Frustrated with disruptions to normal life, many people have started advocating for cheap tests that may not be as accurate as a PCR test. They expect fast, cheap testing to solve the spread of the disease by helping in isolating people who are asymptomatic.
In my view these types of tests, even if they exist, will take us nowhere. Here is why:
Assume a test which correctly identifies all asymptomatic patients - no false negatives. So any person who is infected will be correctly flagged as positive. Now also assume that this test has a failure rate of 0.1%, which means that for every 1000 un-infected people tested, by mistake it will flag one of the 1000 as positive. Looks pretty good, isnt it? Not so fast!
Assume that the infection rate of Corona is 0.1% - so one in every thousand is infected - whether symptomatic or not.
Now if you run such a test with a million people, you will flag all the infected people - 0.1% of 1 million = 1000 people. Good so far. But additionally you will also flag 0.1% of the rest - 0.1% of 999,000 healthy people = 999 false positives.
So you end up with 1,999 positives, 1000 of which are real cases, while the rest are actually not sick at all. Your test accuracy is just 50%.
If you do this test for even 10% of the US population daily (30 million tested daily), you will flag incorrectly 30*999 = 29,970 false positives daily.
The actual rate of corona spread in the US, as of today, is around 15,000 per million, or 0.015%. If we redo these numbers for 30Million people testing daily and assuming infection rates of 0.015% and test accuracy rate of 0.1% false positives, we get:
4500 real cases correctly flagged.
29,996 false positives on a daily basis!
A person flagged as positive actually has only a 13% chance of really being infected!
(All calculations here inspired by Baye’s theorem, and Sidhartha Mukherji’s book The Laws of Medicine)
In my view these types of tests, even if they exist, will take us nowhere. Here is why:
Assume a test which correctly identifies all asymptomatic patients - no false negatives. So any person who is infected will be correctly flagged as positive. Now also assume that this test has a failure rate of 0.1%, which means that for every 1000 un-infected people tested, by mistake it will flag one of the 1000 as positive. Looks pretty good, isnt it? Not so fast!
Assume that the infection rate of Corona is 0.1% - so one in every thousand is infected - whether symptomatic or not.
Now if you run such a test with a million people, you will flag all the infected people - 0.1% of 1 million = 1000 people. Good so far. But additionally you will also flag 0.1% of the rest - 0.1% of 999,000 healthy people = 999 false positives.
So you end up with 1,999 positives, 1000 of which are real cases, while the rest are actually not sick at all. Your test accuracy is just 50%.
If you do this test for even 10% of the US population daily (30 million tested daily), you will flag incorrectly 30*999 = 29,970 false positives daily.
The actual rate of corona spread in the US, as of today, is around 15,000 per million, or 0.015%. If we redo these numbers for 30Million people testing daily and assuming infection rates of 0.015% and test accuracy rate of 0.1% false positives, we get:
4500 real cases correctly flagged.
29,996 false positives on a daily basis!
A person flagged as positive actually has only a 13% chance of really being infected!
- Will you be happy to have such a test rolled out nationally?
- And ok with having too many false positives that may overwhelm the outpatient clinics and clog the already strained PCR test pipeline?
- Also do you really think people will believe in this type of test and do it happily?
(All calculations here inspired by Baye’s theorem, and Sidhartha Mukherji’s book The Laws of Medicine)
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