I have microbiome data structured as follows:

where I want to look at differences in the microbiome between patients who did and didn't respond to drug treatment. I have approximately $40$ patients.

I have used phyloseq to generate a Bray-Curtis distance matrix:

bray_dist = phyloseq::distance(physeq, method="bray")

I now want to use that distance matrix to test for differences between patients who did and didn't respond. I was thinking of this:

adonis(bray_dist ~ sample_data(physeq)$Response, distance = "bray", strata = sample_data(physeq)$Treatment)

Is this the correct way to do it? Would the above test the pre and post samples individually?

What is the correct way to do this with anosim or adonis?