I've been working on improving my self-rescue skills, but the skills I've learned so far seem to pertain mostly to single-pitch climbing. For example, a lot of people emphasize knowing how to escape a belay, which is fine, but that seems to be mostly applicable to the situation where you're giving someone a belay from below on a single-pitch climb, you can't just lower them (maybe because they'd end up on a ledge), and you need to run and get help.
If you're in the middle of a multi-pitch climb, it seems like it escaping the belay may not be relevant, or may at best be only part of the solution.
I'm sure there are many different possible self-rescue situations that could come up in multipitch trad. But one likely-seeming situation I can come up with is that I'm giving someone a lead belay, he gets injured too badly to be able to up- or downclimb, and we have more than half the rope out, so I can't just lower him all the way.
What do you do in this situation? My best guess would be to lower him down to the lowest piece of protection I can get him to, escape the belay, ascend the rope, improve that piece of pro to a solid anchor, secure him to the anchor, and free the rope from the gear higher up (either by climbing and cleaning, or by untying and pulling the rope through). Then maybe clip him in to the rope with a locking biner, lower him to the belay station, have him unclip, and then rap down to the belay station myself (possibly leaving a lot of gear). Wow, this seems complicated and difficult, especially if I can't see the situation clearly from the belay station.
I think a solution to this problem would also pretty much apply to single-pitch climbing in an area where it's not possible to run and get help, e.g., because you're in a remote area.
Question: what would be some general strategies for dealing with this type of situation?