It's not about showing correlation. It's about showing that we're not getting what we're paying for.
As others have pointed out, life expectancy is only a single facet of the health of a nation and with many sociological factors such as the fact that americans eat too much which leads to heart disease which is not-incidentally the most common cause of death in the USA.
Assuming you have coverage, what you're paying for is word-class care with minimal waiting times.