binGroup2: Statistical Tools for Infection Identification via Group Testing

Group testing is the process of testing items as an amalgamation, rather than separately, to determine the binary status for each item. Its use was especially important during the COVID-19 pandemic through testing specimens for SARS-CoV-2. The adoption of group testing for this and many other applications is because members of a negative testing group can be declared negative with potentially only one test. This subsequently leads to significant increases in laboratory testing capacity. Whenever a group testing algorithm is put into practice, it is critical for laboratories to understand the algorithm’s operating characteristics, such as the expected number of tests. Our paper presents the binGroup2 package that provides the statistical tools for this purpose. This R package is the first to address the identification aspect of group testing for a wide variety of algorithms. We illustrate its use through COVID-19 and chlamydia/gonorrhea applications of group testing.

Christopher R. Bilder (University of Nebraska-Lincoln) , Brianna D. Hitt (United States Air Force Academy) , Brad J. Biggerstaff (Centers for Disease Control and Prevention) , Joshua M. Tebbs (University of South Carolina) , Christopher S. McMahan (Clemson University)

0.1 Supplementary materials

Supplementary materials are available in addition to this article. It can be downloaded at

B. Abdalhamid, C. Bilder, E. McCutchen, S. Hinrichs, S. Koepsell and P. Iwen. Assessment of specimen pooling to conserve SARS CoV-2 testing resources. American Journal of Clinical Pathology, 153: 715–718, 2020. URL
M. Abdelmalek. With all eyes on coronavirus testing, some researchers say ’group testing’ could make up the shortage. ABC News, 2020. URL May 13; Retrieved November 11, 2023.
D. Altman and J. Bland. Diagnostic tests 2: Predictive values. BMJ, 309: 102, 1994. URL
Altona Diagnostics. RealStar. 2023. URL Retrieved November 11, 2023.
American Red Cross. Infectious disease testing. 2023. URL Retrieved November 11, 2023.
N. Ando, D. Mizushima, K. Watanabe, M. Takano, D. Shiojiri, H. Uemura, A. Takahiro, Y. Yanagawa, Y. Kikuchi, S. Oka, et al. Modified self-obtained pooled sampling to screen for Chlamydia trachomatis and Neisseria gonorrhoeae infections in men who have sex with men. Sexually Transmitted Infections, 97: 324–328, 2021. URL
E. Anthes. A CDC airport surveillance program found the earliest known US cases of Omicron subvariants. The New York Times, 2022. URL March 24; retrieved November 11, 2023.
R. Barathidasan, F. Sharmila, R. Raj, G. Dhanalakshmi, G. Anitha and R. Dhodapkar. Pooled sample testing for COVID-19 diagnosis: Evaluation of bi-directional matrix pooling strategies. Journal of Virological Methods, 114524, 2022. URL
BD. BD Max CT/NG/TV. 2023. URL Retrieved November 11, 2023.
C. Bilder. Group testing for identification. Wiley StatsRef: Statistics Reference Online, 2019. URL
C. Bilder, P. Iwen and B. Abdalhamid. Pool size selection when testing for severe acute respiratory syndrome coronavirus 2. Clinical Infectious Diseases, 72: 1104–1105, 2021a. URL
C. Bilder, J. Tebbs and P. Chen. Informative retesting. Journal of the American Statistical Association, 105: 942–955, 2010a. URL
C. Bilder, J. Tebbs and C. McMahan. Discussion on "Is group testing ready for prime-time in disease identification". Statistics in Medicine, 40: 3881–3886, 2021b. URL
C. Bilder, J. Tebbs and C. McMahan. Informative group testing for multiplex assays. Biometrics, 75: 278–288, 2019. URL
C. Bilder, B. Zhang, F. Schaarschmidt and J. Tebbs. BinGroup: A package for group testing. The R Journal, 2: 56–60, 2010b. URL
