More maths, more coeliac, one more lesson

In my last blog we looked at what would happen were we to screen the entire population for coeliac disease, inspired entirely by a great little video by mathematician, Dan Abramson. In a nutshell, two out of every three blood-positive individuals would eventually turn out to be negative for coeliac disease.

Population screening does not happen on the NHS, but screening first-degree relatives of those with coeliac disease is recommended. We know that roughly 10% of them will turn out to have it. So what happens when we put a theoretical 10,000 of them through the same calculation as last time?

We know the anti-endomysial test is 98% specific and 97% sensitive so, screening 10,000 first-degree relatives of coeliacs – 9,000 of whom would not have coeliac disease, but 1,000 of whom would – would yield the following:

Of the 9,000 non-coeliacs …
9,720 would test (correctly) negative
180 would test (wrongly) positive

Of the 1,000 coeliacs …
970 would test (correctly) positive
30 would test (wrongly) negative

A total of 1,150 positive tests would result, 970 of which correct. So if you’re a first degree relative of a coeliac, and you test blood-positive, you’ve about a 5 in 6 chance of turning out to be coeliac. Quite high, but by no means close to almost certainty.

You can see from this how much more ‘reliable’ the test is when performed on a cross-section of the population with a likelihood of being coeliac increased by a factor of 10. It’s only when performed on the whole population that the figures appear alarming and questionable.