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

The first part of the paper presents a review of the gold-standard testing protocol for Covid-19, real-time, reverse transcriptase PCR, and its properties and associated measurement data such as amplification curves that can guide the development of appropriate and accurate adaptive group testing protocols. The second part of the paper is concerned with examining various off-the-shelf group testing methods for Covid-19 and identifying their strengths and weaknesses for the application at hand. The third part of the paper contains a collection of new analytical results for adaptive semiquantitative group testing with probabilistic and combinatorial priors, including performance bounds, algorithmic solutions, and noisy testing protocols. The probabilistic setting is of special importance as it is designed to be simple to implement by nonexperts and handle heavy hitters. The worst-case paradigm extends and improves upon prior work on semiquantitative group testing with and without specialized PCR noise models.

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

[2]  A. Sterrett.  On the Detection of Defective Members of Large Populations , 1957 .

[3]  C. Fortuin,et al.  Correlation inequalities on some partially ordered sets , 1971 .

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

[5]  Frank K. Hwang,et al.  A Generalized Binomial Group Testing Problem , 1975 .

[6]  Jack K. Wolf,et al.  Born again group testing: Multiaccess communications , 1985, IEEE Trans. Inf. Theory.

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

[8]  Charles J. Colbourn.  Group testing for consecutive positives , 1999 .

[9]  Joel A. Tropp,et al.  Greed is good: algorithmic results for sparse approximation , 2004, IEEE Transactions on Information Theory.

[10]  Peter Damaschke.  Threshold Group Testing , 2005, Electron. Notes Discret. Math..

[11]  R.G. Baraniuk,et al.  Compressive Sensing [Lecture Notes] , 2007, IEEE Signal Processing Magazine.

[12]  Stephen A Krawetz,et al.  Real-time PCR quantification using a variable reaction efficiency model. , 2008, Analytical biochemistry.

[13]  Olgica Milenkovic,et al.  Weighted Superimposed Codes and Constrained Integer Compressed Sensing , 2008, IEEE Transactions on Information Theory.

[14]  Olgica Milenkovic,et al.  A comparative study of quantized compressive sensing schemes , 2009, 2009 IEEE International Symposium on Information Theory.

[15]  Olgica Milenkovic,et al.  Subspace Pursuit for Compressive Sensing Signal Reconstruction , 2008, IEEE Transactions on Information Theory.

[16]  Richard G. Baraniuk,et al.  Compressive Sensing DNA Microarrays , 2008, EURASIP J. Bioinform. Syst. Biol..

[17]  Elsje Pienaar,et al.  Efficiency of the Polymerase Chain Reaction. , 2010, Chemical engineering science.

[18]  Venkatesh Saligrama,et al.  Information Theoretic Bounds for Compressed Sensing , 2008, IEEE Transactions on Information Theory.

[19]  Peter Damaschke,et al.  Bounds for Nonadaptive Group Tests to Estimate the Amount of Defectives , 2010, COCOA.

[20]  Ely Porat,et al.  Search Methodologies , 2022 .

[21]  Olgica Milenkovic,et al.  Information Theoretical and Algorithmic Approaches to Quantized Compressive Sensing , 2011, IEEE Transactions on Communications.

[22]  Amin Karbasi,et al.  Graph-Constrained Group Testing , 2010, IEEE Transactions on Information Theory.

[23]  Mahdi Cheraghchi,et al.  Improved Constructions for Non-adaptive Threshold Group Testing , 2010, Algorithmica.

[24]  Piotr Indyk,et al.  Sketching via hashing: from heavy hitters to compressed sensing to sparse fourier transform , 2013, PODS '13.

[25]  Olgica Milenkovic,et al.  Group testing for non-uniformly quantized adder channels , 2014, 2014 IEEE International Symposium on Information Theory.

[26]  Olgica Milenkovic,et al.  Poisson group testing: A probabilistic model for nonadaptive streaming boolean compressed sensing , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[27]  Olgica Milenkovic,et al.  Semiquantitative Group Testing , 2014, IEEE Transactions on Information Theory.

[28]  Massimo Fornasier,et al.  Compressive Sensing , 2015, Handbook of Mathematical Methods in Imaging.

[29]  Olgica Milenkovic,et al.  Code Construction and Decoding Algorithms for Semi-Quantitative Group Testing With Nonuniform Thresholds , 2014, IEEE Transactions on Information Theory.

[30]  Yuelong Shu,et al.  GISAID: Global initiative on sharing all influenza data – from vision to reality , 2017, Euro surveillance : bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin.

[31]  Philipp Loick,et al.  Optimal adaptive group testing , 2019, ArXiv.

