Pooling samples to increase SARS-CoV-2 testing

You may have heard of this puzzle about identifying a fake coin: You have eight of Rs. 1 coins. Real coins weigh 10g each, but you are told that one of the coins is fake and weighs less than the others. Using a simple weighing machine, on which you can place some coins and read out their total weight, what is the least number of weighings in which you can locate the fake coin? 

You could check each coin one by one, which could need upto eight weighings if you're unlucky (see Figure 1A). Another way would be to `pool' the coins into two sets of 4 coins and then weigh one pool and then the next. One of these pools will weigh 40g and the other less, so you will already know that 4 coins are real. Then you could split the coins in the second pool into two each and weigh them, and then finally test each coin from the group of 2 that weighed less than 20g. This would take 3 weighings to identify the fake coin (see Figure 1B).

A similar idea can be used to pool samples to test for the virus SARS-CoV-2 which causes COVID-19. Instead of coins, we have samples taken from the nose, throat or saliva of people we are testing. Instead of weighing them, we use an RT-qPCR assay to test for the presence of the virus.

Suppose we had samples from 8 people of whom one was infected. We could have tested each sample individually. In the worst case we would need 8 tests to identify the infected person. But if we pooled the samples into sets of 4, and then sets of 2, as with the coins, then we would need merely 3 tests! Pooling samples can thus save tests. This can save time, reagents and plastics, human resource, money, and most importantly -- by enabling more testing -- lives.

Testing for SARS-CoV-2 is more involved than the setting of this puzzle. For starters, we do not know how many people are infected. We could modify the coin puzzle so that we do not know how many coins are fake either. In that case too, pooling coins reduces the number of weighings needed as long as the number of fake coins is much smaller than the number of real coins. So pooled testing of SARS-CoV-2 should help even if we do not know beforehand how many people are infected.

Another difference is that the RT-qPCR assay has a limit to its sensitivity. Though this is one of the most remarkable assays known to humans --- it can reliably catch a single molecule present in the test tube --- it can still fail to detect very small amounts of the virus. This is because the RT-qPCR machine works with a fixed volume of sample. It might happen that the virus is so dilute in the sample that the volume of sample that found its way into the assay had no virus molecules. Then the assay has correctly reported that there were no virus molecules found in the tube. However, the implication that the patient is not infected turns out to be incorrect.

This happens rarely enough when a single sample is tested at a time. But the problem can get amplified when multiple samples have to be pooled. This is because we take less amounts of each sample, leading to further effective dilution of a sample that might have had molecules from the virus.

So pooling samples dilutes them and a sample with a low viral load may fall below the level detectable by RT-qPCR. It is as if the coin weighing machine could fit only one coin. So to weigh a set of 4 we would have to cut out a quarter piece of each coin and weigh the 4 pieces, rather than 4 full coins. For a large pool, say 10 coins, perhaps a weighing machine with limited sensitivity may not be able to tell the difference between all pieces being real and one piece being fake.

With samples from people, it is quite possible for a sample to have very few viruses, close to the limit of the detection by RT-qPCR. This depends on many things that are impossible to control, like how sick the person was from whom the sample was taken, or precisely how much material was taken from the nose, throat or saliva of the person, or how long the sample was stored before testing. From more than 30,000 samples that were tested positive at the testing centre at InStem (Institute for Stem Cell Science and Regenerative Medicine) and NCBS-TIFR (National Centre for Biological Sciences, Tata Institute of Fundamental Research), Bangalore, we found that the viral load ranged across 5 to 6 orders of magnitude.

Another difference works to the advantage of virus testing. A single RT-qPCR machine can test a little under 100 pools simultaneously in one “round” of testing - it is as if we had 100 weighing machines that we could load with coins.



Figure 1 : Find the fake coin puzzle. There are many variations of this puzzle – for example see  https://en.wikipedia.org/wiki/Balance_puzzle


 A simple pooling strategy known as Dorfman pooling has been widely deployed to test for SARS-CoV-2 using the RT-qPCR test in India and other parts of the world. In this method, we pool groups of 5 samples each. For this size of pool, with well-designed assays, we are confident of detecting even small viral loads. Each pool is tested in the RT-qPCR machine. All samples in a pool that tested negative are declared free of the virus. All samples in a pool that tested positive are then tested individually one more time, to determine if they are positive or negative (see the left side of Figure 2).

Dorfman pooling is a variant of the coin weighing strategy described above. It has one advantage that it works in just two rounds with a single RT-qPCR machine, as long as the number of pools is a bit less than 100. So if there were 10 infected people amongst 200, we would need at most 90 tests done in two rounds, which would take one day. If instead we split 200 into two pools of 100 each, then pools of 50 each and so on, we would need fewer tests but it could take 8 rounds, which would take several days.

Is it better to save on tests at the cost of time, or save on time at the cost of more tests? There is no one correct answer to this question, but it’s important to remember that treatment of a person is not based on whether they test positive or not, it is based on the symptoms they exhibit. Testing is important for contact tracing and quarantining and thereby limiting the spread of the infection. So, one advantage of getting test results quickly is that any infected person will spend less time unknowingly meeting others. Any contact tracing effort will find it easier to identify the people who might have come into contact with the infected person because there will be fewer such people. Similarly, any uninfected person will more quickly have their anxiety lifted and can get back to work without fear of infecting others.

