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.
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.