Ideal method for confounder adjustment

Question

I have a fairly large dataset (15,000) in which I assessed the association of a three-level categorical risk factor to the outcome. The outcomes were significantly different for the three levels. Subsequently I tested the impact of a pre-specified confounder (which is on an ordinal scale, 10 levels, unequal samples in each group) in a regression model that substantially attenuated the first association (as determined by model coefficients).

My question is: Is it appropriate to also stratify the comparisons by the various levels of the potential confounder? It seems simpler to understand for a general audience. My concern is that I would need to resort to multiple hypothesis testing for each of these ten groups based on the various ordinal levels. The sample sizes are reasonable for this approach (> 500 in each comparison), although they are unequal.

Thank you in advance!

Answer 1

If your confounder is an effect modifier (i.e., the treatment effect varies across its levels), then it is important to stratify based on the confounder. A single treatment effect doesn't tell the whole story.

If your confounder is not an effect modifier, you can still stratify based on the confounder, but rather than present a separate effect estimate for each level, you can compute a marginal effect, which is a weighted average of the stratum effects (where the weights are the proportion of individuals in each stratum). This way, you can present a single effect estimate to your readers, you don't have to consider multiple comparisons, and you still address the bias due to the confounder.

This latter method is called "standardization" or the "g-formula" in the epidemiology literature. You can still perform standardization in the presence of effect modification, but you need to ensure your readers understand that the marginal effect is generalizable only to a population with the same proportion of individuals in each level of the confounder.