Doctor_Nick

Say a test is 98% specific, that is it results negative correctly 98% of the time, but 2% of the time is positive in someone who doesn’t have antibody. 

Furthermore some of these tests being used appear to be around 90% sensitive currently, which means 90% of the time they pick up the people with antibodies and 10% of the time they miss it. 

Let's say you use your test in an area with 2% COVID antibodies in the population.  

So therefore out of 1000 people 20 actually have COVID antibodies.  How does your test do?

Your sensitivity is 90%, so you detect 18 real positives.  You miss 2, so you have 2 false negatives.

Your test is 98% specific.  So you have 980 people without COVID antibodies, so (98% * 980 people without COVID) is 960 negative tests.  So 20 real negatives test false positive. 

So your totals for this population are:

You have a total of 38 positives.
You have a total of 962 negatives.

Before you adjust for the test, it looks like your prevalence of disease is 3.8%.

However, the positive predictive value of a positive test is less than 50%.  Only 18/38 positives truly have COVID antibodies - that's 47%.  This is what they mean when the test can be wrong half the time.  So if you test positive in this situation, it's slightly worse than a coinflip as to whether you actually have antibody.

What about a negative?  You have 2 false negatives and 960 real negatives.  So if you have a negative test, you chances of being a true negative are (960 / 962) or 99.7%.  So there is a 0.3% chance you tested negative but had antibodies. 

So I think we can be pretty confident that @fidoz is actually negative.

What happens with the same test in a high prevalence situation:

If 20% have COVID antibodies out of 1000 people 

200 positives.  Your test misses 20 of them and 180 are true positives. (200*0.9 sensitivity)

There are 800 negatives, and with your test 784 test negative (800 * 0.98 specific).  So you have 16 false positives. 

So you have 196 total positives.  If you test positive, what does it mean for whether you have the antibodies?

So now there's a 180/196=  91% chance you really do have COVID antibodies, when using the same test as before.  

And for the negatives there are 804 total negatives (784 + 20 false negatives).  So the chances of a negative being real in this case is 
784/804= 97.5% chance.

Note how you'd like your test to be more sensitive and not miss any real positives, because the false negatives are becoming more significant as the number of real negatives drops.  

Marci said:

Antibody tests are not turning out to be reliable at all (wrong about half the time, according to the CDC):

https://amp.cnn.com/cnn/2020/05/26/health/antibody-tests-cdc-coronavirus-wrong/index.html?fbclid=IwAR0Op5B170HL--ZJGBb_M7H1D0qNmuKUXYgqyTmM0eywccqjgusB1koHq5Q