Re: Dose-response threshold from A-bomb survivor data

[John Goldsmith <gjohn@bgumail.bgu.ac.il>]

Professor Cohen:
     You may have come to a reasonable conclusion, but the use of Gaussian
assumptions on difference data can lead to instable results.  The Y values
you use are differences between observed and expected cancer ( presumably
rates ).  This is confirmed by the negative Y for the lowest exposure.
This problem can be obviated I think, by using actual observations. I
suggest you consult a good mathematical statistician at Pitt.  
                    John Goldsmith  gjohn@bgumail.bgu.ac.il

On Tue, 16 Dec 1997, Bernard L Cohen wrote:

> 	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
> 
>