Prostate cancer screening and innumeracy

"Research has shown that numeracy among the American public is shockingly low." Wouldn't be surprised if "shocking" innumeracy isn't confined to the United States.

Many laypersons do not understand that a control group is needed in order to evaluate the effectiveness of a medical intervention or test. By attending primarily to cell A and by giving insufficient attention to cells C and D, many members of the general public will not comprehend a central basis for the task force’s negative opinion of the PSA test.

This insufficient attention to disconfirming information is the good old fallacy of confirmation bias.

Given a 4ng/ml cutoff, PSA screening has a laughable sensitivity of only 21%. And even with a specificity of 94%, the false discovery rate still comes out to a whopping 81% for a cancer prevalence of 6.3%. That just means that out of every 5 men who test positive, 4 were incorrectly tagged. Epic fail.

Now I read in some cancer website that 1 in 7 men will have prostate cancer. Let's round that up to 15%. If we take that as our base rate (prevalence), we obtain a false discovery rate of 61.8%. So out of every 5 we will still be erroneously labeling 3 as having cancer.

Now that's just the false positives--those who don't have cancer. What about the true positives--those who actually have some type of prostate cancer? PSA does not distinguish between aggressive cancers and those that progress very slowly. The latter need not be treated, will probably not cause discomfort or some disability in the patient's life, and will almost surely not be the cause of his death. But the fact that cancer has been discovered almost certainly will prod both patient and doctor to fiddle around with it further, calling for more tests and even (invasive) treatment of sorts.

[http://citrixweb.mpib-berlin.mpg.de/montez/upload/PaperOfTheMonth/arkes.gaissmaier.2012-1.pdf
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