RE: Cohen's Ecologic Studies

[epirad@mchsi.com]

Dr. Cohen,



To ignore non-linearity is the root cause of your 

findings. In an ecologic analysis you are limited to a 

summary statistics to adjust for confounding.  Since you 

do not have information on covariates at the county 

level, accurate ratio functions cannot be calculated.  

This becomes very problematic if the data structure is 

non linear (e.g. not everyone in the county smokes 

cigarettes for the same duration and intensity; not 

everyone spends the same amount of time in their home, 

not everyone is exposed to the same radon concentration, 

etc...), and non additive, which is the case at hand.



I believe the onus is on you to show that multiple non-

linear covariates are not the cause of your problem.  

The only way I know you can attempt to do this is use 

the methods of Sheppard and colleagues.



Lubin has demonstrated the problem in a recent paper 

just using smoking.  Your inverse associations are found 

for other smoking related cancers that should not be 

related to radon.  This further strengthens my argument 

that your inability to adjust adequately for smoking is 

driving your findings.  Or do you believe the reason the 

other smoking related cancers also have an inverse 

association with your radon concentrations is because of 

a hormetic response due to alpha radiation exposure to 

the lung?  I find it far more credible that the 

explanation is lack of control of confounding by smoking 

and other factors as Lubin has just demonstrated.



You 1997a) claim that simple linear least squares 

regression of m on S indicates that nearly all lung 

cancer is due to smoking.  However, the results of this 

analysis do not support such a claim.  We repeated the 

regression of lung cancer mortality rates on your 

adjusted smoking percentages.  The resulting R2 values 

indicated that S explains only 23.7% of the variation in 

lung cancer mortality rates among females and 34.5% 

among males.  Puntoni et al. (1995) compared six 

mathematical models relating cigarette smoking to lung 

cancer risk using data from nine large cohort studies.  

They found that 67% of the variation in relative risks 

could be explained by a two-stage model of 

carcinogenesis.  In comparison, very few of the lung 

cancer deaths are explained by your smoking variable.  

Therefore, the smoking variable is inadequate to adjust 

for the effects of smoking.



I will limit further comments on this topic to avoid 

another ecologic marathonic discussion, I will however 

look forward to your letter regarding Dr. Lubin’s recent 

paper.



Bill Field

> 

> 	--Linearity has nothing to do with my analyses. I don't assume

> anything is linear except lung cancer vs radon

> 	--They don't have to show how they affect my results. All I ask is

> that someone suggest a specific confounding factor that might possibly

> affect my results and I will have to prove that it cannot. Is that asking

> for too much?

> 

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