I don't think it's the food prices, because the cheapest foods tend to be the ones that lead to obesity (among other health problems). Fast food burgers and white bread are not expensive here in Japan, but fresh fruits and vegetables are.

I think there are many factors, but the pretty great universal health care system has to be a big one. As a working adult in Tokyo, I receive tons of preventative care and thorough annual check ups. It's cheap, and virtually all health care for my kids is completely free until they turn 15.

The lack of equal access to health care in the USA is almost certainly a reason that poor people die 5 years earlier than affluent people[1]. I would guess good access to health care is a big reason that Cuba does so well on that front, despite its obvious economic obstacles.

[1]: http://news.rice.edu/2012/06/21/poorer-us-citizens-live-five...

Canada, which has even fewer physicians, has a life expectancy only 2 years less than Japan.