When assessing many potential confounders, do you analyze each separately, then add those with CIE >10% in the final model? Let's say my predictor is X, my outcome is Y, and a have say 5 potential confounders (Z1 up to Z5), and all of my variables are binary.  I am using Stata for my analysis.
I have already ran the crude analysis (i.e., logistic Y X).  When assessing for confounding using the change-in-estimate (CIE) criterion, do I analyze each confounder individually (i.e., logistic Y X Z1; logistic Y X Z2; ... logistic Y X Z5), then see if the odds ratio for each has a CIE > 10%?  And those individually-assessed confounders with CIE > 10% will be the only ones included in the final model.
Is this approach wrong?
 A: Yes, the whole approach is wrong. The CIE criterion is invalid itself, but it also makes any resulting p-values from the final model invalid. The way to choose whether a covariate should be adjusted for is by consulting a substantively-informed graph of the causal structure of the variables. Any variables that cause both the focal predictor and the outcome are confounders and should be adjusted for. Any variable caused by the focal predictor should not be adjusted for. These are not statistical criteria, but rather causal criteria.
A problem with the CIE criterion is that due to the noncollapsibility of the odds ratio, the estimates may change even if the variable isn't a confounder. It is also possible that a variable needs to be adjusted for even if it doesn't induce a change in the estimate (i.e., to prove to readers you correctly adjusted for known confounders). Also, any behavior observed in the "individual" models may not reflect behavior in an overall model, so the individual models tell you very little.
It's also worth noting that the interpretation of the effect of X depends on which covariates are in the model. You should choose an adjustment set or statistical method that aligns with your desired interpretation. FOr example, if you decide to do inverse probability weighting instead (e.g., using teffects ipw), the interpretation of the treatment effect is different than the coefficient on X in a covariate-adjusted logistic regression.
