For the purposes of this article, the term "medical malpractice claim" means any claim for damages resulting from the death of or injury to any person arising out of:

(1) Health, medical, dental, or surgical service, diagnosis, prescription, treatment, or care, rendered by a person authorized by law to perform such service or by any person acting under the supervision and control of a lawfully authorized person; or

(2) Care or service rendered by any public or private hospital, nursing home, clinic, hospital authority, facility, or institution, or by any officer, agent, or employee thereof acting within the scope of his employment.