# Q&A: Professor David Donoho discusses mathematics of mass testing

July 29, 2020, 9:49 a.m.

The Daily had the opportunity to sit down with David Donoho, Anne T. and Robert M. Bass Professor of Humanities and Sciences and professor of statistics, to discuss his work and the implications it holds. Donoho recently authored an article in SIAM News about the importance of mass testing and the math behind this development. Donoho suggests that mass testing is the way to safely open up the economy and resume education, all over the world.

This transcript has been lightly edited for clarity.

The Stanford Daily (TSD): Can you describe the work that you’ve been doing with mass testing?

David Donoho (DD): Our article concerns [mass testing] work not only being done by Stanford but also by research teams around the world. In the U.S., Israel, India, Austria, Italy, Spain and Germany. There are people doing important math sciences work on this. [The math] is based on ideas that were first published in my field 80 years ago, and have been used again and again with various diseases, for example, during the initial AIDS crisis. [These models] can also be used anytime we want to test any group of people efficiently to find out who among them might be infected. What we all want to know is if these ideas, where the math has been known for some time, could be used on today’s COVID-19 pandemic, using the tests that we know how to do with COVID-19. With the ideas, if they would work, which they do by the way, [researchers] say that we can determine the disease status of 100 people using only 10 test kits, and that gives you a big improvement in efficiency.

TSD: How is it possible to reduce the amount of tests needed to diagnose people with COVID-19?

DD: What you do is you make a Sudoku puzzle out of the [COVID-19 testing]. You divide each person’s specimen into, let’s say three, and you use it in three different ways. You form pool specimens, where each pool has material from say seven people, combined into one pool sample and mixed together, then you test all of your pool specimens. Once you know which pools are positive, you now have a puzzle — which patients must have been the ones who were infected? If you solve that puzzle, then you know who was infected.

TSD: What does this mass testing look like when it’s implemented in communities?

DD: We recently heard that Cornell University is doing a fully in-person reopening in the fall. The way that it will work there is everyone on campus will have to get COVID tested every five days. Certain groups could be tested more frequently, like those who are involved in healthcare.

TSD: How long did it take to come up with this method/how did you discover that this math could be applied to COVID-19, and what changes, if any, did you have to make?

DD: The basic idea of solving these Sudoku puzzles is to determine who has this disease. [This method] has been around for decades. As I said before it’s been used with HIV, AIDS, STDs. You can set it up so that you use almost no math, but then it’s not as clever and you don’t save as much in testing. You can also set it up so that you can use a more advanced math, and some of those methods are really recent.

What had to be figured out [for COVID-19], is if we were pooling together seven people, and there is only one infected, you might have only 1/7th the amount of virus. [With] a smaller amount of virus than you expected, could [the test] still work? That’s a combination of the sensitivity and specificity of the test. And how does the test behave under dilution? These are things about COVID-19 testing that actually involve the technology of those tests.

TSD: What allows us to mass test?

DD: The fact that most people in the testing groups most likely do not have COVID-19 allows us to do mass testing. Why waste so many tests when most of the people are not going to be infected?

TSD: If all of the people in the testing group have COVID-19 will the math models still be able to figure out the results accurately?

DD: It depends on whose math you are using. There are methods that will still work. Some of the simpler methods might break down, some of the most sophisticated ones would not. If you limit yourself to only one round of testing you might have problems. You can always re-test a small fraction just to make sure you got it right, and as long as you are not re-testing everybody it does not end up costing as many tests. You have to think of it as a problem of how can we as a society get the most people’s disease status determined most efficiently, rather than what does one person individually want or need.

TSD: Why wasn’t this method employed before?

