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There is another consideration:

1. You have an aggressive (i.e. non-treatable) cancer, maybe you feel slightly off, but you go on with your life, until you finally got worse and die. Or you performed screening, focus on treatment, bankrupt your family and ... die anyway,

2. You have a slow growing cancer (e.g. prostate), live your life and die of some other causes. Or you performed screening, got surgery, got tons of problems and die of myocardial infarction (yes, that's one of complications after prostate surgery).

If you read the original JAMA publication you would notice that there is a research on quality of life metric. That metric for breast cancer is higher among non-screened women.