Community aware group testing

Group testing pools together diagnostic samples to reduce the number of tests needed to identify infected members in a population. The observation we make in this paper is that we can leverage a known community structure to make group testing more efficient. For example, if $n$ population members are partitioned into $F$ families, then in some cases we need a number of tests that increases (almost) linearly with $k_f$, the number of families that have at least one infected member, as opposed to $k$, the total number of infected members. We show that taking into account community structure allows to reduce the number of tests needed for adaptive and non-adaptive group testing, and can improve the reliability in the case where tests are noisy.

[1]  Venkatesh Saligrama,et al.  Non-adaptive group testing: Explicit bounds and novel algorithms , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[2]  Wenhao Huang,et al.  Group testing with prior statistics , 2014, 2014 IEEE International Symposium on Information Theory.

[3]  Olivier Gossner,et al.  Group testing against Covid-19 , 2020 .

[4]  Junan Zhu,et al.  Noisy Pooled PCR for Virus Testing , 2020, bioRxiv.

[5]  Matthew Aldridge,et al.  The capacity of adaptive group testing , 2013, 2013 IEEE International Symposium on Information Theory.

[6]  Ajit Rajwade,et al.  Tapestry: A Single-Round Smart Pooling Technique for COVID-19 Testing , 2020, medRxiv.

[7]  Amin Coja-Oghlan,et al.  Optimal Group Testing , 2020, COLT.

[8]  Matthew Aldridge,et al.  Group testing: an information theory perspective , 2019, Found. Trends Commun. Inf. Theory.

[10]  R. Dorfman.  The Detection of Defective Members of Large Populations , 1943 .

[11]  F. K. Hwang,et al.  A Boundary Problem for Group Testing , 1981 .

[12]  Mayank Bakshi,et al.  Efficient Algorithms for Noisy Group Testing , 2017, IEEE Transactions on Information Theory.

[13]  Amin Coja-Oghlan,et al.  Information-Theoretic and Algorithmic Thresholds for Group Testing , 2020, IEEE Transactions on Information Theory.

[14]  Oliver Johnson,et al.  Strong Converses for Group Testing From Finite Blocklength Results , 2015, IEEE Transactions on Information Theory.

[15]  Matthew Aldridge,et al.  Performance of Group Testing Algorithms With Near-Constant Tests Per Item , 2016, IEEE Transactions on Information Theory.

[16]  K. Mullis,et al.  Enzymatic amplification of beta-globin genomic sequences and restriction site analysis for diagnosis of sickle cell anemia. , 1985, Science.

[17]  L. Kucirka,et al.  Variation in False-Negative Rate of Reverse Transcriptase Polymerase Chain Reaction–Based SARS-CoV-2 Tests by Time Since Exposure , 2020, Annals of Internal Medicine.

[18]  M. Sobel,et al.  Group testing to eliminate efficiently all defectives in a binomial sample , 1959 .

[19]  David S. Fischer,et al.  Group Testing for SARS-CoV-2 Allows for Up to 10-Fold Efficiency Increase Across Realistic Scenarios and Testing Strategies , 2020, Frontiers in Public Health.

[20]  Matthew Aldridge,et al.  Individual Testing Is Optimal for Nonadaptive Group Testing in the Linear Regime , 2018, IEEE Transactions on Information Theory.

[21]  Paul S. Albert,et al.  Revisiting Nested Group Testing Procedures: New Results, Comparisons, and Robustness , 2016, The American statistician.

[22]  Brendan J. Frey,et al.  Factor graphs and the sum-product algorithm , 2001, IEEE Trans. Inf. Theory.

[23]  Volkan Cevher,et al.  Phase Transitions in Group Testing , 2016, SODA.

[24]  F. Hwang.  A Method for Detecting all Defective Members in a Population by Group Testing , 1972 .

[25]  D. Du,et al.  Combinatorial Group Testing and Its Applications , 1993 .