The @US_FDA has now authorized “pooled testing” for #COVID19 to save testing reagents and speed results. I’m a big fan. But, this only works in low prevalence situations. To see why, here is some fun Sunday morning math for you all.
fda.gov/news-events/pr…
Pooled testing works like this. You get individual swabs from a bunch of people, set aside some of the sample for each person in case needed later, and mix the rest together. Now test the mixed (pooled) sample. If negative, you’re done! One test for N people, saving N-1 tests.
If the pool is positive, you have to go retest each individual sample to identify the positive(s). Plus, you already did one extra test for the initial pooled sample. So a positive pool costs N+1 tests. You can see where we are going here...
The FDA has approved pooling for 4 samples at a time, so let’s set our N to 4 for the sake of example. Neg pool=1 test, pos pool=5 tests. Individual testing=4 tests. Clearly, the key is the ratio of positive to negative pools. The more positives, the fewer tests we save.
The probability of a positive pool is related to the underlying prevalence in the group being tested. That is, how many people in the group are likely to be positive? Right now, national positive test rate is 7.4%. Let’s start with that. coronavirus.jhu.edu/testing/indivi…
The negative test rate is the inverse, or 92.6%. Prob that all 4 tests are negative is 0.926^4=0.735. So on average, 73.5% of pools will be negative, and 26.5% will have at least one positive. Call it 74&26. If we do 100 pools of 4, we will need 74+(26*5) tests=204 tests.
Bonanza! If we had done all those individually, we would have needed 400 tests. We have saved 196 tests - or put another way, we have boosted our test capacity by 50%! BUT suppose we are in Arizona, where current test positive rate is 24.2%.
Probability of a negative pool is now only 33%. Total tests needed for 400 people = 33+(67*5)=368 tests. Only saving 8%, and adding a lot of time by retesting 2/3 of the pools. Not worth it.
OTOH, in CT where I live, test positivity is 0.8%. We could pool a whole classroom of 20 kids and still have 85% of pools be negative, saving 80% of the tests! Now, accuracy falls off with pools that large, so we wouldn’t actually, but we’d still save 72% with pools of 4.
Pooled testing is great for surveillance activities with expected low prevalence, like routinely testing asymptomatic people in schools or workplaces. I would LOVE to see this be part of safe back to school plans. But, where infections are rampant, it’s not the right strategy.
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