Mediation vs Confounding [was: Introducing a 3rd variable makes the correlation coefficient non-significant. What's happening?]



Bill H wrote:
Bruce Weaver wrote:

That sounds like confounding to me. Here are some notes that might be
helpful.

www-personal.umich.edu/~bobwolfe/560/review/kkm13confoundeffectmodify.txt



Bill H:

Or it could be that C mediates the effect of A on B, which is
statistically indistinguishable from confounding. You could test for
the significance of the "indirect effect" which is the product of the
path coefficients from A->C and C->B. Bill H, MS, Wash U School Med,
St Louis

http://www.public.asu.edu/~davidpm/ripl/mediate.htm

Bills comment about mediation and confounding reminded me of some reading I did on that topic last year. One of the sources I consulted while trying to sort it out was this set of notes by Dave Howell.

www.uvm.edu/~dhowell/gradstat/psych341/lectures/MultipleRegression/multreg3.html

When I read Howell's explanation of mediation, I was a little hard-pressed to distinguish it from "confounding". So I did a little more searching, and landed on another site that gave these definitions:

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Confounding

This is similar to bias and is often confused. However, whereas bias involves error in the measurement of a variable, confounding involves error in the interpretation of what may be an accurate measurement. A classic example of confounding is to interpret the finding that people who carry matches are more likely to develop lung cancer as evidence of an association between carrying matches and lung cancer. Smoking is the confounding factor in this relationship- smokers are more likely to carry matches and they are also more likely to develop lung cancer.

What is a confounder?

A confounder is a factor that is prognostically linked to the outcome of interest and is unevenly distributed between the study groups. A factor is NOT a confounder if it lies on the causal pathway between the variables of interest. For example, the relationship between diet and coronary heart disease may be explained by measuring serum cholesterol level. Cholesterol is not a confounder because it may be the causal link between diet and coronary heart disease.

That was downloaded in October 2005 from _www.faem.org.uk/site/research/technical_guide/techpages/biasconfound.htm_

PLEASE NOTE: THAT SITE NOW HAS NOTHING BUT LINKS TO OTHER SITES, INCLUDING ONE WHERE YOU MIGHT BE ABLE TO PURCHASE THE DOMAIN faem.org.uk, SO DON'T WASTE YOUR TIME GOING TO IT!

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If I understand all of that, the distinction between a confounder and a mediator is that the latter falls on a suspected* causal pathway between X and Y.

* Notice that I changed "on the causal pathway" from the webpage to "on A SUSPECTED causal pathway". IMO, "on the causal pathway" is far too strong a statement, because it suggests that there is just one cause, and that it is known. But many things we study have multiple causes. I say "suspected cause", because in observational studies, we can't establish causation conclusively.

Question: Is this how others understand the distinction between mediation and confounding?

I suppose that if that is the only distinction, they would be statistically indistinguishable, as Bill H stated.

One other observation. The Kenny's and MacKinnon's of this world promote tests of mediation. With regard to confounding, on the other hand, I think the traditional stance is that one should not test for it. Bob Wolfe certainly takes that view in his notes on confounding and effect modification--the title of section C is "Testing for confounding (don't do it)".

http://www-personal.umich.edu/~bobwolfe/560/review/kkm13confoundeffectmodify.txt

Cheers,
Bruce

--
Bruce Weaver
bweaver@xxxxxxxxxxxx
www.angelfire.com/wv/bwhomedir
.



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