Censored binomial models

Oh, this is actually the first time I’d heard of a Bradley-Terry model! My hunch is that it would likely end up being the same since the censoring in a censored binomial is handled by summing up PMFs (CDF) of censored observations, so it should be equivalent to a Bradley-Terry model in the same way standard logistic regression is.

One thing that’s easier to use (since there isn’t a whole lot of support for censored binomial models) is a censored Poisson (you would use the log of N as an offset), which is implemented in more packages (mgcv, brms, INLA, and probably others as well). You would need to use robust standard errors to rectify the CIs (which I was planning to do anyway since I have a few clusters) and you would need to be okay with RRs rather than ORs as the default contrast.