A stay in the hospital was not medically necessary, so the doctor said he could go home.

medically 是形容词 medical 的副词形式，medical 来自名词 medicine（医学），表示"医学的、医疗的"。medically 作为副词，意思是"从医学角度、在医疗方面"，用来修饰形容词 necessary，说明判断的依据是医学标准。