My understanding is that most research is done from academic centers. There are various reasons for this, including:
1. Most research required a fair amount of overhead expenses related to regulation (e.g., IRB submissions, liability insurance, grant writers, research assistants), and this expense is more efficiently handled by a larger institution
2. Most research requires external funding sources. Non-profit agencies are probably biased in favor of academic centers for the perceived high ethical standards, and industry likes to say that the utility of their products have been verified at academic centers
3. most private practices don't especially care to research
4. Few private practices can afford the costs of research
That said, there are some private practices that do research. Certainly case reports/series. Certainly research that doesn't require substantial external funding. Some even use their clinical revenue to fund their own research.