Interactions versus Confounding

Lead Author(s): Jeff Martin, MD

Confounding vs Interaction

How do confounding and interaction differ?


An extraneous or nuisance pathway that an investigator hopes to prevent or rule out

Confounding is an extraneous pathway that we want ro rule out or preclude Interaction:

A more detailed description of the relationship between the exposure and disease

A richer description of the biologic or behavioral system under study

A finding to be reported, not a bias to be eliminated

Interaction, however, when present, is a more detailed description of the biological or behavioral system under study. When interaction is present, the issue of confounding becomes irrelevant.

Reporting or Ignoring Interactions

When to report or ignore interaction is not clear cut and we can give no absolute rules for this. When to report or ignore is a clinical, statistical, and practical decision.


Clinical: Is the magnitude of stratum-specific differences substantively (clinically) important?

*By clinical, we mean that we have to look at the magnitude of the stratum-specific differences. Differences that are so small to be of very little relevance from a clinical or biologic perspective are not worth reporting. In contrast, very large differences are really telling us something clinically and we should want to report these.


* By statistical, we mean that we need to look at the p value and confidence intervals, but what p value should we use? There are inherent limitations in the statistical power of tests of homogeneity. Only relatively large magnitude of difference between stratum-specific estimates or large sample sizes can achieve p values of less than 0.05. Hence, it may be worthwhile to use a higher threshold - not for declaring statistical significance of interaction but for when deciding when to report stratum-specific estimates as opposed to pooling them. It should be emphasized that we are not condoning a different cut off of statistical significance for tests of interaction as if to say that they are fundamentally different than any other hypothesis testing. They are indeed interpreted just like any other p value.


Practical: How complicated is the story? i.e., if it is not too complicated to report stratum-specific estimates, it is often more revealing to report potential interaction than to ignore it.

* Finally, from a practical perspective, the question is just how complicated is it to report stratum-specific estimates individually instead of just one number which would apply for all strata. If there are 10 different strata to report on, this could make for a complicated message. On the hand, if there are just two strata, then it is probably worthwhile to report this than ignore it.

Guidelines for Reporting vs Ignoring Interactions

The table below looks at several examples to get a feeling for when we should report, rather than ignore interaction. You'll see that this an art form and requires consideration of both clinical and statistical significance.


Let's say we are looking at the association between a given exposure and a given disease and we have to then look at the effect of a potential effect modifier that has two levels: present and absent.

No Report - Chance As a Cause of Interaction

Does every time the stratum-specific estimates differ indicate that we have interaction going on and that we should not adjust for the third variable but rather that we should declare that interaction is present and report all the stratum-specific estimates? The example of sperimicide use and Down Syndrome looks at the association of these two variables and the influence of age on this association. There is a reasonable differences in the ORs in the two strata, but look at the sample sizes.