Re: Linearity of covariates and radon exposure - Concrete "theoretically" plausible explanantion!

[epirad@mchsi.com]

In response to your question, I was referring the Lubin's papers below. 



Lubin J H 2002 The potential for bias in Cohen's ecological analysis of lung 

cancer and residential radon J. Radiol. Prot. 22 141-8 



J. Radiol. Prot. 22 (September 2002) 307-309



LETTER TO THE EDITOR



Reply to Cohen's letter on `The potential for bias in Cohen's ecological 

analysis of lung cancer and residential radon'

Dear Sir



In the above letter, Cohen [1] repeats arguments that he as made in the past; 

however, the thrust of those comments indicates a fundamental misunderstanding 

of the point of my article [2] and indeed of my prior articles on this topic. 

It was not and has never been my goal to identify a specific factor (or several 

factors) that induced the negative correlation between the estimates of county-

level mean radon concentration and county lung cancer mortality rates. Other 

investigators have offered powerful examples, both theoretical and practical, 

that Cohen's results are indeed an artifact of ecological regression [3-9]. The 

primary purpose of my contributions to this topic has been to demonstrate the 

fundamental deficiencies of the methodology itself, in particular the 

unboundedness of the bias [10]. The current article [2] demonstrates that the 

ecological fallacy always applies, that the addition of county-level adjustment 

variables does not reduce bias and increase validity, and that an observed 

ecological risk pattern can differ markedly from the true risk pattern. Because 

of these deficiencies, epidemiologists have never used ecological regression as 

a tool for confirmatory analysis. For radon and lung cancer, results of 25-30 

analytic studies of individuals clearly prove the deficiency of the method.



There are numerous risks factors for lung cancer, including smoking, age, 

various occupational exposures, air pollution, previous lung diseases, and so 

on. In [2], I take an extremely simplified model for lung cancer in radon and 

smoking status, and demonstrate that the induced county-level model is non-

linear. A more realistic, and complex, model for lung cancer would include all 

principal risk factors, and would also generate a non-linear model at the 

county level. Cohen's claims, which are based on his linear (or linear-

quadratic) model for county lung cancer rates, are therefore built on a false 

premise, and his continual reference to the `scientific method' is fatuous. One 

could equally fit and reject a sinusoidal relationship for county lung cancer 

rates and radon concentrations; the factual basis of an inadequate model is 

true, but of little inferential value for evaluating risk.



Given two counties with equal proportions of smokers and equal patterns of 

smoking, I showed that a positive association for radon and lung cancer at the 

individual level can be easily transformed into an observed negative 

relationship between lung cancer rates and mean radon levels at the county 

level through simple manipulations of the within-county correlation between 

smoking and radon [10]. Moreover, the within-county correlations can be 

extremely small, on the order of 0.05 to 0.10 (see table 1 in [10]). The 

current paper [2] extends that two-county analysis, and shows that the reversal 

in trend can be extended to all 1,599 counties in Cohen's regression, even when 

the ecological regression is assumed to perfectly fit the data with no residual 

variation. Those results demonstrate the potential for extreme distortion of 

any ecological regression.



A relatively simple within-county adjustment was needed to show the 

compatibility of Cohen's regression with the BEIR VI extrapolation of risk. 

Contrary to Cohen's view, the vast majority (84 per cent) of within-county 

correlation coefficients for radon and smoking were between -0.3 and 0.3. In 

addition, those correlations are artificially elevated due to measurement 

error. The implicit assumption is that all covariates are measured without 

error. However, it is clear cigarette smoking is very poorly measured. A total 

of 85-90 per cent of all lung cancers are attributed to cigarette consumption, 

while Cohen's smoking variable explains only about 25 per cent of the variation 

in lung cancer rates among counties. Equation (3) in [2] defines the risk-

adjusted radon concentration for a county (denoted w) as represented in the 

true county-level regression. The risk-adjusted mean radon depends on the 

proportion of smokers and the relative risk of smoking for the county. Thus, 

even if errors in smoking status and residential radon concentration were 

independent at the individual level, equation (3) shows that the proportion of 

smokers and w are correlated. Thus, county-level correlations between smoking 

and radon are further distorted by the joint misclassification of two factors.



