It’s a Myth that Single-payer Systems Provide Better Care
People who make this claim usually note that life expectancy is higher in countries where socialized medicine is practiced, such as Canada and Europe. But life expectancy is influenced by variables aside from the quality of a country’s health care system including diet, genetics, infant mortality, exercise, smoking, pollution, and even marital status.
A better way to evaluate health care systems is to review the outcomes of certain health problems. For example, a study published last year in the British medical journal Lancet Oncology suggests America is much better at treating cancer than Europe or Canada. Researchers found Americans have better survival rates five years after diagnosis for 13 of the 16 most prominent cancers. An American man has nearly a 20 percent better chance of living five years after being diagnosed with prostate cancer than his European counterpart. Among women who are diagnosed with breast cancer, only one-fifth die in the U.S., compared to one third in France and Germany and almost half in the U.K. and New Zealand. Data about outcomes tells us a lot more about the quality of a health care system than life expectancy rates because the relationship between treatment and outcomes is much more direct.

The article tha PRI cites does not include any data on the US.
Another article in Lancet Oncology does include the appropriate statistics:
but they are not nearly as favorable to the American health system. America
is behind Japan for colorectal and only slightly ahead of #2 Canada for breast cancer .
The US is way ahead on the treatment prostate cancer .
It looks to me as if the US achieves only slightly better results in treating cancer, but has much worse overall health stats and spends much more money on health care !
Breast: 83.9 vs. Canada: 82.5 & Sweden 82
Colon: (M): 60.2 vs. Japan 63
Rectum (M): 57.3
Colorectum (M): 59.3 vs. Japan 61.1 and 58.2
Prostate: 92.3 vs. Austria 86.1 and Canada 85.1
SourceL
"Cancer Survival Rates in Five Continents: a World Wide Population Based Study"
Lancet Oncology 2008, 9: 730-756.