Many a times when problems overwhelm us, we tend to lose sight of simple solutions that can help reduce the problem's impact to a large degree, if not solve the problem itself.
For some time now the world has been confidently asserting that the low number of Corona cases in India have been because of under-testing. Rather than getting into the debate about such assertions, it is a fact that India has been conservatively testing - possibly to avoid wasting valuable test-kits on unlikely cases. Everyone is aware about the danger Corona poses to a densely populated country like ours. If it gets into social transmission stage, it will be a DDoS (distributed denial of service) attack on our health-care system (like it has proven to be in the Europe and the US). For a delicately poised health-care system like ours, it will turn out to be a monumental crisis. Long story short, since test kits can be in short supply, wide-scale testing in an over-populous country like ours, is hardly practical, and the powers that be would try to conserve this 'fire-power' till the right time.
While all this has been happening, today I came across a smart way of addressing this very problem of increasing test coverage without burdening the available resources, namely: test-kits and time taken for testing. And this method is a perfect example of how simple solutions hide under plain sight when we are overwhelmed with the monstrosity of a problem. Here's the tweet a friend shared with me, and light bulbs went off! -
It refers to a research paper published by researchers at Goethe University, Frankfurt about a method to increase Covid-19 test coverage across the world. The english translation of corresponding news is available here - [3]
At a higher level, the method suggests pooling of test samples from a large group of people, and then using binary search to drill down to the positive cases.
In layman's terms, if let's say the test was conducted using blood samples of people, then we mix blood samples of say 100 people and conduct the test once for that "mixed" sample. If the test is negative: voila! all 100 people are corona-negative and no further testing is needed.
If, on the other hand, the test is positive, then it indicates that there are one or more corona-positive samples in that "mixed" sample. So, as a next step, we bifurcate the samples into groups of 50 each, and then conduct a test on each of those 2 groups. Apply the same method again: if negative, all the samples in the groups are corona-negative; and if positive, bifurcate the group further into groups of 25 each, and then wash, rinse and repeat till you drill down to the corona positive sample(s).
In simpler terms, the effectiveness of this method in a city like New York will be far less, since the prevalence of corona-positive cases there is very high (projected to be 50% of population in a few days). But in India, which fortunately seems to be at a much earlier stage, and hence the prevalence of the cases are low, due to group elimination, this method will be quite effective.
So far, we have been concentrating on testing only highly probable cases - like people with travel-history or people with corona-positive contacts. If we adopt this method, we can bring additional categories of people, like probables, less-probables, precautionary-test-needed, flu-patients etc, under the ambit of tests. Increasing the scope of tests in such way, will not only help us strike down the "under-testing" assertions, but will help us detect and contain/quarantine corona cases at a much higher rate, without increasing costs or time required to test in proportion.
test-1: 100 samples => positive
test-2 and test-3: 50 samples each => 1 group positive
test-4 and test-5: 25 samples each => 1 group positive
test-6 and test-7: 12/13 samples each => 1 group positive
test-8 and test-9: 6 samples each => 1 group positive
test-10 and test-11: 3 samples each => 1 group positive
test-12 and test-13: 1/2 samples each => 1 group positive
test-14 and test-15: 1 sample each => 1 positive
So instead of needing 100 tests for 100 people, we needed only 15 test kits to come to the same conclusion/result.
Also, a major boost will come in the form of all-negative tests, i.e. if the first "mixed" test of 100 samples itself turns out to be negative - it will mean all 100 people are corona-negative and no further tests are needed. This can be used to pool all less-likelies and less-probables together into 1 test - to verify the assumption that they are indeed corona-negative.
Now the obvious question will be - what if all 100 are to be corona-positive? In that case, we will end up using more test-kits than 100, specifically: N + 2LogN + 1 = about 115. In other words, the effectiveness of such binary search will be directly proportional to the prevalence of corona in the demography under test. Higher the prevalence (think New York), lower the effectiveness. Lower the prevalence (think tier-2 cities in India), higher the effectiveness. Here, prevalence is expected rate/spread of infection, not measured one.
Turns out the clinical term for such group testing is - "pooling". Pooling of samples is not a novel technique per se. I came across a research paper that asserts that such pooling has been in use since the times of world-war-2.
