IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v12y2010i3d10.1007_s11009-008-9104-4.html
   My bibliography  Save this article

A Two-Stage Group Testing Model for Infections with Window Periods

Author

Listed:
  • Shaul K. Bar-Lev

    (University of Haifa)

  • Onno Boxma

    (Eindhoven University of Technology)

  • Wolfgang Stadje

    (University of Osnabrück)

  • Frank A. Duyn Schouten

    (Tilburg University)

Abstract

We present a two-stage group testing model for the detection of viruses in blood samples in the presence of random window periods. As usual, if a tested group is found to be positive, all its members are treated individually. The groups that were tested negative return for a second round after a certain time, new blood samples are taken and tested after pooling. The given system parameters are the size of the population to be screened, the incidence rates of the infections, the probability distributions of the lengths of the window periods, and the costs of group tests. The objective is to minimize the expected cost of running the system, which is composed of the cost of the conducted group tests and penalties on delayed test results and on misclassifications (noninfected persons declared to be positive and, more importantly, persons whose infections have not been identified). By an appropriate choice of the group size and the waiting time for the second round of testings one wants to optimize the various trade-offs involved. We derive in closed form all the probabilistic quantities occurring in the objective function and the constraints. Several numerical examples are given. The model is also extended to the case of several types of viruses with different window periods.

Suggested Citation

  • Shaul K. Bar-Lev & Onno Boxma & Wolfgang Stadje & Frank A. Duyn Schouten, 2010. "A Two-Stage Group Testing Model for Infections with Window Periods," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 309-322, September.
    • Handle: RePEc:spr:metcap:v:12:y:2010:i:3:d:10.1007_s11009-008-9104-4
    DOI: 10.1007/s11009-008-9104-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-008-9104-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-008-9104-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Shaul K. Bar‐Lev & Wolfgang Stadje & Frank A. Van der Duyn Schouten, 2006. "Group testing procedures with incomplete identification and unreliable testing results," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 22(3), pages 281-296, May.
    2. Lei Zhu & Jacqueline M. Hughes-Oliver & S. Stanley Young, 2001. "Statistical Decoding of Potent Pools Based on Chemical Structure," Biometrics, The International Biometric Society, vol. 57(3), pages 922-930, September.
    3. Lawrence M. Wein & Stefanos A. Zenios, 1996. "Pooled Testing for HIV Screening: Capturing the Dilution Effect," Operations Research, INFORMS, vol. 44(4), pages 543-569, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yaakov Malinovsky, 2019. "Sterrett Procedure for the Generalized Group Testing Problem," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 829-840, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Claeys, Dieter & Walraevens, Joris & Laevens, Koenraad & Bruneel, Herwig, 2010. "A queueing model for general group screening policies and dynamic item arrivals," European Journal of Operational Research, Elsevier, vol. 207(2), pages 827-835, December.
    2. Bar-Lev, Shaul K. & Boxma, Onno & Kleiner, Igor & Perry, David & Stadje, Wolfgang, 2017. "Recycled incomplete identification procedures for blood screening," European Journal of Operational Research, Elsevier, vol. 259(1), pages 330-343.
    3. Shaul K. Bar-Lev & Hans Blanc & Onno Boxma & Guido Janssen & David Perry, 2013. "Tandem Queues with Impatient Customers for Blood Screening Procedures," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 423-451, June.
    4. Bar-Lev, S.K. & Parlar, M. & Perry, D. & Stadje, W. & van der Duyn Schouten, F.A., 2007. "Applications of bulk queues to group testing models with incomplete identification," Other publications TiSEM 0b1bfa5e-c1e6-43ec-9684-1, Tilburg University, School of Economics and Management.
    5. Bar-Lev, Shaul K. & Parlar, Mahmut & Perry, David & Stadje, Wolfgang & Van der Duyn Schouten, Frank A., 2007. "Applications of bulk queues to group testing models with incomplete identification," European Journal of Operational Research, Elsevier, vol. 183(1), pages 226-237, November.
    6. Shaul K. Bar‐Lev & Onno Boxma & Andreas Löpker & Wolfgang Stadje & Frank A. Van der Duyn Schouten, 2012. "Group testing procedures with quantitative features and incomplete identification," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(1), pages 39-51, February.
    7. Hae-Young Kim & Michael G. Hudgens & Jonathan M. Dreyfuss & Daniel J. Westreich & Christopher D. Pilcher, 2007. "Comparison of Group Testing Algorithms for Case Identification in the Presence of Test Error," Biometrics, The International Biometric Society, vol. 63(4), pages 1152-1163, December.
    8. Bar-Lev, S.K. & Stadje, W. & van der Duyn Schouten, F.A., 2002. "Hypergeometric Group Testing with Incomplete Information," Other publications TiSEM bbeda767-e037-4441-a6d4-6, Tilburg University, School of Economics and Management.
    9. Yongxi Cheng & Yinfeng Xu, 2014. "An efficient FPRAS type group testing procedure to approximate the number of defectives," Journal of Combinatorial Optimization, Springer, vol. 27(2), pages 302-314, February.
    10. Yaakov Malinovsky, 2019. "Sterrett Procedure for the Generalized Group Testing Problem," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 829-840, September.
    11. Tarun Jain & Bijendra Nath Jain, 2021. "Infection Testing at Scale: An Examination of Pooled Testing Diagnostics," Vikalpa: The Journal for Decision Makers, , vol. 46(1), pages 13-26, March.
    12. Hrayer Aprahamian & Douglas R. Bish & Ebru K. Bish, 2020. "Optimal Group Testing: Structural Properties and Robust Solutions, with Application to Public Health Screening," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 895-911, October.
    13. Hrayer Aprahamian & Hadi El-Amine, 2022. "Optimal Screening of Populations with Heterogeneous Risk Profiles Under the Availability of Multiple Tests," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 150-164, January.
    14. Nguyen, Ngoc T. & Bish, Ebru K. & Bish, Douglas R., 2021. "Optimal pooled testing design for prevalence estimation under resource constraints," Omega, Elsevier, vol. 105(C).
    15. Sarah Kok & Alexander Rutherford & Reka Gustafson & Rolando Barrios & Julio Montaner & Krisztina Vasarhelyi, 2015. "Optimizing an HIV testing program using a system dynamics model of the continuum of care," Health Care Management Science, Springer, vol. 18(3), pages 334-362, September.
    16. Jiejian Feng & Michael Zhang, 2017. "Reducing cost and abandoned E-components in incomplete identification," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(3), pages 281-290, March.
    17. Hrayer Aprahamian & Douglas R. Bish & Ebru K. Bish, 2019. "Optimal Risk-Based Group Testing," Management Science, INFORMS, vol. 65(9), pages 4365-4384, September.
    18. Yongxi Cheng & Ding-Zhu Du & Yinfeng Xu, 2014. "A Zig-Zag Approach for Competitive Group Testing," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 677-689, November.
    19. Shaul K. Bar-Lev & Wolfgang Stadje & Frank A. van der Duyn Schouten, 2004. "Optimal Group Testing with Processing Times and Incomplete Identification," Methodology and Computing in Applied Probability, Springer, vol. 6(1), pages 55-72, March.
    20. Wang, Dewei & McMahan, Christopher S. & Tebbs, Joshua M. & Bilder, Christopher R., 2018. "Group testing case identification with biomarker information," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 156-166.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:12:y:2010:i:3:d:10.1007_s11009-008-9104-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.