In order to sustain a medical malpractice action against a hospital based on apparent agency, a plaintiff must prove (a) that the hospital acted in a manner that would lead a reasonable person to conclude that the treating physician was an employee or agent, (b) that the patient actually believed the physician was an employee or agent, and (c) that the patient relied to his detriment on the physician's care and skill. Rodrigues v. Miriam Hospital, 623 A.2d 456 (R.I. 1993).