One class of people who have become loud of twitter of late is what I call the "testing mafia". Every time someone tweets some covid-19 related news that seems mildly positive, they instinctively react "but we aren't testing enough".

I want to take a small maths class here

This is one of our learnings from the AIDS epidemic of the 1980s and early 90s, and is a staple feature of high high school and college maths classes in the last 2 decades. This has to do with Bayes's Theorem.

The fundamental concept is that testing is never perfect. Never. You can have a test that is accurate "to a high degree" but never perfect.

So inevitably we will have a lot of "false positives" (no disease marked as with disease) and "false negatives" (other way round)

The other key concept here is the "prior probability" or the "base rate". How accurate or reliable a test is is dependent on the prior probability that someone being tested has the disease.

Through the first half of the 20th century this was a controversial concept. For more on Bayesian reasoning, and the great Bayesian versus Frequentist debates, I urge you to read "The Theory That Would Not Die" by Sharon Bertsch McGrayne https://www.amazon.in/dp/B0050QB3EQ/ref=dp-kindle-redirect?_encoding=UTF8&btkr=1

Back to testing. So if you catch a random guy off the street and decide to test him, the "prior probability" he has the disease is the overall incidence of disease in the region. Let's assume for now it's 1%.

Let's assume we have a very very high accuracy test. 99.9% accuracy (only 1 in 1000 with the disease is marked as "no disease"). Also assume we have a low false positive rate (only 1 in 1000 without the disease is marked as "diseased").

Let's start with 100,000 "random guys off the street". Statistically, 1000 of them have the disease.

The test will mark 999 of them as "have disease". 1 as "no disease".

Among the other 99,000, test marks 99 as "have disease". And the rest as "no disease"

So if the test says "have disease", what is the likelihood that the tested person has the disease? it's 999 / (999 + 99). Around 10/11.

Or 91%. So when you test "randomly", 1 in 10 people you find positive are actually not positive. And this is with a highly accurate test.

What if we were to test more carefully? Only people with higher "prior probabilities"? Let's say people living in hotspots. Or those who have come in contact with already infected. Or have respiratory infection.

Let's assume a prior probability of 10%.

Now, of our base of 100,000, 10000 have the disease.
Test marks 9990 as "have disease". 10 as "no disease".

Of remaining 90000, test marks 90 as "have disease" and 89910 as "no disease".

Now, 9990/(9990+90) or 99.1% of people marked out by the test as "have disease" have it.

All this is assuming a highly accurate test (1 in thousand error either way, positive or negative). This graph shows the likelihood of having a disease conditional on testing positive as a function of the prior probability of having the disease

Yes, the accuracy is highly sensitive to the prior probability of having the disease.

Still, see that the higher the prior, the higher the accuracy of the test.

Now let's assume the test is not that accurate. Let's assume it is wrong once every 100 times (or a 99% accuracy. let's assume a 1% false positive rate as well).

The curve looks very different

Right now we don't know how accurate the test for Covid-19 is. If you ask the experts they'll tell you "it's accurate" without a number on it. It's impossible to put a number on it since it's a new disease.

So a prudent strategy in this case is to test when the prior probability is already high.

People who have travelled abroad.
People who have come in contact with infected people
People with respiratory illnesses.
People who "travelled to Delhi".

Exactly what India is doing.

OK this went viral. I don't have any soundcloud, but to lighten up your day and distract you from your covid and lockdown-related anxiety, I offer you this absolutely hilarious video by @MarriageAuntie on "shit parents in the arranged marriage market say" https://twitter.com/MarriageAuntie/status/1250273958592516098?s=20

One addendum. A lot of people have misunderstood my tweetstorm to think I'm "supporting whatever the government is doing".

All I'm saying is - unless prior probability of infection is high (>= 5%, as a goood rule of thumb), DON'T TEST

The converse is also true. If someone has a high (>= 5%) prior probability of being infected, they NEED TO BE TESTED.

I understand from multiple sources that's not really happening, and if that is true, it is unfortunate.

What we don't need is to increase testing for the heck of it. What we don't need is "random testing".

What we need is to ensure that people in these categories (for a start) get tested. Also whenever "base rate" goes over 5%, test. https://twitter.com/karthiks/status/1250362120039878657