I have an experiment where two groups of individuals get some variable repeatedly measured at regular intervals. I'd like to know if one group is trending faster or slower than the other (and in what direction).
If I only had two measurements, it would probably make sense to calculate the difference first to last measurement, and then do Mann-Whitney U test on the differences in one group vs differences in the other group. This first to last measurement difference is the simplest possible "trend" (with just two data points), but what happens when there are more data points?
I can think of a few (bad) ways of doing this: for example, do Mann-Whitney from day 1 to day k for every k (some of which will be significant, but this doesn't take into account all the days together). Or, do a linear fit on each individual, and then do a Mann-Whitney on the slopes in one group vs the slopes of the other group, etc. Intuitively, it seems all the variants on this I can think of will lose some power.
What is the right way to do this kind of analysis?
(It doesn't have to be an analytical formula; methods like bootstrap are perfectly okay for me, I just need to know the general approach)