# Does conditional logistic regression effectively “throw away” concordant pairs like McNemar's test?

We are interested in analyzing pre-post data from a randomized control trial. The outcome is binary and I am trying to explain the heuristics of the model formulation for conditional logistic regression. I am not working with likelihoods per se but I want to be sure I correctly understand the appropriate model justifications.

In conditional logistic regression we are working with a probability model for the post event conditional upon what is seen in the pre-event. Like McNemar's we can think of 4 cases and the evidence presented:

1. Treated: Baseline negative, follow-up positive: Evidence for efficacy of intervention
2. Treated: Baseline positive, follow-up negative: Evidence against efficacy of intervention
3. Control: Baseline negative, follow-up positive: Evidence against efficacy of intervention
4. Control: Baseline positive, follow-up negative: Evidence for efficacy of intervention

But I am positing that because the baseline assessment is used to inform the risk of the follow-up event through conditioning, that we extract more information. Concordant pairs still contribute something to the likelihood.

My question is:

1. is this argument above valid?
2. How is this different from adjusting for baseline assessment as a covariate in a logistic regression model?