Cohen's January 1995 _Health Physics_ paper

[js_dukelow@ccmail.pnl.gov]

I have been watching the discussions of the linear no-threshold 
hypothesis (LNTH) and the exchanges re Cohen's January 1995 Health 
Physics paper with some interest. 

Cohen is justified in complaining, since the general tenor of comments on 
his paper in RADSAFE was (paraphrasing): "It's only an ecological study, 
so we don't have to deal with it's conclusions."  The problem with that 
sort of comment is that Cohen dealt with it extensively in the paper, 
arguing that an ecological study was adequate for statistical hypothesis 
testing of the LNTH, considered as the null hypothesis.  This places the 
obligation on people raising the comment again to show why Cohen's 
arguments are mistaken.  As I understand Cohen's reasoning: 

        1.  He assumes (but as far as I can find, does not explicitly 
            state) that the radiation dose delivered to the lung of 
            persons occupying a house is a linear function of the 
            measured (usually measured in the basement) radon 
            concentration in the house, implying an equation of the form: 

                Dose2lung = alpha*Radon_conc, 
               
                where alpha is the proportionality coefficient.

        2.  He assumes as the null hypothesis that

                Probability of lung cancer/year = beta*Dose2lung.

            This is just the LNTH dose response assumption.

        3.  If the distribution of radon concentrations in a county is:

                C1, C2, ..., Cn, where n is the number of houses in the 
            county, then 

                Total person dose to lung = 
                     the Sum from 1 to n of (alpha*Ci), and

                Number of lung cancers in the county per year = 
                     the Sum from 1 to n of (beta*alpha*Ci) = 
                     beta*alpha*(the Sum from 1 to n of Ci) = 
                     n*beta*alpha*(the Sum from 1 to n of Ci)/n = 
                     n*beta*alpha*(county average radon concentration).

        4.  Thus, for the linear no-threshold hypothesis, it doesn't 
            matter how the radon concentrations are distributed 
            throughout the county, and it doesn't matter how the person-
            rem total dose is distributed across the population of the 
            county, the same number of lung cancers will be predicted by 
            Cohen's assumption about alpha, plus the LNTH assumption 
            about the dose-response curve (a straight line in this case).  
            Note that the LNTH is the only dose-response assumption for 
            which this assertion is valid.  If you introduce ANY non-
            linearity into the dose-response curve, then the ecological 
            study is no longer formally adequate, and the impact of the 
            non-linearity will have to be assessed in order to decide if 
            the ecological study tells you anything useful. 

A few other comments about Cohen's paper:

1.  I think his assumption about the linear dependence of Dose2lung on 
    household radon concentration is at least approximately accurate.

2.  Cohen states his result in the first two pages of his paper and 
    devotes the remaining 15 pages to statistical evaluation of the 
    impact of a wide variety of possible confounding factors, including:
      
      o   distribution of smoking vs non-smoking,
      o   migration of people from one county to another,
      o   uncertainties in the radon data,
      o   sampling uncertainties,
      o   uncertainties in lung cancer mortality rates, 
      o   uncertainties in smoking prevalence, 
      o   confounding factors that correlate with 54 different socio-
            economic variables,
      o   confounding by combinations of socio-economic variables, 
      o   confounding by geography (since radon concentrations tend to be a 
            function of geographic location), 
      o   Confounding by physical features of geographic location 
            (altitude, summer and winter temperatures, precipitation, 
            wind speed, and amount of sunlight),
      o   effect of recognized correlations between radon concentrations 
            and smoking prevalence,
      o   LNT theories other than BEIR IV, and
      o   constraints on the existence of some unrecognized confounding 
            factor.

3.  Cohen ends the paper with a discussion of the problems with 
    ecological studies, a page of references, and three appendices giving 
    details of computations and descriptions of the 54 socio-economic 
    variables considered. 

4.  Finally, Cohen's analysis of potential confounding factors asserts 
    that the negative correlation between county average radon 
    concentrations and county lung cancers rates is so strong and so 
    striking that it can stand a lot of confounding by other factors, and 
    still leave intact the conclusion that the probability that the LNTH 
    applied to radon dose to the lung is correctly predicting lung cancer 
    rates is vanishingly small.  Or, to state it baldly, the null 
    hypothesis (the LNTH applied to radon-derived lung doses) can be 
    rejected at a high level of significance. 

5.  I can't claimed to have verified all of Cohen's statistical 
    arguments, but I have read through the paper a couple of times in 
    some detail and find Cohen's treatment of possible confounding 
    factors and of complaints about the ecological analysis plausible.
    It seems to me that anyone who wants to reject Cohen's conclusion has an 
    obligation to deal explicity with the details of his analysis.

I may be missing something here, in which case I would be happy to be 
corrected by those who better understand these issues.

Jim Dukelow
Pacific Northwest National Laboratory
Richland, WA

js_dukelow@pnl.gov

These are my opinions and have not been reviewed and/or approved by my 
management or by the Department of Energy.