Sensitivity (True Positive Rate)

Sensitivity is read down one column of the 2×2 table and nowhere else. Take everyone who genuinely has the condition — never mind what the test said — and ask what share of them the test called positive. Everything outside that column is irrelevant to the number, which is both its strength and the source of almost every misunderstanding about it.

The attribution is worth getting right, because it is repeated wrongly nearly everywhere. Jacob Yerushalmy's 1947 paper on the reliability of chest X-ray readings named sensitivity and specificity; it did not originate them. The underlying quantities were already in use in the diagnostic and screening literature of the 1930s and 1940s, and the deeper structure is older still — this is a conditional probability, P(test positive | disease present), and the mathematics goes back to Bayes and Laplace. What Yerushalmy gave the field was a vocabulary, and vocabulary is not a small gift: before it, the same two quantities were being described in prose, differently by every author.

The memory aid is SnNout: a highly Snsitive test, when Negative, rules out. It works because a sensitive test produces few false negatives, so a negative result from one is hard to argue with. But notice what the aid quietly assumes — that the pre-test probability was not already very high. A 95 % sensitive test returning negative on someone with a classic presentation still leaves substantial risk, and the arithmetic that shows this is on the post-test odds page.

What sensitivity does not tell you is whether the test is worth running. It says nothing about how many healthy people it will alarm, nothing about how common the condition is in the people you are testing, and nothing about whether finding a case early changes what happens to that person. A screening test can be 99 % sensitive and still be a bad idea, and several have been. Sensitivity is one input to that decision and never the decision itself.