a negative slope (hormesis).
There would be no difficulty in joining a line with such slopes smoothly
to the higher dose data.  
	Therefore, if a linear theory is not assumed, the statement by
Pierce et al (1) should be modified to read dm = 0.25 Sv, and even then,
the statistical significance should be greatly reduced from their stated
value. Actually, it is clear from a careful reading of Ref. (1) and from a
follow up Letter-to-the-Editor (4) that their statement was based on the
assumption of a linear dependence, and it is therefore inappropriate to
cite it as evidence in support of a linear theory down to very low doses,
as is done in Ref. 2 and 3.
	
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)
2. R. Clarke. Address at Massachusetts Institute of Technology, December
8, 1997
3. W. Sinclair, quoted in Nucleonics Week 37 (46), November 14, 1996 
4. D.A. Pierce, Y. Shimizu, D.L. Preston, M. Vaeth, and K. Mabuchi.
Response to the letter of M.P. Little. Radiation Research 148:
400-401 (1997)
								Sincerely
Yours,


								Bernard L.
Cohen


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