Group testing with prior statistics

Li, Tongxin; Chan, Chun Lam; Huang, Wei; Kaced, Tarik; Jaggi, Sidharth

doi:10.1109/isit.2014.6875253

Cited by 54 publications

(75 citation statements)

References 21 publications

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“…Of the 5 pools which contained one individual sample with an "indeterminate" result (in each pool), one was found to be negative suggesting potential yet negligible loss of sensitivity. 20,21,23), and 4 out of 5 pools containing a single indeterminate sample detected as indeterminate (pools 16,17,18,19,22); Pools containing 1-2 samples with low amount of SARS-CoV-2 are detected at a similar Ct (pools [9][10][11][12][13][14][15][16][17][18], showing clinical sensitivity is retained and the risk of false negatives is minimal. UD= Undetected.…”

Section: Resultsmentioning

confidence: 99%

“…We assume all samples are independent and identically distributed, and denote the probability of a sample to be positive by p (prevalence of detectable COVID-19 patients in the relevant population) and the pool size by n. The efficiency of the algorithms described above depends on both p and n. The best theoretical efficiency is (− " ( ) − (1 − ) " (1 − )) ,! [23]. The efficiency of Dorfman pooling [22].…”

Section: Discussionmentioning

confidence: 99%

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Large-scale implementation of pooled RNA-extraction and RT-PCR for SARS-CoV-2 detection

Ben-Ami

Klochendler

Seidel

et al. 2020

Preprint

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Testing for active SARS-CoV-2 infection is a fundamental tool in public health measures taken to control the COVID-19 pandemic. Due to the overwhelming use of SARS-CoV-2 RT-PCR tests worldwide, availability of test kits has become a major bottleneck. Here we demonstrate the reliability and efficiency of two simple pooling strategies that can increase testing capacity about 5-fold to 7.5-fold, in populations with a low infection rate. We have implemented the method in a routine clinical diagnosis setting, and already tested 2,168 individuals for SARS-CoV-2 using 311 RNA extraction and RT-PCR kits.

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Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Large-scale implementation of pooled RNA-extraction and RT-PCR for SARS-CoV-2 detection

Ben-Ami

Klochendler

Seidel

et al. 2020

Preprint

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“…Kealy, Johnson and Piechocki [120] give a Hwang-type binary splitting algorithm (see Section 1.5) in the adaptive case, building on an earlier work of Li et al [128] who developed the Laminar algorithm for the prior defectivity model (Definition 5.1). They discard very low probability items (which are unlikely to be defective anyway, so can be assumed nondefective without wasting tests).…”

Section: Adaptive Testingmentioning

confidence: 99%

“…It should be noted, however, that using the same number of tests as the uniform setting does not amount to achieving the same rate; the rate can be much smaller for a given number of tests when H(U) k log 2 n k . Nonadaptive test designs that introduce block structure into the test matrix were explored in [128]. The performance guarantee given for this approach does not quite amount to a positive rate, as the scaling achieved is T = O(H(U) log n) rather than T = O(H(U)).…”

