# Group testing - Barokong

Christian Gollier and Olivier Gossner pass on a beautiful and simple idea: Group testing. It's also known as test pooling.)

To stop the virus, we need testing. But we don't have enough tests. As a result, a trillion dollars a month stands to go down the toilet, unemployment is skyrocketing, and a big financial crisis looms. What to do?

Test groups. Group testing works particularly well given that so far, the percentage of infected people is low.

Get a group of 32 people, and they each spit in a bucket. Test the bucket. (Metaphorically. Actually, the samples are swabs, and we mix parts of the samples.) If it's negative, everyone in the group is clean and they can go back to work.

If not, split the samples into two groups of 16, and test again. Again, if a group of 16 is negative, they're all clear. Keep going 8, 4, 2, 1. (You don't get new samples, of course. You take the original samples and split them apart, and test them again.)

If nobody has it, you find out in 1 test, not 32. If 1 out of the 32 has it, you find him or her with 12 tests not 32.

Often the goal of testing is not to find one particular person. And if tests take a day to come back, repeated testing is impractical. But with two rounds of testing you can at least very quickly find groups of 32 and 16 who are all clear, and isolate the smaller groups.

There are distinct reasons to test. If you have a very sick patient and you need to find out what he or she has, you need to test that person. But now testing has moved to public health questions. We want to find and certify the vast majority who do not have it. We want to find out what fraction of a neighborhood has it. And so on. For these purposes, group testing makes sense.

This idea strikes me as particularly good because of the spatial concentration of a virus. With one test we can find out if a city of 10,000 has any infected people. With one test, we can find out if a zip code is free of virus.

Update:This seems like an especially useful idea to get business going again. Every morning, test the group sample of everyone at a business, plant, or building, say even groups of 100. As long as they are all clear the business stays open. To show a business does not have a virus, you only need to test the group.

Update 2: In response to comments. For the purpose of slowing a virus, it doesn't have to be perfect. Paul Romer's simulations are good on this. Just lower the probabilities and you lower transmission rates.