Simple pooling saves substantially only when relatively few people are infected. Taking the example of 200 people as above, suppose now 30 people were infected instead of 10 (15% instead of 5% prevalence). In that case, simple pooling could need as many as 190 tests. One might as well test all 200 individually! In the NCBS-TIFR and InStem testing centre, we reached this situation in July and therefore stopped doing simple pooling. Many hospitals are reporting that 15-20% of their
suspected COVID-19 patients are testing positive. Similarly, amongst health care workers the prevalence of infection is reaching similar levels. Even large scale surveys of several cities, such as Delhi, Mumbai, Pune, are reporting that 20-40% of people tested (using rapid antibody test) have had SARS-CoV-2. In such a scenario, are there cleverer ways of using pooled testing successfully?


Covid 2

Figure 2 : Comparison of two sample pooling strategies for testing SARS-CoV-2. On the left is depicted the “simple pooling” scheme. Samples are grouped into ‘pools’ of a specified size, and in the first round each pool is tested using RT-qPCR. In the second round, each sample from every pool that tested positive is retested individually. If the only consideration is to reduce the number of tests, then the best pool size p to choose is p=√(n/k), for n people of whom k are infected. For this choice, needed would be 2√(kn). However, large pool sizes do result in samples being more diluted so one may want to limit the pool size. The Indian Council of Medical Research has approved a scheme which limits the pool sizes to 5 samples, and this has been used in testing centres across India. On the right is an alternative scheme for pooling called Tapestry pooling. Here, unlike simple pooling, each sample goes into multiple pools. These pools are then tested in a single round of RT-qPCR. Which sample goes into which pool (see Figure 3) is chosen carefully to allow an algorithm, based on a computer science technique called Compressed Sensing, to reconstruct precisely which individual samples are positive or negative from knowledge of which pools are positive or negative. With n people of whom k are positive, this can be done in as few as k*log2(n) tests. Both pooling schemes work best when the prevalence, k/n, is small. Simple pooling works upto 5% prevalence, while Tapestry pooling can work upto 15-20%.


Tapestry Pooling, a pooling scheme invented at IIT Bombay and validated at NCBS-TIFR and InStem, is such a scheme. It can work even when upto 20% of a population is infected and give results in a single round, leading to even faster detection of positives and negatives. Unlike the simple pooling strategy described before, in their scheme each sample goes into more than one pool, and each pool has a different combination of samples within it. Specifically, each sample is split into three different pools, each pool can have anywhere from 4 to 32 samples combined in it, and no two samples occur together in more than one pool. This allows us to use some techniques from computer science, called Compressed Sensing to reconstruct which individuals are positive and which are negative directly from the results of a single round of RT-PCR tests of each pool.

In Tapestry Pooling, we use not just the positive or negative result of each test, but also the estimate of the total viral load of each pool that the RT-PCR provides. Again, using the analogy to the coin puzzle, the weighing machine does not just tell you which pool of coins is heavier or lighter than expected it gives you the actual weight of the pool. Similarly, the RT-PCR machine reports not just whether the sample or pool tested was positive or negative, it gives an estimate for the viral load in that test. This is additional information the computer scientists can use to reconstruct which individual is positive or negative with more accuracy. It allows us to obtain accurate results with a small number of tests for scenarios where simple pooling would not work, such as when the prevalence rate rises beyond 5%.


Figure 3 : An example of how samples are combined into different pools in Tapestry pooling. The matrix shows which samples go into which pools. In total, t pools are formed from n samples. Typically, each sample is used in no more than three pools, and no two samples occur together in more than one pool. These properties, along with the assumption that very few samples are positive, allow us to reconstruct which samples is positive (red) and which negative (green), given the results of testing each of the t pools. This scheme can work for prevalence rates as high as 20% where simple pooling will not work.


A team at NCBS-TIFR and InStem, Bangalore, has extensively tested this combinatorial Tapestry pooling strategy using real SARS-CoV-2 samples. The method worked successfully for many different cases, which can be broadly classified into two categories: First, for identifying positives amongst 100 or less individuals, in about half that number of tests, when the prevalence is 15-20%. This would be useful for testing and diagnosis centres that are seeing such high levels of prevalence, where simple pooling does not work. Several testing centres and hospitals, such as the Tata Memorial Hospital, the Malabar Cancer Centre, and the Bangalore Medical College and Research Institute, are now testing this method to see if it works for the samples they receive. Second, for testing many hundreds to a thousand samples in less than 100 tests, but where the prevalence is not more than a few percent. Such large scale screening of populations could be used, for example, in campuses, factories or offices that want to re-open safely. The savings could potentially be huge because the method needs a very small number of tests, even compared with simple pooling. For this, it is important to build automated devices that can split the samples and pool them in the correct combinations because doing this manually for so many samples is very tedious and error prone. Setting up such devices and making them available across the country is the next challenge in deploying this method for COVID-19 testing.

More details about how Tapestry pooling works and some of the tests used to validate it can be found in the preprints https://arxiv.org/abs/2005.07895 and https://www.medrxiv.org/content/10.1101/2020.04.23.20077727v2.
Glossary of terms:
RT-qPCR assay: This is a method to detect the presence of a specific sequence of RNA or DNA in a sample. For the SARS-CoV-2 virus we look for a sequence in its RNA that we know is not present in other viruses
Viral load: The number of copies of the virus per millilitre
Contact tracing: Finding the contacts of a person who has tested positive, and testing them for the virus.
Prevalence: The number of infected people divided by population size.
We thank C. S. Anirudh and Uma Ramakrishnan for their inputs on the essay