What fraction of people getting a particular medical treatment will be helped versus harmed?
This is a follow-up to a previous commentary on the “number needed to treat” calculation mentioned in this previous post.
Here Dr Carroll offers in passing a more self-explanatory way of presenting a “number needed to treat.” If the “number needed to treat” is 50, for example, all that really says is that on average 1 out of every 50 people getting a particular treatment see a benefit from it.
He also contrasts this with the fraction harmed. If 1/50 are helped but 1/20 are seriously harmed, then maybe the treatment isn’t such a good idea. Of course, you also have to consider the nature of the benefit and the harm.
Incidentally, it’s easier to compare two fractions if both have the same numerator or both have the same denominator. For example, it’s easy to see that one in 50 is smaller than one in 20, and it’s also easy to see that 2 out of a hundred is smaller than 5 out of a hundred. But you might have to stop and think a second about how 1 in 50 compares with 5 out of 100.
A real world comparison I found very interesting appeared in a discussion of PSA testing on the National Cancer Institute website. According to an analysis taking into account data from two large studies, if 1000 men receive regular PSA testing a follow-up exams and treatment over the course of 10 years, then on average
- 0 to 1 death from prostate cancer would be avoided.
- 100 to 120 men would have a false-positive test result that leads to a biopsy, and about one-third of the men who get a biopsy would experience at least moderately bothersome symptoms from the biopsy.
- 110 men would be diagnosed with prostate cancer. About 50 of these men would have a complication from treatment, including erectile dysfunction in 29 men, urinary incontinence in 18 men, serious cardiovascular events in 2 men, deep vein thrombosis or pulmonary embolism in 1 man, and death due to the treatment in less than 1 man.
This is a very informative comparison, though the conclusion remains ambiguous (and in any case, whether to get a PSA test is something to discuss with your doctor, not a decision to base on a website, especially given medical progress and the recent introduction of such things as MRI-guided biopsy).