How to statistically compare two groups with one of them being repeatedly resampled? Supposed I have two groups of patients' response to different treatment A and B, with sample size of B greatly larger than A. To control for same age distribution of patients and also equal sample size, I repeatedly resample from B to construct B'. What statistical test should I use to demonstrate treatment B is better than A (B > A)?
Can I use the difference of mean(or median)A and B' of every repeation and compared to zero?

I'm not completely sure if this answer makes sense from a statistical point of view but, I would:

*

*Get all the cases from B that match the age interval of A (if age is a concern/confounding);

*If you still have a big difference regarding the sample size, subsample B to get the same sample size as A and compare it, both using an effect size measure and p-value;

*Repeat the previous step some times (depending on how many subsamples of B you can produce);

*Check the distribution of p-values and effect size. Ideally, the first will have a majority of values of 0.05, while the effect size should be different from 0.

Important Note: based on the sample size of A, and after getting a notion of the effect size distribution, you should see if this approach is underpowered or not.
