If you want to report a physician you should contact your state licensing board. They gather and investigate complaints about unethical behavior as well as unprofessional conduct and malpractice. They can sanction, reprimand, discipline, and fine a physican as well as temporarilly suspend, limit, or actually revoke their license to practice in the state.
NY state has a Web site devoted to professional licenses. You can check to see if any actions have been taken against a physician or against any other holder of a professional license.
I spent several hours one day reading the sorts of disciplinary actions taken against certain physicians and other health professionals, and why those actions were taken. Quite an eyeopener! The sorts of things that dentists got involved in seemed even worse. But most of these people are still engaged in practice--so it pays to check out your own health care providers if your state has a similar Web site.
Your county Medical Society is another good place to lodge a complaint against a physician. They will also investigate the matter and they do have a watchdog function.
The AMA is just a professional organization without much clout. The most they can do is drop someone from their membership roles for an ethical violation. But belonging to the AMA is not that big a deal and being dropped as a member really wouldn't affect a physician very much.
Your state licensing board is the real governing authority for the practice of medicine in your state and they have the most muscle to take action. They also have the resources to conduct a thorough inquiry into any complaint.
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Still Crazy After All These Years