Q: Mean of individual percentage changes vs. percentage change of aggregated means? Apart from the valid criticism of percentage changes, sometimes we are asked to use them by our employers or clients.
Let's assume we have 5 patients. Each has a pair of pre-treatment and post-treatment values (I'm gonna ask also about the paired data with missing observations later).
P1: pre1 ; post1
P2: pre2 ; post2
P3: pre3 ; post3
....

Now, w have two options:
Option 1
Calculate individual changes and calculate the mean of them.
P1: pre1 ; post1 ; %change1
P2: pre2 ; post2 ; %change2
P3: pre3 ; post3 ; %change3
....
mean(%change1, %change2, %change3)

Option 2
Calculate separately means, and the % change of it: mean_pre, mean_post, %change_of_both
The two may differ wildly, one may be negative, the other - positive.
Bot say something about the data, but IMO the first one, the "mean (or median) of changes" reflects better the paired nature of the data. Would you agree?

From the other side, if some pairs have gaps, like here:
P1: pre1 ; post1
P2: pre2 ; N/A
P3: N/A  ; post3
....

then the paired % changes cannot be calculated and we need to use the second option. Or maybe we shouldn't? This one treats the data as if it were unpaired groups.
If there are practitioners in medical research, please tell me which one you prefer and - most importantly! - why?
