Negative Predictive Value (NPV)

The negative predictive value asks the other row's question: of everyone the test cleared, how many were genuinely clear? It moves with prevalence just as PPV does, but in the opposite direction, and that opposition is the quiet consolation buried in the false-positive problem.

Return to the low-prevalence table. The same 99 %/99 % test on a million people where 1 in 1,000 has the condition produces 989,020 negative results, of which only 10 are wrong. The NPV is 99.999 %. The very rarity that made a positive result nearly meaningless makes a negative result nearly certain — because most people really are healthy, and a test that agrees with that is usually right by default.

Which is exactly why a high NPV is weak evidence that a test is any good. A test that simply reported "negative" for everyone would have achieved an NPV of 99.9 % on that population without measuring anything, and its sensitivity would have been zero. Any negative predictive value has to be read against the baseline of doing nothing, and in a rare condition that baseline is already very high. The number that says how hard a negative result actually pushed is the negative likelihood ratio.

The clinical trap is the reverse of the PPV trap and rather more dangerous. A test with a fine NPV in the general population is quoted at a patient whose pre-test probability is nothing like the general population's — someone with the classic history, the exposure and the symptoms. For that person the prevalence is not 0.1 %, and the reassurance the published NPV offers is not the reassurance they are owed. Post-test probability always depends on where you started, and a published predictive value is a statement about somebody else's starting point.