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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
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    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.

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