I have run multiple imputation using MICE. I would now like to run a Cox model on it (using with,pool), and make sure that is justified. That is, I need to make sure that the proportional hazards assumption holds for the pooled model, and as well, to make sure that hazards are constant over time.
How can I go about actually verifying that this is the case? I've proposed two methods, but I don't think that either are correct.
Method 1: "stack" my multiple imputations as in here using "complete". Basically, I get one long dataset, and run this as if we have one dataset. I can check the assumptions on this dataset. I don't think this is right though. When checking the variance of the fitted parameters, it was extremely low, leading me to believe that there may be more problems in addition to this, and I also doubt the validity of it.
Method 2: Run model checks on each individual imputed data set. I could see if the assumptions hold for each individual dataset, but I am not sure if the assumptions holding individually implies that they will hold all together.
Method 3: Average the imputed values to obtain one dataset of the original size. This is certainly wrong because this would discard all of the work we did for multiple imputation (and would be akin to just single imputation).
This question was partially answered here, and the answer seems to check each set individually (option 3) but it doesn't give any theoretical justification as to why this will actually work for it in total.
Are my concerns valid? And is there a more correct way to check the assumptions?
1) I read chapter 6 in Stef van Buuren's Flexible imputation of missing data. It echoed my concerns.
On page 153, he states that "stacking" will yield unbiased point estimates, but inferences on that will not be valid because of the large sample size (which I also assume implies that the variance is too low)
As well, he states that averaging the data makes it similar to single imputation, which is pretty much what I said.
It looks like method two is the winner by default, but I'm still looking for a justification as to why. I'll keep y'all updated should I find out.