Four professors have written an article titled "Do Poor People Sue Doctors More Frequently? Confronting Unconscious Bias and the Role of Cultural Competency."
The article concludes that "Contrary to popular perception, existing studies show poor patients, in fact, tend to sue physicians less often. This may be related to a relative lack of access to legal resources and the nature of the contingency fee system in medical malpractice claims."
Quite frankly, there is no original research in this article, but it is a good collection of research that has been out there for several years.
My own experience is that poor people are less likely to sue and more likely to understand why they do not have a claim that can be pursued. The most difficult conversations I have when I have to decline a medical malpractice case are with people who have money - they are used to getting there way and cannot understand why every bad result does not automatically result in compensation of some amount. Quite frankly, my view is that poor folks are so used to getting kicked that one more kick (the inability of a lawyer to take a case) is not viewed with particular surprise or consternation.