Many of them probably belonged to families that moved westward in the vanguard of white settlers. Settlements in frontier locations like ‘the Ohio’ provided a large contingent of the soldiers that fought in ‘upper’ Ohio near the current Canadian border.
My own ancestor was lost as his contingent marched on Fort Maledn as did his brother.
Heritage Books has published a very good reference book that covers the names, army regiments and battles fought by soldiers from Ohio titled, “Roster of the Ohio Soldier in the War of 1812.
Working with Google Books they have given us a sample of the book online to both entice us and to make us aware of its existence.