I'm not sure the decisions are linked-- Medicare vs Social Security.
The SS calculations are complex, but typically no matter when you start taking it, around age 84 or so (+/-) you will have drawn the exact same amount of money.
Rising above all the financial wizardry and calculations, I recall a financial expert who specializes in this boil it down this way:
"If you don't need the money from SS to make monthly expenses, start taking it right away. If you do need the money from SS for monthly expenses, avoid taking it for as long as possible."
Seems counter-intuitive but it does make sense-- if you rely on it for monthly expenses it makes sense to make that amount as big as possible each month.
A close friend of our family chose to delay. Regrettably she died from an illness before collection, and I've never forgotten the unfairness of that.
I also think a significant decision, rising about the numbers themselves, is will you enjoy some extra $$ in your life today, or more enjoy it at age 84 on? That was an easy decision for me ... good luck.