It's probably more helpful yet if the study/statistics are relevant to the case at hand. In the linked study, the WHO and the OECD marked down the US for having inefficient care (duh--we know that), for having poor "equity" (i.e. some people get better care), as well as something they called "healthy lives," and other categories that deal with overall cost and social goals of the HC systems, not whether sick people who have access tocare in each system (which would appear to have been Bamaman's niece's situation) would be more likely to have positive outcomes. In the case of the US, the country did quite well (3rd overall of 11) in "effectiveness of care."
More specifically, and more relevant than what the OECD or WHO thinks:
79% of women diagnosed with uterine cancer in England and Wales survive their disease 5 years or more
82% of US women diagnosed with uterine cancer survive 5 years or more.
Obviously, early detection matters a lot, as well as the specific type of uterine cancer. Every case is unique and it is not possible to know if a particular patient would benefit from being in a particular nation's health care system.
But, overall, women in England and Wales who have been diagnosed with uterine cancer have a 17% higher probability of succumbing to the disease within 5 years than US women with uterine cancer.