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I have a multiple regression where I have been asked to consider two exposure measures (say X1 and X2) and outcome Y.

The overall aim of the analysis is to examine the evidence for an association between Y and the two exposure measures using regression methods.

There are four potential confounders (C1, C2, C3, C4).

How can I check that the adjustment of the potential confounders affect the associations between the exposures of interest and Y.

Charlotte
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  • Welcome to the site. How many observations do you have? If you have enough, you can just include them all in the model. – Frans Rodenburg Oct 29 '19 at 07:39
  • Thank you @FransRodenburg I have 239 observations. My understanding is that if I had only one exposure measure, I would run a simple linear regression, and then run another regression adjusted with a potential confounder to see if there has been at least 10% change. How do I check for confounding if I have two exposure measures? Thank you. – Charlotte Oct 29 '19 at 07:46
  • Do you run into any troubles running `lm(Y ~ X1 + X2 + C1 + C2 + C3 + C4)`? If you include potential confounders in the model, they do not confound the effects of `X1` and `X2` on `Y`. – Frans Rodenburg Oct 29 '19 at 07:48
  • @FransRodenburg It's possible that not all of them confound the effects of X1 and X2 with Y. I'm unsure what to look for. Thanks. – Charlotte Oct 29 '19 at 07:58
  • I'd say you have more than enough samples to include them all. Sure, including a nuisance variable that does not actually confound the effect of interest does not *improve* the estimation of the effect of interest, but unless they are [mediators](https://en.wikipedia.org/wiki/Mediation_(statistics)), there is little harm in including them (but much to be gained by preventing potential confounding). – Frans Rodenburg Oct 29 '19 at 08:09
  • Related: https://stats.stackexchange.com/a/314648/176202 – Frans Rodenburg Oct 29 '19 at 08:11

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