>> The breast cancer blood screening test, NMP66 , produced the following results: …Ruled out breast cancer in 26 of 28 women with normal or benign breast conditions. <<
That’s 2/28 false positives, which is 7%.
These data illustrate the mathematical/economic challenge underlying cancer diagnostics. Let’s be generous and assume that the test can find 100% of the cancers in a pool from the general population. (Your data contained one missed case of DCIS, but I’ll be magnanimous and ignore that miss.)
Say that you test 1,000 women from the general population and you expect 4 of them, on average, to have breast cancer. Of the 996 test subjects who don’t have breast cancer, a 7% rate of false positives gives an expectation of 69.7 false positives in the pool. Hence, even if you detect 4/4 of the cancer cases, you will have 69.7/4=17.4 false positives for each cancer detected! (The specificity of the test is 4/(4+69.7)=5.4%.)
Because false positives will presumably be followed by consultation and further testing, such as a biopsy, the economic premise of the diagnostic tool can disintegrate. This is why I think these kinds of tests may not be ready for prime time.
“The efficient-market hypothesis may be
the foremost piece of B.S. ever promulgated
in any area of human knowledge!”