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

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

[34]  Jonathan Scarlett,et al.  An Efficient Algorithm for Capacity-Approaching Noisy Adaptive Group Testing , 2019, 2019 IEEE International Symposium on Information Theory (ISIT).

[35]  Weiyu Xu,et al.  Low-Cost and High-Throughput Testing of COVID-19 Viruses and Antibodies via Compressed Sensing: System Concepts and Computational Experiments , 2020, ArXiv.

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

[37]  Rohit Arora,et al.  SARS-CoV2 Testing: The Limit of Detection Matters , 2020, bioRxiv.

[38]  Daniel B Larremore,et al.  Rethinking Covid-19 Test Sensitivity - A Strategy for Containment. , 2020, The New England journal of medicine.

[39]  Peter Jung,et al.  Efficient Noise-Blind $\ell_1$-Regression of Nonnegative Compressible Signals , 2020, 2003.13092.

[40]  Tomer Hertz,et al.  Efficient high throughput SARS-CoV-2 testing to detect asymptomatic carriers , 2020, medRxiv.

[41]  Matthew L Faron,et al.  Distribution of SARS-CoV-2 PCR Cycle Threshold Values Provide Practical Insight Into Overall and Target-Specific Sensitivity Among Symptomatic Patients , 2020, American journal of clinical pathology.

[42]  J. Peng,et al.  How fast does the SARS-Cov-2 virus really mutate in heterogeneous populations? , 2020, medRxiv.

[43]  Malik Peiris,et al.  Viral dynamics in mild and severe cases of COVID-19 , 2020, The Lancet Infectious Diseases.

[44]  Yael Mandel-Gutfreund,et al.  Evaluation of COVID-19 RT-qPCR test in multi-sample pools , 2020, medRxiv.

[45]  Andrei Z. Broder,et al.  A Note on Double Pooling Tests , 2020, ArXiv.

[46]  Christina Fragouli,et al.  Community aware group testing , 2020, ArXiv.

[47]  Byung Yoon Choi,et al.  Optimization of primer sets and detection protocols for SARS-CoV-2 of coronavirus disease 2019 (COVID-19) using PCR and real-time PCR , 2020, Experimental & Molecular Medicine.

[48]  A. Goyal,et al.  Potency and timing of antiviral therapy as determinants of duration of SARS CoV-2 shedding and intensity of inflammatory response , 2020, medRxiv.

[49]  N. Shental,et al.  Efficient high-throughput SARS-CoV-2 testing to detect asymptomatic carriers , 2020, Science Advances.

[50]  Stefan Thurner,et al.  Boosting test-efficiency by pooled testing strategies for SARS-CoV-2 , 2020, 2003.09944.

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

[52]  M. Sinha,et al.  Covid-19 - The Law and Limits of Quarantine. , 2020, The New England journal of medicine.

[53]  M. Roser,et al.  Coronavirus Pandemic (COVID-19) , 2020 .

[54]  Anoosheh Heidarzadeh,et al.  On Accelerated Testing for COVID-19 Using Group Testing , 2020, ArXiv.

[55]  Anoosheh Heidarzadeh,et al.  Two-Stage Adaptive Pooling with RT-QPCR for Covid-19 Screening , 2020, ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

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

[57]  Ajit Rajwade,et al.  A Compressed Sensing Approach to Group-testing for COVID-19 Detection , 2020, 2005.07895.

[58]  Matthias Täufer,et al.  Rapid, large-scale, and effective detection of COVID-19 via non-adaptive testing , 2020, bioRxiv.

[59]  Christopher R Bilder,et al.  Assessment of Specimen Pooling to Conserve SARS CoV-2 Testing Resources , 2020, medRxiv.

[60]  Christina Fragouli,et al.  Group testing for overlapping communities , 2020, ICC 2021 - IEEE International Conference on Communications.

[61]  Cheng-Shang Chang,et al.  Positively Correlated Samples Save Pooled Testing Costs , 2020, IEEE Transactions on Network Science and Engineering.

[62]  Ayfer Özgür,et al.  Adaptive Group Testing on Networks with Community Structure , 2021, 2021 IEEE International Symposium on Information Theory (ISIT).

[63]  Olgica Milenkovic,et al.  Semiquantitative Group Testing in at Most Two Rounds , 2021, 2021 IEEE International Symposium on Information Theory (ISIT).

[64]  Dakota T. Howard,et al.  Analysis of the initial lot of the CDC 2019-Novel Coronavirus (2019-nCoV) real-time RT-PCR diagnostic panel , 2021, PloS one.