I am wondering if it is appropriate to use the term "multiple comparison problem" when applied to multiple imputation. I know that the multiple comparison problem arises when we have one set of data and ask many questions about it. Is this theoretically the same thing as having multiple data sets, and asking the same question on each dataset?
The reason I ask is because I have a MI dataset, and want to run a log rank test on each of the 50 datasets, but I don't believe that running the test on each dataset and then pooling is valid (because of the multiple comparison problem).