Confounders and Coincidences - Numerical Examples

[epirad@mchsi.com]

Dr. Cohen,



Your response 



"If there is a problem, please give me a concrete numerical example (made-up 

is fine)."



confirms our (Field, R.W., Smith, B.J., and Lynch, C.F.) view we wrote in 

Cohen’s Paradox, Health Physics 77(3): 328-329,1999.



A quote from that letter published in the Health Physics Journal states, 

"Cohen has not accepted the fact that it may be impossible to explain Cohen's 

Paradox in definitive analytical terms with his existing data because it is 

not always possible to identify empirical sources of ecologic bias from 

aggregate (ecologic) data alone (Field et al. 1998a)."



I don't know if you recall, but subsequently I contacted you directly and 

others discussed it on the list



http://www.vanderbilt.edu/radsafe/0201/msg00923.html



that you may be able to explain your findings if you wanted to improve your 

analyses by following the examples of papers such as:  



Journal of the Royal Statistical Society: Series A (Statistics in Society)

Volume 164 Issue 1 Page 141  - 2001 

  

Overcoming biases and misconceptions in ecological studies 



Katherine A. Guthrie1 & Lianne Sheppard 1

 

The aggregate data study design provides an alternative group level analysis 

to ecological studies in the estimation of individual level health risks. An 

aggregate model is derived by aggregating a plausible individual level 

relative rate model within groups, such that population-based disease rates 

are modelled as functions of individual level covariate data. We apply an 

aggregate data method to a series of fictitious examples from a review paper 

by Greenland and Robins which illustrated the problems that can arise when 

using the results of ecological studies to make inference about individual 

health risks. We use simulated data based on their examples to demonstrate 

that the aggregate data approach can address many of the sources of bias that 

are inherent in typical ecological analyses, even though the limited between-

region covariate variation in these examples reduces the efficiency of the 

aggregate study. The aggregate method has the potential to estimate exposure 

effects of interest in the presence of non-linearity, confounding at 

individual and group levels, effect modification, classical measurement error 

in the exposure and non-differential misclassification in the confounder.



Have you followed up on that suggestion?

 

Also of interest in the same issue:



Journal of the Royal Statistical Society: Series A (Statistics in Society)

Volume 164 Issue 1 Page 205  - 2001 

  

A parallel analysis of individual and ecological data on residential radon and 

lung cancer in south-west England 



Sarah Darby1, Harz Deo1, Richard Doll1 & Elise Whitley2 



Parallel individual and ecological analyses of data on residential radon have 

been performed using information on cases of lung cancer and population 

controls from a recent study in south-west England. For the individual 

analysis the overall results indicated that the relative risk of lung cancer 

at 100 Bq m3 compared with at 0 Bq m3 was 1.12 (95% confidence interval (0.99, 

1.27)) after adjusting for age, sex, smoking, county of residence and social 

class. In the ecological analysis substantial bias in the estimated effect of 

radon was present for one of the two counties involved unless an additional 

variable, urban-rural status, was included in the model, although this 

variable was not an important confounder in the individual level analysis. 

Most of the methods that have been recommended for overcoming the limitations 

of ecological studies would not in practice have proved useful in identifying 

this variable as an appreciable source of bias.

 

Regards, 

Bill Field

epirad@mchsi.com







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

> On Thu, 8 May 2003 epirad@mchsi.com wrote:

> 

> >

> > Yes, using ecologic data to control confounding is helpful sometimes.  In

> > fact, it does help especially if there are not large inter and intra county

> > non linear effects.  However, we know without question that these non linear

> > sources of confounding and effect modification exist in Dr. Cohen's data.

> 

> 	--If there is a problem, please give me a concrete numerical

> example (made-up is fine).

> 

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