So now the question remains if such pooling of samples is possible in case of Corona virus testing. Turns out not only the Goeth University, Frankfurt, but even a university from Israel, with the help from a private lab, has managed to successfully test [5] pooling of samples for Corona testing. The false-negative rate mentioned in the paper [4] is about 10% when testing for 1-in-32 samples, and I assume it can be brought down further for 1-in-16 tests.
One small technical point to note here is - this method makes things scale even faster, since it potentially allows detecting 1-in-16 i.e. one positive case out of 16 samples. So the 'N' that we were considering above, will actually itself become log-to-the-base-16 of the actual size of the group, increasing the testing capacity at an even higher (exponentially higher) rate. In simpler terms, every one of those 16 samples, can themselves be a mixture of 16 samples, since the final test can detect 1-in-16 of the "mixed" sample which may have showed up positive in an earlier test run.
I am no medical/clinical expert here, and this is not a declaration that this will bring us out of the clutches of this Corona pandemic. Nevertheless, this is a ray of hope for a densely populated country like ours, and I will love to hear what our medical professionals have to say about this. I am sure there will be some practical/logistical issues/obstacles in adopting this, but I, for one, would like to believe that the benefits to efforts ratio, for efforts required in overcoming those obstacles, will be high enough, given the whole economy is being held hostage due to the spread of this pandemic.
Here's hoping for a quick recovery.
[1] Chennai Firm Close to Developing First India-Made Coronavirus Test Kits, But 'Govt Nod May Take 2-3 Weeks'
[2] Meet the woman behind India's first covid testing kit
For some time now the world has been confidently asserting that the low number of Corona cases in India have been because of under-testing. Rather than getting into the debate about such assertions, it is a fact that India has been conservatively testing - possibly to avoid wasting valuable test-kits on unlikely cases. Everyone is aware about the danger Corona poses to a densely populated country like ours. If it gets into social transmission stage, it will be a DDoS (distributed denial of service) attack on our health-care system (like it has proven to be in the Europe and the US). For a delicately poised health-care system like ours, it will turn out to be a monumental crisis. Long story short, since test kits can be in short supply, wide-scale testing in an over-populous country like ours, is hardly practical, and the powers that be would try to conserve this 'fire-power' till the right time.
THE GAME CHANGER
India has been importing test-kits from Germany [1], and the test costs almost 4-5k per head, which is pretty high, if considered at the scale of Indian population. One Indian lab came up with a homogeneous test-kit [2] that can not only test faster and more accurately, but is also more cost effective. Cost of testing still remains in the range of 1k-1.5k per head though - again not exactly cheap, when considered at the scale of Indian population.While all this has been happening, today I came across a smart way of addressing this very problem of increasing test coverage without burdening the available resources, namely: test-kits and time taken for testing. And this method is a perfect example of how simple solutions hide under plain sight when we are overwhelmed with the monstrosity of a problem. Here's the tweet a friend shared with me, and light bulbs went off! -
It refers to a research paper published by researchers at Goethe University, Frankfurt about a method to increase Covid-19 test coverage across the world. The english translation of corresponding news is available here - [3]
At a higher level, the method suggests pooling of test samples from a large group of people, and then using binary search to drill down to the positive cases.
In layman's terms, if let's say the test was conducted using blood samples of people, then we mix blood samples of say 100 people and conduct the test once for that "mixed" sample. If the test is negative: voila! all 100 people are corona-negative and no further testing is needed.
If, on the other hand, the test is positive, then it indicates that there are one or more corona-positive samples in that "mixed" sample. So, as a next step, we bifurcate the samples into groups of 50 each, and then conduct a test on each of those 2 groups. Apply the same method again: if negative, all the samples in the groups are corona-negative; and if positive, bifurcate the group further into groups of 25 each, and then wash, rinse and repeat till you drill down to the corona positive sample(s).
HOW EXACTLY DOES IT WORK
The bifurcation part is where this method derives its power from. It's a standard binary search algorithm. Well, a little less than standard maybe - because in this case the effectiveness of the algorithm depends on probabilistic distribution of corona-positive cases across a demography, rather than the textbook pre-condition of having a "sorted-set" to give it the edge.In simpler terms, the effectiveness of this method in a city like New York will be far less, since the prevalence of corona-positive cases there is very high (projected to be 50% of population in a few days). But in India, which fortunately seems to be at a much earlier stage, and hence the prevalence of the cases are low, due to group elimination, this method will be quite effective.
