I think that's more of an attitude question than a placebo effect. Take for example, the 5 year surivival rate for untreated breast cancer, according to this NIH study it's under 20%, however, according to the American Cancer Society the 5 year survival rate for stage 0 and stage 1 intervention is 100%.
So. iIf a pacebo-based treatment were to delay a woman from seeking intervention from stage 1 to stage 2, her survival rate drops from 100% to 93%, if gets to stage 3, it drops to 72%, if she waits until stage 4, it drops to 22%, and if she never seeks any treatment it drops to less than 20% for 5 years (and around 4% after 10 years). That's the danger of treatments that rely on the placebo effect, they can delay the application of real timely medical treatment. In the worst case, the placebo treatment has effectively killed 96% of the people taking it by preventing them from seeking out real treatments.
Interestingly, it seems that having a positive attitude doesn't seem to have any measurable effect on breast cancer survival rates, and even if it did, the detrimental effect of not seeking a real treatment would almost always be worse. Of course, this is all much simpler than I'm making it out to be. After all, what would be better? Getting real life-saving treatment and having a positive attitude or getting nothing and having a positive attitude?