M. Black, C. Bilder and J. Tebbs. Group testing in heterogeneous populations by using halving algorithms. Journal of the Royal Statistical Society: Series C (Applied Statistics), 61: 277–290, 2012. URL
M. Black, C. Bilder and J. Tebbs. Optimal retesting configurations for hierarchical group testing. Journal of the Royal Statistical Society: Series C (Applied Statistics), 64: 693–710, 2015. URL
Q. Bui, S. Kliff and M. Sanger-Katz. How to test more people for coronavirus without actually needing more tests. The New York Times, 2020. URL July 27; retrieved November 11, 2023.
C. Cheng, Y. Hung and N. Balakrishnan. rBeta2009: The beta random number and dirichlet random vector generating functions. 2012. URL
R. Dorfman. The detection of defective members of large populations. Annals of Mathematical Statistics, 14: 436–440, 1943. URL
L. Graff and R. Roeloffs. Group testing in the presence of test error; an extension of the Dorfman procedure. Technometrics, 14: 113–122, 1972. URL
G. Hepworth and B. Biggerstaff. Bias correction in estimating proportions by pooled testing. Journal of Agricultural, Biological and Environmental Statistics, 22: 602–614, 2017. URL
B. Hitt. Group testing identification: Objective functions, implementation, and multiplex assays. 2020. URL
B. Hitt, C. Bilder, J. Tebbs and C. McMahan. The objective function controversy for group testing: Much ado about nothing? Statistics in Medicine, 38: 4912–4923, 2019. URL
C. Hogan, M. Sahoo and B. Pinsky. Sample pooling as a strategy to detect community transmission of SARS-CoV-2. Journal of the American Medical Association, 323: 1967–1969, 2020. URL
Hologic. Aptima STIs. 2023. URL aptima-stis. Retrieved November 11, 2023.
P. Hou, J. Tebbs, D. Wang, C. McMahan and C. Bilder. Array testing for multiplex assays. Biostatistics, 21: 417–431, 2020. URL
ICBSS. Iowa community-based screening services procedures manual. 2014. URL Retrieved November 11, 2023.
N. Johnson, S. Kotz and X. Wu. Inspection errors for attributes in quality control. CRC Press, 1991. URL
H. Kim, M. Hudgens, J. Dreyfuss, D. Westreich and C. Pilcher. Comparison of group testing algorithms for case identification in the presence of test error. Biometrics, 63: 1152–1163, 2007. URL
S. Kim, H. Kim, H. Kim, H. Ann, J. Kim, H. Choi, M. Kim, J. Song, J. Ahn, N. Ku, et al. Pooled nucleic acid testing to identify antiretroviral treatment failure during HIV infection in Seoul, South Korea. Scandinavian Journal of Infectious Diseases, 46: 136–140, 2014. URL
LabCorp. Emergency Use Authorization summary: COVID-19 RT-PCR test. 2022. URL Retrieved November 11, 2023.
S. Lendle. Gtcorr: Calculate efficiencies of group testing algorithms with correlated responses. 2011. URL Retrieved November 11, 2023.
S. Lendle, M. Hudgens and B. Qaqish. Group testing for case identification with correlated responses. Biometrics, 68: 532–540, 2012. URL
J. Lewis, V. Lockary and S. Kobic. Cost savings and increased efficiency using a stratified specimen pooling strategy for Chlamydia trachomatis and Neisseria gonorrhoeae. Sexually Transmitted Diseases, 39: 46–48, 2012. URL
E. Litvak, X. Tu and M. Pagano. Screening for the presence of a disease by pooling sera samples. Journal of the American Statistical Association, 89: 424–434, 1994. URL
T. Liu, J. Hogan, M. Daniels, M. Coetzer, X. Yizhen, B. Gerald, A. DeLong, L. Ledingham, M. Orido, L. Diero, et al. Improved HIV-1 viral load monitoring capacity using pooled testing with marker-assisted deconvolution. Journal of Acquired Immune Deficiency Syndromes, 75: 580, 2017. URL
