Thanks for you reply! Allow me to clarify a little bit. The issue is that I am looking for the confidence interval for the percent difference in hazard ratio. I calculate this in the main sample by first running the crude model using proc phreg and saving the output, then running the adjusted model and saving the output. Then I merge the saved output from both models and calculate the difference using the formula which I posted above. Since this requires multiple steps, I have not figured out how to calculate the bootstrap confidence intervals for this difference in hazard ratio. The examples that I find in SAS are based on a statistic that SAS can directly return in one proc step, which I don't think is possible in my case. In the Stata example that I linked to above, there is a command that seems to repeat the whole process (crude model, adjusted model, HR difference) using bootstrap sampling, but I have not found a way to do this in SAS.
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