Negative predictive value

The formula

• NPV = TN / (TN + FN)

TN, the true negatives, are the people without the condition whom the test clears; FN, the false negatives, are the people with it whom the test clears by mistake. The denominator is everyone with a negative result, and the NPV is the share of them who really are free of the condition: what a negative result is worth to the person who gets it.

A worked example

40 true negatives and 10 false negatives: NPV = 40 / (40 + 10) = 0.80. Four negative results in five are right. Turned round, an NPV of 0.80 with 10 false negatives means 40 true ones.

Why a rare condition makes it high

Take a test with a sensitivity of 90% and a specificity of 90%. Among 1,000 people of whom 10 have the condition, it clears 891 of the 990 healthy and misses 1 of the 10 cases: NPV = 891 / 892 = 99.9%. Among 1,000 of whom 500 have it, it clears 450 healthy and misses 50: NPV = 450 / 500 = 90%. A negative result is more reassuring when the condition was unlikely to begin with, which is Bayes’ theorem read for the negative row.

Its mirror

The positive predictive value reads across the top row, TP / (TP + FP), and moves the other way with prevalence: rare conditions give a high NPV and a low PPV from the same test. A screening programme for a rare disease lives with that: its negatives are reliable and its positives need a second test.

Common mistakes

• Reading it as the specificity. Specificity reads down a column; NPV reads across a row.
• Carrying it between populations. It travels with the prevalence.
• Reading 1 − NPV as the miss rate of the test. The miss rate is FN over the sick, 1 − Se.

Frequently asked questions