RE: Cohen's Ecologic Studies

[epirad@mchsi.com]

Dr. Cohen,



It is clear you do not understand the points I am trying 

to make. If you really believe that non linearity of 

confounding has nothing to do with your findings than 

there is no point to continue this dialogue.  After all, 

it is not the first time we agreed to diagree.  I think 

we can both agree on that.



Lubin has recently given you an example of the problem, 

there is no need for me to repeat it.  



J. Radiol. Prot. 22 (June 2002) 141-148



The potential for bias in Cohen's ecological analysis of 

lung cancer and residential radon



Jay H Lubin



Biostatistics Branch, Division of Cancer Epidemiology 

and Genetics, National Cancer Institute, EPS/8042, 6120 

Executive Blvd, Rockville, MD 20892-7244, USA



Abstract. Cohen's ecological analysis of US lung cancer 

mortality rates and mean county radon concentration 

shows decreasing mortality rates with increasing radon 

concentration (Cohen 1995 Health Phys. 68 157-74). The 

results prompted his rejection of the linear-no-

threshold (LNT) model for radon and lung cancer. 

Although several authors have demonstrated that risk 

patterns in ecological analyses provide no inferential 

value for assessment of risk to individuals, Cohen 

advances two arguments in a recent response to Darby and 

Doll (2000 J. Radiol. Prot. 20 221-2) who suggest 

Cohen's results are and will always be burdened by the 

ecological fallacy. Cohen asserts that the ecological 

fallacy does not apply when testing the LNT model, for 

which average exposure determines average risk, and that 

the influence of confounding factors is obviated by the 

use of large numbers of stratification variables. These 

assertions are erroneous. Average dose determines 

average risk only for models which are linear in all 

covariates, in which case ecological analyses are valid. 

However, lung cancer risk and radon exposure, while 

linear in the relative risk, are not linearly related to 

the scale of absolute risk, and thus Cohen's rejection 

of the LNT model is based on a false premise of 

linearity. In addition, it is demonstrated that the 

deleterious association for radon and lung cancer 

observed in residential and miner studies is consistent 

with negative trends from ecological studies, of the 

type described by Cohen.



URL: stacks.iop.org/0952-4746/22/141



Regards, Bill Field

> 

> On Tue, 4 Jun 2002 epirad@mchsi.com wrote:

> 

> > Dr. Cohen,

> >

> > To ignore non-linearity is the root cause of your

> > findings.

> 

> 	--Linearity of confounding factors has no relevance to my study

> 

>  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.

> 

> 	--Why can't you make up a specific numerical example?

> 

> 

> > 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.

> 

> 	--Why can't you make up a specific numerical example and show how

> it can affect my results?

> 

> >

> > 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.

> >

> 

> 	--I never assume anything is linear, except lung cancer vs radon.

> I need a numerical example to understand what you are talking about.

> 

> > Lubin has demonstrated the problem in a recent paper

> > just using smoking.

> 

> 	--My papers give examples of how errors in smoking can explain my

> results, but then I show that the required correlations are completely

> implausible. Lubin never addresses the issue of plausibility.

> 

>  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 have addressed this in previous messages

> 

>  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.

> >

> 	--In BEIR-IV, smoking is not a confounder. Smokers and non-smokers

> are treated as entirely different species.

> 

> 

> > 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 have addressed the R-squared issue previously and shown that

> it is irrelevant

> 	--I have also shown that any choices of the smoking prevalences in

> the various counties that are not completely implausible would not affect my 

> results.

> 

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