I am using Stata for a survival analysis project involving inverse probability weighting (IPW). The question has arisen as to how to analyze weighted continuous data between two groups with a Wilcoxon rank sum test? Is this easily implemented in any other package?
There may be an easy way to do this, but it's not obvious to me what that would be. The Wilcoxon test sort of implicitly gives equal weight to each of the observations because it relies on the randomization distribution for the null hypothesis.
One possibility may be to do a bootstrapping sample from your data with the new probability weights rather than the uniform distribution and calculate the Wilcoxon statistic on that, but you would have to do the math on what the large sample variance of that statistic is. That might be something you could work out in an afternoon, but I don't think it's trivial.
Another option is that you could use a difference in means test instead of the Wilcoxon, though the variance of that with the new weights is not trivial either and it may be intractable for survival data.
This is a tough problem.