actually some home antibody tests were sold in Germany for 30 or 70 euros and reported 95% accuracy but they were quickly illegal to sell.
Why? several reasons:
- a test done at home can be contaminated etc.
- it takes 5 days to develop the antibodies.
- if somebody tests positive and are asymptomatic they won't be treated and had to stay home anyway. If they live alone they will still have to go out and buy food etc. and take the same precautions like everyone else.
- if somebody tests positive and feel so bad they need a hospital they will be restested anyway because the hospital doesn't believe a home test
- if they test negative it doesn't exclude the virus anyway because of the 5 days and the inaccuracy, also people could get infected 30 minutes after the test anyway.
Also at current levels a 90% accuracy rate is very inaccurate. Let's take New York, which had lots of cases. Statistics (worldometer) show 275,000 "active cases" with a 1% "serious or critical". Interesting that official statistics are hard to come by, and the very low "serious or critical" (50% lower than the world average) can suggest "active cases" is inflated.
But fine 275,000 in a population of 19.5 million that's 1.4 %
So, out of 10,000 people in New York state, 140 have the virus and 9860 are healthy.
If the test is 90% accurate, then it will show 10% of the healthy people to be sick = 986 false positives.
And it will miss 10% of the true positives = 126 real positives
in total, the test will show 1012 people to be positives.
But we know that only 140 are actually infected.
So if somebody in New York tests positive, they have a 140/1012 chance that the positive is accurate at current infection levels, which is 14%.
Now with the negatives:
Out of 9860 real negatives, 90% will be accurate, which is 8874 reported negative (9860-986)
Out of 140 real positives, at 90% accuracy, 14 will be reported negative.
In total, 8888 will be reported negative.
We know that there are really 9860 negative. If somebody is negative on the test, they have at current infection levels a 8888/9860 chance of being truly negative, which is 91.8% accuracy.
Here is Wikipedia making it more complicated as it goes is more detail (
https://en.m.wikipedia.org/wiki/Positive_and_negative_predictive_values )
there's an online calculator at
https://www.medcalc.org/calc/diagnostic_test.php so you can play with the numbers, I tried with a test that is 99% accurate, I still got 59% in the positive predicted value (but almost 100% in the negative predicted value) for a disease that exists in 1.4% of the population.
Note that the 1.4% refer to the population in general, so if you increase that 1.4% by testing only people with symptoms or people who came from areas with the virus, or anything, the results change.