Section: Nonadaptive Testingmentioning

confidence: 99%

Group Testing: An Information Theory Perspective

Aldridge¹,

Johnson²,

Scarlett³

2019

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The group testing problem concerns discovering a small number of defective items within a large population by performing tests on pools of items. A test is positive if the pool contains at least one defective, and negative if it contains no defectives. This is a sparse inference problem with a combinatorial flavour, with applications in medical testing, biology, telecommunications, information technology, data science, and more.In this monograph, we survey recent developments in the group testing problem from an information-theoretic perspective. We cover several related developments: efficient algorithms with practical storage and computation requirements, achievability bounds for optimal decoding methods, and algorithmindependent converse bounds. We assess the theoretical guarantees not only in terms of scaling laws, but also in terms of the constant factors, leading to the notion of the rate of group testing, indicating the amount of information learned per test. Considering both noiseless and noisy settings, we identify several regimes where existing algorithms are provably optimal or near-optimal, as well as regimes where there remains greater potential for improvement.In addition, we survey results concerning a number of variations on the standard group testing problem, including partial recovery criteria, adaptive algorithms with a limited number of stages, constrained test designs, and sublineartime algorithms.S 0 , S 1 partition of the defective set (Equation (4.4)) ı information density (Equation (4.6)) X 0,τ , X 1,τ sub-matrices of X corresponding to (S 0 , S 1 ) with |S 0 | = τ (Equation (4.14))τ ) (Equation (4.16)) 2. If the preceding test is negative, A contains no defective items, and we halt. If the test is positive, continue. 3. If A consists of a single item, then that item is defective, and we halt. Otherwise, pick half of the items in A, and call this set B. Perform a single test of the pool B. 4. If the test is positive, set A := B. If the test is negative, set A := A \ B. Return to Step 3. A BRIEF REVIEW OF ZERO-ERROR GROUP TESTINGObserve that S(i) is the set of tests containing item i, while S(K) is the set of positive tests when the defective set is K.Definition 1.10. A matrix X is called k-separable if the support unions S(L) are distinct over all subsets L ⊆ {1, 2, . . . , n} of size |L| = k.A matrix X is calledk-separable if the support unions S(L) are distinct over all subsets L ⊆ {1, 2, . . . , n} of size |L| ≤ k.Clearly, using a k-separable matrix as a test design ensures that group testing will provide different outcomes for each possible defective set of size k; thus,

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“…While there is significant literature on multiple alternative models of group testing [3][4][5][6][7][8][9][10][11], the focus of this work is primarily on non-adaptive group testing, under ǫ-error and zero-error reconstruction guarantee metrics. We thus restrict the discussion of prior work to the literature on lower bounds and algorithms (both deterministic and randomized) for ǫ-error and zero-error non-adaptive group testing.…”

Section: Related Workmentioning

confidence: 99%

Nearly optimal sparse group testing

Gandikota

Grigorescu

Jaggi

et al. 2016

2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Group testing is the process of pooling arbitrary subsets from a set of n items so as to identify, with a minimal number of disjunctive tests, a "small" subset of d defective items. In "classical" non-adaptive group testing, it is known that when d = o(n 1−δ ) for any δ > 0, θ(d log(n)) tests are both information-theoretically necessary, and sufficient to guarantee recovery with high probability. Group testing schemes in the literature meeting this bound require most items to be tested Ω(log(n)) times, and most tests to incorporate Ω(n/d) items.Motivated by physical considerations, we study group testing models in which the testing procedure is constrained to be "sparse". Specifically, we consider (separately) scenarios in which (a) items are finitely divisible and hence may participate in at most γ tests; and (b) tests are size-constrained to pool no more than ρ items per test. For both scenarios we provide information-theoretic lower bounds on the number of tests required to guarantee high probability recovery. In particular, one of our main results shows that γ-finite divisibility of items forces any group testing algorithm with probability of recovery error at most ǫ to perform at least Ω(γd(n/d) (1−2ǫ)/((1+2ǫ)γ) ) tests. Analogously, for ρ-sized constrained tests, we show an information-theoretic lower bound of Ω(n log(n/d)/(ρ log(n/ρd))). In both scenarios we provide both randomized constructions (under both ǫ-error and zero-error reconstruction guarantees) and explicit constructions of computationally efficient group-testing algorithms (under ǫ-error reconstruction guarantees) that require a number of tests that are optimal up to constant factors in some regimes of n, d, γ and ρ. We also investigate the effect of unreliability/noise in test outcomes.

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Group testing with prior statistics

Cited by 54 publications

References 21 publications

Large-scale implementation of pooled RNA-extraction and RT-PCR for SARS-CoV-2 detection

Large-scale implementation of pooled RNA-extraction and RT-PCR for SARS-CoV-2 detection

Group Testing: An Information Theory Perspective

Nearly optimal sparse group testing

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