Can I include covariates outside of the minimally sufficient set in a causal framework that aren't in the causal pathway?

Question

I am applying a causal method to a cohort study analysis on pollutant exposure and disease X. Based on our understanding of the disease, we believe that aging is the only confounder.

From what I understand, age would be the item in our minimally sufficient set required to evaluate the outcome/exposure relationship.

Assuming all other causal assumptions are met, does the minimally sufficient set represent the only variable that should be included in the model outside of the exposure?

Could I still include covariates like smoking history and gender that effect the outcome versus age which effects the outcome and the exposure?

Please help! I can’t seem to find anything conclusive online. I want to include the other covariates because I feel their effect sizes contextualize the effect of the exposure.

Answer 1

Yes, you can add additional variables to your analysis. They will either be good, neutral, or bad, depending on the causal structure of your problem.

I strongly recommend the paper A Crash Course in Good and Bad Controls by Cinelli, Forney, and Pearl, for a comprehensive classification of possible cases.

Your description of gender and smoking status affecting only the outcome seems to comply with model 8 in the paper. These are, in general, good variables to add, since they will help explaining the variance of the outcome, therefore reducing the variance left for the treatment to explain - practically increasing the precision of the treatment effect estimation.