I've been trying to search in the literature to see whether it makes sense to adjust for the variables I used to create matched pairs. To give context, I have a population of schizophrenia patients and a population of "general health" patients. I conducted a 1:1 matching of schizophrenia patients and general health patients, matching on age (within 5 years), sex, and race. Now, I have a dataset of about 90,000 patients, with 45,000 matched pairs.
I want to run logistic regression models and want to quantify the effects of age, sex, and race on my outcome variables and therefore want to throw them into my generalized estimating equations (GEE) or my mixed effects models (with a random effect for each matched pair). However, I was wondering if this makes sense to do, since I've already matched on those demographic variables. What's interesting is that when I add in those variables, they are statistically significant. I understand that age can still be a confounding factor, since it's not an exact match, but sex and race were exact matches, yet I saw multiple instances where they were significant.
Is this because while the within-pair differences may not be significant, the between-pair differences are? Any insight on this would be greatly appreciated!