When using regression models with a binary exposure, how do you choose whether to adjust for a confounders as covariates or to match the two exposure groups according to the confounders and then performing univariate regression?
I appreciate there are issues with practicality, such as how many covariates there are and how easy it is to match them (eg categorising a bunch of continuous covariates is not ideal) etc.
For simplicity, let's say it's a prospective cohort study, the outcome is binary, exposure is binary, and there is just one confounder, age. You could use logistic regression adjusting for age as covariate, or match by age and then compare proportions of the outcome according to exposure. Practicality aside, what's the reason to chose one or the other?
I have a feeling the answer is to do with how much the distribution of the confounder, in this case age, overlap between exposure groups, but do not have a formal understanding of why one would chose one or the other method.
This article, for example, performs the analysis using both methods, except the covariates were, confusingly, different for each method.