'hospital-based' originates from modern English, specifically the compound of the words 'hospital' and 'based'. 'Hospital' ultimately comes from Old French 'hospital' (from Latin 'hospitale'), where the root 'hospit-' related to 'host/guest'. 'Base' (in 'based') comes via Old French 'base' from Latin/Greek 'basis', where 'basis' meant 'foundation' or 'step'.

'hospital' changed from Latin 'hospitale' (a guest house) to Old French 'hospital' and then to Middle/Modern English 'hospital'; 'base' came from Old French 'base' and Latin/Greek 'basis', later forming the past-participle/adjectival 'based'. The compound form 'X-based' (e.g., 'school-based', 'hospital-based') developed in modern English (notably in the 20th century) to indicate something having its base or centre in X.

Initially 'hospital' referred more broadly to a lodging or guest house (from Latin 'hospitale'); over time it narrowed to mean an institution for medical care. 'Base' originally meant 'foundation' and in the compound '-based' it came to mean 'having its base or centre in'. Together, 'hospital-based' now means 'having its base or primary operations in a hospital'.