Re: Cohen's Fallacy

[RuthWeiner@AOL.COM]

Ok maybe my question wasn't clear to Don who tried to answer it, so let me try again.  First some definitions I use: a positive correlation between smoking and radon means ( to me) either that people who smoke get more radon exposure than people who don't smoke, or that people who get high radon exposure are more likely to be smokers than people who get low radon exposure.  A negative correlation, on the other hand,  means ( to me) either that people who smoke get LESS radon exposure than people who don't smoke, or that people who get high radon exposure are LESS likely to be smokers than people who get low radon exposure.


I don't see how a negative correlation could even be possible, let alone demonstrated, and it is not what Dr. Cohen's papers demonstrated (if I remember correctly).  What Cohen's paper demonstrated was that THERE WAS NOT A POSITIVE CORRELATION BETWEEN LUNG CANCER AND RADON EXPOSURE.  (Once again, a positive correlation would mean more radon exposure, more lung cancer; a negative correlation, the opposite).  The graphs appear to show a negative correlation, but that is not even what Cohen claimed.


I have not yet received Dr. Field's papers (I have requested them).  Moreover, I am neither an epidemiologist nor a statistician (though I am probably as knowledgeable about both as decision makers at EPA), but it just seems to me that if we are trying to find some sort of relationship between lung cancer and radon exposure (NOT between smoking and radon exposure), it is necessary to determine the following:


1.  How much radon a given population is exposed to.

2.  How many lung cancers are observed in that population.

3.  IN THAT PARTICULAR POPULATION, how many smokers (ever-smokers) there are and what is the average amount  (and distribution) of the smoking they did (e.g., years and packs per year).

4. How many of the observed lung cancers occurred in smokers.

5.  Subtract the observed lung cancers in smokers from the total observed lung cancers.  

6.  Look at whatever relationship exists between radon exposure and the remaining lung cancers (those that occurred in non-smokers).   It is also necessary to look at the secondary smoke exposure in non-smokers, since secondary smoke is also a pretty well extablished carcinogen.


Maybe this is what Field et al did -- I will have to get their papers and see.  But it seems to me that applying some kind of statistical correction for smoking that says, in effect, since the national risk of lung cancer from smoking is x, and the national (or statewide) fraction of smokers is y, then x*y *observed lung cancers are attributable to smoking and the rest to radon, doesn't really cut it.   All that would tell you is the fraction of lung cancers that MIGHT be attributed to smoking.


Moreover, how should radon exposure be measured?  Combining radon measurements with the fraction of time women on the average are at home, and then looking at lung cancers in women, is pretty imprecise.  I got more radon exposure at work than at home, because I have worked for 12 of the last 20 years in places where I couldn't open the windows and depended on artificial ventilation. 


I have tried to restate this whole problem in words the way I understand it.  As a former colleague (and economics professor) at WWU once put it: statistics are like a bikini, in that they show what you want to show and hide what you want to hide.



Ruth Weiner, Ph. D.

ruthweiner@aol.com