Vicarious Liability refers to legal liability arising from acts of others.
In medicine, there are several doctrines that can lead to vicarious liability on the part of the physician.
Respondeat Superior. This basically means 'let the master answer'. If the file clerk you employed to work in your clinic negligently or intentionally releases confidential patient information you, as the 'master' or employer, are liable. If a clerk rushing a lab specimen from your clinic to the lab gets into an auto accident in the course of her duties, you, as the 'master' or employer are liable.
Borrowed Servant. Respondeat Superior relates specifically to your employees working under your direction and control. However, a physician may find himself directing and controlling an employee of someone else. That employee is then a 'borrowed servant' and you are responsible for that person's errors just as if he were your employee so long as you are in control of his activities. Imagine, a situation in which you are performing a surgery and a nurse who is present and taking direction from you is actually an employee of the hospital. During that time the nurse is a 'borrowed servant' and you may be liable for that person's errors during the time he is under your control.
Master of the Ship. This doctrine has confused students in the past, so it has been addressed more fully HERE.
Ostensible Agency. Increasingly courts have been finding that if someone has been allowed to appear to the public to be an employee or agent of an employer he will be treated as if he actually were an agent or employee for purposes of determining vicarious liability. For example: if a hospital contracts with an independent team of physicians to manage its ER and treat patients coming there, and if the hospital fails to make clear that those physicians are an independent business and not part of the hospital, the negligence of those physicians may also be extended to the hospital. Independent physicians sharing office space and expenses must also make clear that they are separate enterprises or they may be facing vicarious liability under the related ostensible partnership doctrine. Note this.