Doctors are most often liable when their direct actions cause you to suffer harm.
Most hospitals contract doctors rather than employ them. The contractual agreements are often a way for hospitals to distance themselves in the event of malpractice. However, some issues may arise that allow the hospital to hold liability in this type of case.
You may prove that the hospital holds liability if they contract a doctor who they knew had a history of negligence or was not properly trained. Hospitals must ensure you have the proper care. When they put you in harm’s way by allowing a negligent or untrained doctor to practice medicine, they’re liable for any damages you sustain.
If both parties are liable, you may be able to take legal action against both the hospital and the doctor.