An upper bound to the benefits of implementing positive assortative matching in pooled testing

What is it about?

Pooled testing combines individual specimens (e.g., blood samples) into one test; if the pooled sample tests positive for infection, each specimen is tested separately. At low prevalence levels, this method is known to reduce the expected number of tests required to screen a population, as individual tests occur only when a pooled test indicates an infection. In my previous research (https://lnkd.in/dyfYHuaK), I have shown that pooling together those with similar probabilities of infection, a process I call ordered pooling, simultaneously minimizes the expected number of tests, the expected number of false positives, and the expected number of false negatives. So, in my previous research, I showed that there is a lower bound of zero to the benefits of implementing ordered pooling. In the current paper, I show that one can also derive an upper bound to these benefits when pool sizes are required to be homogeneous. To compute these upper bounds, we only need information regarding the prevalence of the disease, the maximum and minimum observable probabilities of infection (e.g., as a function of demographics) and an estimate of the dilution effect associated with pooled testing. I also show that the benefits per subject of implementing ordered pooling tend to increase as the batch size increases (i.e., as the number of specimens tested in a day increases).

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Photo by National Cancer Institute on Unsplash

Photo by National Cancer Institute on Unsplash

Why is it important?

If the upper bounds derived in this article indicate that the savings in costs associated with ordered pooling are too small, testers may find it more practical to simply match samples randomly or by the order they arrive for testing. Moreover, the upper bounds can be used to assess the maximum achievable gains associated with the collection of more data from patients. Indeed, as we collect more data from patients (e.g., whether they exhibit symptoms or not) we might increase the maximum and/or the minimum observable probabilities of infection, which in turn tends to increase the upper bounds derived in the paper.

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