@blatham,
Read the mission statement and history of the Commonwealth Fund.
I don't need to do anything. I happen to know a great deal about mathematics and statistical analysis. I outlined for you the omissions and defects in their methodology, and noted correctly that the methods they used could easily have established any ranking among the handful of nations they chose - chiefly because all are very prosperous and enjoy far better health care than any other nations in the world, and that the very small statistical differences among them are more likely to derive from other lifestyle factors and population mobility than health care.
Look up the statistical data for life expectancy, infant mortality and survival data for diseases like cancer. You'll find that the nations in the Commonwealth survey occupy a tiny compact cluster at the top, and that the differences within this cluster are trivial compared to the differences among subgroups or individual nations below them.
The rest you can find in any basic text in statistics, or just in thinking about the many unquantified (and in some cases unquantifiable ) subjective attributes in their study.
The report was merely a listing of their opinions, with as deceptive veneer of statistics to make it look convincing. That's what advocacy groups do.
Perhaps you aren't as widely read as you imagine.