'method-based' originates from Modern English, specifically the words 'method' + 'based', where 'method' ultimately comes from Greek 'methodos' meaning 'pursuit, method' and 'base' comes from Old French/Latin roots meaning 'foundation' or 'basis'.

'method' changed from Greek 'methodos' to Late Latin 'methodus' and then into Middle/Modern English as 'method'; 'base' came into English via Old French 'base' (and Latin/Greek 'basis'), and the compound adjective 'method-based' was formed in Modern English by combining these elements.

Initially the components meant 'pursuit/way' (method) and 'foundation/basis' (base); over time the compound came to mean 'anchored in or determined by a particular method', a straightforward compositional meaning.