What word does your mother always say?
coined 1909 by Austrian-born doctor Ignatz L. Nascher (1863-1944) in "New York Medical Journal" on the model of pediatrics (cf. -ics), from the same elements found in geriatric (q.v.). The correct formation would be gerontiatrics.
geriatrics ger·i·at·rics (jěr'ē-āt'rĭks)n. The branch of medicine that deals with the diagnosis and treatment of diseases and problems specific to old age. Also called presbyatrics.