DD: The [Food and Drug Administration (FDA)] only approved pooling for mass testing on June 16; without FDA approval only certain organizations can do this sort of thing. Stanford, led by Professor Benjamin Pinsky, was one of the first to do it, they did it months ago. Pinsky is an associate professor of pathology and infectious diseases at the Stanford School of Medicine. [Pinsky] could do it as a research project because he was at Stanford. The University of Nebraska is another leader and they also used their research status. So if we tried to do it at a non-research institution, we would need some kind FDA approval. The other thing is that from society to society there might be different obstructions. I’ve been talking to people in Canada about doing this. Just because of the way Canadian healthcare is set up, they have to use their equipment in a very specific way and it doesn’t allow them the flexibility to do [mass testing].

TSD: Do you have an estimate for how many more people could we test for COVID-19 with one test?

DD: If we are in a situation with a low prevalence rate, then as a rule of thumb, we can get 10 times as many people as tests. As prevalence goes up you have to use more tests. There is still a benefit as prevalence goes up, but you have to use fancier and fancier math.

TSD: What are possible consequences from this method?

DD: The basic problem would be the dilution effect. This is where someone has an amount of virus that would be detectable if you just did one person one test, but for some reason, [the tests] don’t detect [COVID-19] when it’s seven people one test. A lot of the research is about asking if this is a real problem. All kinds of measurements show that this is not a real problem. The underlying technology is called the RT-qPCR, and it can detect as little as 10 virus particles in a sample. In general if someone were to actually be infected, they would have many more than 10 particles in a sample. Therefore, even if there is some dilution, you would still see more than 10 [virus particles], and be able to identify if someone is infected.

TSD: Why is mass testing in the U.S. important?

DD: Professor Paul Rommer of NYU, who won the 2018 Nobel Prize in Economics, has been arguing for mass testing as the way to open our economy and get people back to work.  We are right now in the deepest recession, in almost 100 years, and we have a very high unemployment rate. A lot of people live paycheck to paycheck, [and] many businesses are failing. In addition, students are just not learning. There is plenty of evidence that shows that online is not working as an instructional technique. Many young people and children are not getting the benefit they should be getting from their formative years. By having mass testing we can confidently re-engage in the economy and education. That is why Cornell University has decided that they can use mass testing, and they can open up in the fall.

TSD: Are there places that have used this method and successfully reduced/identified the amount of COVID-19 cases? If so, where?

DD: It’s being used in Israel and India, and in both places it’s very successful. It started from very engaged researchers, but it’s been picked up by hospitals and public health systems.

TSD: How will mass testing allow us to open the economy and go back to school? As we’ve opened up, we’ve tended to see a spike in cases. Can mass testing help reduce this spike?

DD: That’s the whole point of it, because each person that gets infected is walking around for two weeks in an infectious state. But if you’re testing frequently, then you learn that the person is infected. They can self-quarantine until the two week period is over and then they are not infecting people all that time. That’s exactly what this is all about, to more quickly bring it to people’s attention, so even while they are pre-symptomatic, they know that they could be infecting people, and they are able to avoid that.

TSD: Is testing every two weeks possible, even with our large population? If not what would be needed to make it sustainable?

DD: The response of various private businesses to producing tests has been really amazing. We are now able to test several percent of the population per month. At low prevalence that means we can test almost the whole population every month, just using the current capacity. The capacity is growing, more machines are being installed and more reagent is being produced, so in a few months we will be able to do even better. The need for mass testing that professor Romer has been pointing to, we can get there by building out the current capacity and using these group testing ideas. There are new genomic technologies on the horizon, and that would also help. New tests may come along that may also help.

TSD: Anything else you would like to add that we didn’t cover?

DD: The point of my article in SIAM News is many researchers worldwide understand that mass testing is really the way out of the lockdown and to avoid excess deaths. The really cool thing is that [researchers] now have medRxiv, which allows us to share new discoveries very quickly. So the information about just how effective this would be with COVID-19 is getting out very quickly. We now know this works and can bring the curve down. Often research takes a long time for people to be persuaded, but there is no need for that [with mass testing].

Contact Sonali Muthukrishnan at sonali.muthukrishnan ‘at’ gmail.com.

Sonali Muthukrishnan is a high schooler writing as part of The Daily's Summer Journalism Workshop.