But the population prevalence is much more than 1%: 80k deaths at a 1% infection fatality rate (and I believe this is high, but I'm being conservative) implies 8,000,000 infections so far. This is more like 2.5%. So far. 95% CI for specificity is 99.5%, so you can be reasonably confident that you're doing better than 85%.
It may not be a perfect intervention, but you could really reduce risk. If there's an 85% chance that someone is immune, they do not share a household with a vulnerable person, and they are not in a high risk group themselves-- you've reduced the risk of death to basically nothing.
I disagree with it for other reasons (it incents people to go get sick to be free/be able to work/etc).
On an individual basis yes, but doign large scale scientifically/statistically relevant antibody tests to see just how many people have actually had covid-19, would be very beneficial.
{added: great answers below} well worth understanding this point. In short specificity measures the % of the population tested which had false positives, but doesn't give you the ratio of false positives to positives or the probability that a positive test means you actually have the anti-bodies.
If the number of true positives is 10/1000, and the test gives you 11/1000 positive results, then 1/11 of your tested positive results are false positives. (Actually closer to 9% than 10%).
If 1% of people have had COVID-19, then that's 1000 people who have had it, and 99,000 people who haven't.
The test has a sensitivity of 100%, which means all 1000 people who've had it will test positive.
The test has a specificity of 99.9%, which means 98,901 of the 99,000 people who haven't had it will test negative; but that leaves 99 people who haven't had it, but test positive anyway.
That gives us 1099 people who look like they have immunity; but only 91% of those people are actually immune: 9% of the people are false positives.
If instead we have a specificity of 99%, then only 98,010 of the 99,000 people who haven't had it will test negative, leaving 990 people who haven't had it but test positive anyway.
That gives us 1990 people who look like they have immunity; but only 50% of them actually do -- the other 50% are false positives.
If you test negative, you are clear, guaranteed, no false negatives.
If you test positive, there is a 10% chance it's a false positive.
I guess my follow up question, does a retest of the positive population make that false positive rate drop to 0.1%, or is the reason for false positive significant to an individual and not random chance?
Well, don't misunderstand -- it's got nothing to do with the test per se, but with the probability that you had the disease in the first place.
The test itself has two probabilities:
1. If you've had COVID-19, the probability that it will report positive (sensitivity)
2. If you haven't had COVID-19, the probability that it will report negative (selectivity)
But those probabilities give you a mapping from reality -> test_result. What you want is the reverse of that -- and find the probability from a test_result -> reality. When you do that, you have to factor in the probability that you have the disease in the first place.
If 50% of the population have had COVID-19, then a positive test means a 99.9% probability of having had the virus. If 1% of the population, a positive test means 91% likely you have it. If only 1 in a million people had COVID-19, then the number of false positives would completely overwhelm the number of true positives.
This is sometimes called the "Base rate fallacy": forgetting to factor in the base rate when determining something like this.
It's important for things like, say, systems which automatically detect terrorists at airports. How many travelers at an airport are actually terrorists planning to attack a plane? It's got to be one in hundreds of millions, if not billions. With that low of a base rate, even if you had a system that was 99.999% accurate, the vast majority of people it flagged up would be innocent.
“While all of these tests can still generate false positives—a finding that you have the antibodies when you don’t—that risk can be sharply reduced by repeating the test if it comes back positive. The predictive value of two consecutive positive tests is high enough that you can be confident antibodies are present.”
https://www.wsj.com/articles/antibody-knowledge-can-be-power...
This percentage is based on both the test and the real infection rate.
Of the 900 people who do not have ABs, 99.9% or 899.1 are correctly identified as not having them, 0.9 is identified incorrectly as having them when they actually do not.
Of the 10 who actually have antibodies, 100% are correctly identified.
So 10.9 are identified as having antibodies, in 0.9 person's case incorrectly which is about 10%.
P(I|+)
=
P(+|I)*P(I) / P(+)
=
Sens*P(I) / [Sens*P(I) + (1-Spec)*(1-P(I))]
=
.01 / (.01 + .001*.99)
When the thing you're testing for is very rare, it's just as rare that the people who tested positive will actually have it.
We have good data that the IFR is in the 0.1-1% range, putting cases in say MA in the 7% range a couple of weeks ago (time from infection to death), which based on confirmed cases would put it well above 10% now
That means you’d have 1k false positive and 10k true positive from a test.
South Korea is reporting that as of last week, and say their earlier "reinfection" results and subsequent scare were flawed.
If we ever get to the point where 80% of the population has had the virus, that would be a massive failure.
Testing doesn't need to be 100% to be effective, but it does need to be better than random chance. A mixture of contact tracing, PCR testing, antibody testing and effective quarantines could be used to make the virus go away, but would require a coordinated strategy that the US has not attempted to implement, much to my dismay.
In reality testing can be used as an effective tool regardless of whether or not people can be 'certified'
On a population basis it’s more helpful.