So far, we have been concentrating on testing only highly probable cases - like people with travel-history or people with corona-positive contacts. If we adopt this method, we can bring additional categories of people, like probables, less-probables, precautionary-test-needed, flu-patients etc, under the ambit of tests. Increasing the scope of tests in such way, will not only help us strike down the "under-testing" assertions, but will help us detect and contain/quarantine corona cases at a much higher rate, without increasing costs or time required to test in proportion.
BINARY SEARCH TO REDUCE NUMBER OF TESTS
By definition, and let's say in ideal conditions, binary search will roughly take about 2logN + 1 (base 2) tests to find out a corona-positive sample in a group of N samples. For example, if let's say there is 1 corona positive in a group of 100 people, here's how the testing process will work out -test-1: 100 samples => positive
test-2 and test-3: 50 samples each => 1 group positive
test-4 and test-5: 25 samples each => 1 group positive
test-6 and test-7: 12/13 samples each => 1 group positive
test-8 and test-9: 6 samples each => 1 group positive
test-10 and test-11: 3 samples each => 1 group positive
test-12 and test-13: 1/2 samples each => 1 group positive
test-14 and test-15: 1 sample each => 1 positive
So instead of needing 100 tests for 100 people, we needed only 15 test kits to come to the same conclusion/result.
Also, a major boost will come in the form of all-negative tests, i.e. if the first "mixed" test of 100 samples itself turns out to be negative - it will mean all 100 people are corona-negative and no further tests are needed. This can be used to pool all less-likelies and less-probables together into 1 test - to verify the assumption that they are indeed corona-negative.
Now the obvious question will be - what if all 100 are to be corona-positive? In that case, we will end up using more test-kits than 100, specifically: N + 2LogN + 1 = about 115. In other words, the effectiveness of such binary search will be directly proportional to the prevalence of corona in the demography under test. Higher the prevalence (think New York), lower the effectiveness. Lower the prevalence (think tier-2 cities in India), higher the effectiveness. Here, prevalence is expected rate/spread of infection, not measured one.
CLINICAL VIABILITY: POOLING
Now, in the age of sensationalism, it's but natural to be cynical about such claims, and counter question if all this "mixing" of samples is even clinically viable or practical. That is, can we even "mix" two samples, and reliably test the "mixture" for corona-positivity.Turns out the clinical term for such group testing is - "pooling". Pooling of samples is not a novel technique per se. I came across a research paper that asserts that such pooling has been in use since the times of world-war-2.
So now the question remains if such pooling of samples is possible in case of Corona virus testing. Turns out not only the Goeth University, Frankfurt, but even a university from Israel, with the help from a private lab, has managed to successfully test [5] pooling of samples for Corona testing. The false-negative rate mentioned in the paper [4] is about 10% when testing for 1-in-32 samples, and I assume it can be brought down further for 1-in-16 tests.
One small technical point to note here is - this method makes things scale even faster, since it potentially allows detecting 1-in-16 i.e. one positive case out of 16 samples. So the 'N' that we were considering above, will actually itself become log-to-the-base-16 of the actual size of the group, increasing the testing capacity at an even higher (exponentially higher) rate. In simpler terms, every one of those 16 samples, can themselves be a mixture of 16 samples, since the final test can detect 1-in-16 of the "mixed" sample which may have showed up positive in an earlier test run.
FINAL THOUGHTS
All this information has been compiled from resources available on the internet, solely for making it easier to understand how this technique could be highly useful in Indian context, and why India should aggressively pursue and explore this further.I am no medical/clinical expert here, and this is not a declaration that this will bring us out of the clutches of this Corona pandemic. Nevertheless, this is a ray of hope for a densely populated country like ours, and I will love to hear what our medical professionals have to say about this. I am sure there will be some practical/logistical issues/obstacles in adopting this, but I, for one, would like to believe that the benefits to efforts ratio, for efforts required in overcoming those obstacles, will be high enough, given the whole economy is being held hostage due to the spread of this pandemic.
Here's hoping for a quick recovery.
REFERENCES
Here are some references that I collected from the twitter thread, and elsewhere on the internet.[1] Chennai Firm Close to Developing First India-Made Coronavirus Test Kits, But 'Govt Nod May Take 2-3 Weeks'
[2] Meet the woman behind India's first covid testing kit