T. Liu and Y. Xu. mMPA: Implementation of marker-assisted mini-pooling with algorithm. 2018. URL Retrieved November 11, 2023.
S. Lohse, T. Pfuhl, B. Berkó-Göttel, J. Rissland, T. Geißler, B. Gärtner, S. Becker, S. Schneitler and S. Smola. Pooling of samples for testing for SARS-CoV-2 in asymptomatic people. The Lancet Infectious Diseases, 20: 1231–1232, 2020. URL
A. Mandavilli. Federal officials turn to a new testing strategy as infections surge. The New York Times, 2020. URL July 1; retrieved November 11, 2023.
C. McMahan, J. Tebbs and C. Bilder. Informative Dorfman screening. Biometrics, 68: 287–296, 2012a. URL
C. McMahan, J. Tebbs and C. Bilder. Two-dimensional informative array testing. Biometrics, 68: 793–804, 2012b. URL
Nebraska Veterinary Diagnostic Center. Diagnostic tests & fees. 2023. URL Retrieved November 11, 2023.
Roche. Roche receives FDA Emergency Use Authorization for the cobas SARS-CoV-2 & Influenza A/B Test for use on the cobas 6800/8800 Systems. 2020. URL Retrieved November 11, 2023.
E. Salzer, E. Nixon, G. Drewes, F. Reinhard, G. Bergamini and C. Rau. Screening pools of compounds against multiple endogenously expressed targets in a chemoproteomics binding assay. Journal of Laboratory Automation, 21: 133–142, 2016. URL
H. Sanghani, D. Nawrot, F. Marmolejo-Cossı́o, J. Taylor, J. Craft, E. Kalimeris, M. Andersson and S. Vasudevan. Concentrating pooled COVID-19 patient lysates to improve reverse transcription quantitative PCR sensitivity and efficiency. Clinical Chemistry, 67: 797–798, 2021. URL
A. Sterrett. On the detection of defective members of large populations. The Annals of Mathematical Statistics, 28: 1033–1036, 1957. URL
W. Swallow. Group testing for estimating infection rates and probabilities of disease transmission. Phytopathology, 75: 882–889, 1985. URL
J. Tan, A. Omar, W. Lee and M. Wong. Considerations for group testing: A practical approach for the clinical laboratory. The Clinical Biochemist Reviews, 41: 79–92, 2020. URL doi:10.33176/AACB-20-00007.
M. Thai. Group testing theory in network security: An advanced solution. Springer, 2011. URL
P. Thai, A. Banks, L. Toms, P. Choi, X. Wang, P. Hobson and J. Mueller. Analysis of urinary metabolites of polycyclic aromatic hydrocarbons and cotinine in pooled urine samples to determine the exposure to PAHs in an Australian population. Environmental Research, 182: 109048, 2020. URL
T. Van, J. Miller, D. Warshauer, E. Reisdorf, D. Jernigan, R. Humes and P. Shult. Pooling nasopharyngeal/throat swab specimens to increase testing capacity for influenza viruses by PCR. Journal of Clinical Microbiology, 50: 891–896, 2012. URL
Verily Life Sciences. Emergency Use Authorization summary: Verily COVID-19 RT-PCR test for use with the Verily COVID-19 Nasal Swab Kit. 2022. URL Retrieved November 11, 2023.
Yale University. Emergency Use Authorization summary: SalivaDirect for use with DTC Kits assay. 2022. URL Retrieved November 11, 2023.
K. Zhao and C. Rosa. Thrips as the transmission bottleneck for mixed infection of two orthotospoviruses. Plants, 9: 509, 2020. URL



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For attribution, please cite this work as

Bilder, et al., "binGroup2: Statistical Tools for Infection Identification via Group Testing", The R Journal, 2024

BibTeX citation

  author = {Bilder, Christopher R. and Hitt, Brianna D. and Biggerstaff, Brad J. and Tebbs, Joshua M. and McMahan, Christopher S.},
  title = {binGroup2: Statistical Tools for Infection Identification via Group Testing},
  journal = {The R Journal},
  year = {2024},
  note = {},
  doi = {10.32614/RJ-2023-081},
  volume = {15},
  issue = {4},
  issn = {2073-4859},
  pages = {21-36}