Interesting, and this may be helpful. In this case, I would view each patient as a trial, each readmission as an event, surgeon as the "experimental unit" and year as a repeated effect if and only if surgeons are measured in each year. The contralateral surgeries can be regarded as independent for an initial analysis. Depending on the number of these, they might be repeated, but for a first analysis, try considering each surgery as a separate trial. How many surgeons are observed in all years, and how many years are included in the data? The answers to those questions could lead to a simpler model that uses the binomial distribution rather than the binary distribution.
SteveDenham
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