Censored binomial models

The derivation of the censored likelihood looks correct, but I wonder in this case, because the physicians have to choose it might be best to approach it via a Bradley-Terry/discrete choice type model. I known in the uncensored case Bradley-Terry ends up being equivalent to logistic regression, provided the winner/binary coding is kept consistent. I wonder if the consistency holds for the “win m of n” trials when censoring is present. This might be one of the cases where it’s worth it to go through the combinatorics and derive the appropriate pmf probabilities directly.