Research careers other than professor? My last question about making a career as a research scientist/staff scientist hasn't gotten many replies from people in that career, and when I tried to look for someone at my university who has that job to ask them about it, I didn't have much luck finding people. I am starting to wonder if that might be because this career path is not as common as I thought it was...

Are there PhD-level people who decide that they don't want a tenure-track position, but who really like coding/study design/analysis and decide to specialize in doing that for other people as part of their research team(s)? Or is that pretty much unheard of (or seen as extremely undesirable and only a short-term arrangement, not a career) in academia?

I know there have to be other people like me who decide they really like coding/study design/analysis, and would rather do as much of that as possible instead of taking on all the teaching/management/service responsibilities of a tenure-track professor... where do people like this go? Is it best for someone like this to head into industry, or is it common for us to end up at schools of medicine/etc. helping PIs to carry out their research?

(If this varies by field, my field is epidemiology, and my main focus is genetic epidemiology. I live in the United States, but would be happy to move to a European country too if it was possible to get a work permit.)
Several people I know who studied public health have gone onto research careers at universities that have affiliations with hospitals. They are considered faculty members, but they have no teaching responsibilities. Besides research, they are expected to contribute to submitting research grants for their respective units/departments. Some are more independent than others, with one person essentially having the responsibilities of a senior postdoc, while another runs her own group within the hospital itself. For example, this unit may represent what you're looking for (I am in no way affiliated with them, and just came across this via Google).