## Sensitivity and specificity

Sensitivity and specificity are those sorts of things that can really get knickers twisted up something rotten. They sound like something you should be able to understand, they get used as if you understand them, and then you realise … it’s not quite as you thought …

 Really diseased Really not diseased Test +ve A B 1.. A/(A+B) Test -ve C D 2.. C/(C+D) 3… A/(A+C) 4… D/(B+D)

Looking at the Table above – which of 1.. to 4.. is sensitivity?

And what does sensitivity tell us?

You see, I reckon it’s because we think of them as properties of test results, rather than properties of diseased/undiseased populations that gets us confused. The sensitivity of a test is the proportion of diseased individuals correctly identified as diseased and the specificity the proportion of undiseased individuals correctly identified as undiseased. (It goes ‘down’ the columns.)

What we tend to want to know in practice is “If I have a +ve test result, what proportion of those folk actually have the disease?” or something similar for negative tests. (Now, those are different metrics, and more next time ’cause there are greater confusions.)

With two small exceptions, sensitivity and specificity can’t tell you that.

The exceptions are:

VERY high (perfect?) sensitivity

 Really diseased Really not diseased Test +ve 10 50 10/60 Test -ve 0 50 0/50 Sn = 100% Sp = 50%

For very high SeNsitivity, a Negative test result rules OUT the diagnosis – SnNOut

VERY high (perfect?) specificity

 Really diseased Really not diseased Test +ve 5 0 5/5 Test -ve 5 100 5/105 Sn = 50% Sp = 100%

For very high SPecificity, a Positive test rules IN the diagnosis – SpPIN

For all other things, you need something a bit more complicated …

• Archi

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