Finally, as a practical matter, it is worth noting that Puskin has recently 

offered a plausible explanation for Cohen's negative correlation [11] that 

agrees with the possible role of correlated errors. Puskin conducted ecological 

regressions of radon and smoking for several strongly smoking-related cancers 

(cancers of the lung, oesophagus, larynx, nasopharynx and oral cavity), weakly 

smoking-related cancers (cancers of the bladder and pancreas) and cancers 

unrelated to smoking (cancers of the colon, breast and prostate). He found 

strong negative correlations between county radon concentrations and cancers 

strongly linked to cigarette smoking, weaker correlations between radon and 

cancers weakly associated with smoking, and essentially no correlation between 

radon and cancers not linked to smoking. Puskin concludes that the negative 

trend reported by Cohen for lung cancer is very likely explained by a negative 

correlation between smoking and radon levels across counties.



Yours faithfully,



J H Lubin

Below is the reference list for this article:

Reply to Cohen's letter on `The potential for bias in Cohen's ecological 

analysis of lung cancer and residential radon'

J H Lubin 2002 J. Radiol. Prot. 22 307-309



HyperCiteŽ linking technology enables you to link to abstracts, preprints or 

full text of referenced articles. Links to full text articles from IOP and 

other publishers are displayed in bold type (access is subject to subscription 

status). More information on reference links is available.



[1] Cohen B L 2002 Response to `The potential for bias in Cohen's ecological 

analysis of lung cancer and residential radon' J. Radiol. Prot. 22 305-7 



[2] Lubin J H 2002 The potential for bias in Cohen's ecological analysis of 

lung cancer and residential radon J. Radiol. Prot. 22 141-8 



[3] Greenland S 1992 Divergent biases in ecologic and individual-level studies 

Stat. Med. 11 1209-23 



[4] Greenland S and Robins J 1994 Invited commentary: ecologic studies - 

biases, misconceptions, and counterexamples Am. J. Epidemiol. 139 747-60 



[5] Morgenstern H 1995 Ecologic studies in epidemiology: concepts, principles, 

and methods Ann. Rev. Public Health 16 61-81 



[6] Muirhead C R, Butland B K, Green B M R and Draper G J 1991 Childhood 

leukaemia and natural radiation (letter) Lancet 337 503-4 



[7] Piantadosi S, Byar D P and Green S B 1988 The ecologic fallacy Am. J. 

Epidemiol. 127 893-904 



[8] Stidley C A and Samet J M 1994 Assessment of ecologic regression in the 

study of lung cancer and indoor radon Am. J. Epidemiol. 65 234-51 



[9] Smith B J, Field R W and Lynch C F 1998 Residential Rn-222 exposure and 

lung cancer: Testing the linear no-threshold theory with ecologic data Health 

Phys. 75 11-7 



[10] Lubin J H 1998 On the discrepancy between epidemiologic studies in 

individuals of lung cancer and residential radon and Cohen's ecologic 

regression Health Phys. 75 4-10 



[11] Puskin J S 2002 Smoking as a confounder in ecological correlations of 

cancer mortality rates with average county radon levels Health Phys. at press  



-----------------------------------------

> On Wed, 25 Jun 2003 epirad@mchsi.com wrote:

> 

> > You asked for a concrete theoretical explanation for what was casuing your

> > inverse association - I provided it.   If I perform it, it is no longer

> > theoretical.

> 

> 	--I don't ask you to perform any analyses. I only ask for a

> concrete hypothetical example. I can't dig out anything specific from the

> Lubin paper, so I ask that you just be specific about what you are

> referring to. I don't now remember what Lubin paper you are referring to.

> 

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