A Compressed Sensing Approach to Pooled RT-PCR Testing for COVID-19 Detection

Abstract

We propose Tapestry, a novel approach to pooled testing with application to COVID-19 testing with quantitative Polymerase Chain Reaction (PCR) that can result in shorter testing time and conservation of reagents and testing kits. Tapestry combines ideas from compressed sensing and combinatorial group testing with a novel noise model for PCR. Unlike Boolean group testing algorithms, the input is a quantitative readout from each test, and the output is a list of viral loads for each sample. While other pooling techniques require a second confirmatory assay, Tapestry obtains individual sample-level results in a single round of testing. When testing n samples with t tests, as many as k = O(t/ log n) infected samples can be identified at clinically-acceptable false positive and false negative rates. This makes Tapestry viable even at prevalence rates as high as 10%. Tapestry has been validated in simulations as well as in wet lab experiments with oligomers. Clinical trials with Covid-19 samples are underway. An accompanying Android application Byom Smart Testing which makes the Tapestry protocol straightforward to implement in testing centres is available for free download.

Tropical Group Testing

“…Each curve is 10,000 encoding-decodings, i.e., 450,000 tubes, 100,000 patients, and 1,050,000 test takers. Compare this to Tapestry's data point and its standard deviations (4.50% ± 2.41%, 99.30% ± 2.55%) (TableS.XII of the preprint version[Gho+20]).…”

AC-DC: Amplification Curve Diagnostics for Covid-19 Group Testing

“…The recently proposed Tapestry method [56] combines group testing with compressive sensing and uses combinatorial designs (i.e., Kirkman systems) to construct the measurement matrix. However, there are several factors that do not seem to be accounted for in this approach.…”

“…Tapestry also does not take into account the fact that the number of RT-PCR machines/staff members is limited 6 , and that this inherently suggests using adaptive testing strategies. 7 Finally, the CS methods [56] rely on Gaussian assumptions regarding measurement errors due to cycle inefficiency that are often hard to verify (and do not take into account that the efficiency decays with the number of cycles and with the number of potential mutations in the primer regions; see Section II). As many other quantitative methods, it appears vulnerable to heavy hitters, which are not accounted for in the Tapestry scheme.…”

“…The only other work that explores quantitative testing for Covid-19 is reported in [61]. There, the same problem setup as in [56] is used to postulate an additive viral load model which does not refer further to the C t values. The new contribution is a proposal for a two-stage testing scheme that bears a small resemblance to our methods in so far that we also propose two-stage adaptive pooling schemes.…”

Optimal Pooling Matrix Design for Group Testing with Dilution (Row Degree) Constraints

“…However, most countries including the US are currently experiencing a scarcity [3] of various medical resources including tests [4], and the test throughput or capacity can be limited. Pooled sample testing has been proposed as a method for increasing the effective capacity of existing testing infrastructure using the classical method of group testing or newly introduced compressed sensing techniques for virus testing [5][6][7][8][9][10][11] using the RT-qPCR (real-time Quantitative Polymerase Chain Reaction) tests.…”