I've seen a number of people link to this Bloomberg study concluding that America's health care system ranks 46th out of 48 in efficiency. Since America's health care system is pretty inefficient, I like the table. But it's a terrible methodology. Basically they look at a few measures of cost and then use life expectency as the outcomes metric.
The problem here is that the main thing you're showing is that health care services are not a particularly cost-effective way to increase life expectency. If we raised the taxes on alcohol and gasoline and then spent all the revenue on a pointless bridge in Alaska, American life expectency would go up. Not because our health care system would become more efficient, but because fewer people would die in car wrecks and murders. And as it happens, raising those taxes would be a good idea. Fewer people would die in car wrecks and murders!
But health care services—delivering medical treatment to people who are sick—really are an important subject in there own right. But to judge the efficiency of a country's system for delivering them, you need a more sophisticated measure of outcomes. Do the Americans who do get shot receive good treatment? My understanding is that the U.S. health system is actually pretty excellent at treating gunshot wounds, since for a developed country we fight a lot of wars and have a lot of gun crime and so our hospitals are pretty crackerjack at this. On the other hand, we spend 77% more than other OECD countries on name brand prescription drugs and presumably the medicine doesn't actually work any better here. That's terribly inefficient, from a patient-centered viewpoint. So my point isn't to defend the American health care system (never!), but you do need to be careful here. Lots of things kill people other than lack of health care services. Conversely, health care services do lots of useful things beyond saving lives. Being sick sucks. Even if you are overwhelmingly likely to fully recover from your ailment without treatment, you'll still be very glad if the doctor can help alleviate your symptoms and make the recovery happen faster.