It's not a sensitivity / specificity thing; it's a base rate thing [1]. Suppose that the percentage of people with prostate cancer at any one time is 1 in 1000

It's not a sensitivity / specificity thing; it's a base rate thing [1]. Suppose that the percentage of people with prostate cancer at any one time is 1 in 1000 (i.e., then "base rate" is 1 in 1000). (Turns out this is actually on the same order of magnitude as real number [2].). And suppose this test has 99% sensitivity and 99% specificity. And suppose you test 1,000,000 people. Of those 1,000,000 people, 1,000 will actually have prostate cancer, and 999,000 will not. Of those 1000 that actually have it, 990 will have a positive test (true positive), and 10 will have a negative test (false negative). Of the 999,000 people who don't actually have it, 989,010 will have a negative test (true negative), and 9,990 will have a positive test (false positive). So even with a test of 99% accuracy, if you get a positive result, your chances of actually having prostate cancer are still only 990 / 10980, or about 9%; 91% of the positives will be false positives. And of course, the more rare the cancer, the worse it gets. EDIT2: So, to follow on with GGP's point: "Near perfect accuracy" isn't very specific, but colloquially would imply that if you have a positive test, you have a high chance of actually having cancer. To get that number to 95% you'd need to have only 52 false positives, would require a specificity closer to 99.995%. EDIT: Fixed some math [1] https://en.wikipedia.org/wiki/Base_rate_fallacy https://en.wikipedia.org/wiki/Base_rate_fallacy [2] https://www.cancer.org/cancer/prostate-cancer/about/key-statistics.html https://www.cancer.org/cancer/prostate-cancer/about/key-stat...