Optimal Group Testing: Structural Properties and Robust Solutions, with Application to Public Health Screening

References

• American Red Cross (2017) Details of tests performed for different infectious agents. Accessed February 1, 2017, http://www.redcrossblood.org/learn-about-blood/what-happens-donated-blood/blood-testing.Google Scholar
• Aprahamian H, Bish DR, Bish EK (2016) Residual risk and waste in donated blood with pooled nucleic acid testing. Statist. Med. 35(28):5283–5301.Crossref, Google Scholar
• Aprahamian H, Bish DR, Bish EK (2019) Optimal risk-based group testing. Management Sci. 65(9):4365–4384.Link, Google Scholar
• Berger T, Mehravari N, Towsley D, Wolf J (1984) Random multiple-access communication and group testing. IEEE Trans. Comm. 32(7):769–779.Crossref, Google Scholar
• Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev. 53(3):464–501.Crossref, Google Scholar
• Bertsimas D, Sim M (2004) The price of robustness. Oper. Res. 52(1):35–53.Link, Google Scholar
• Bish DR, Bish EK, Xie RS, Stramer SL (2014) Going beyond “same-for-all” testing of infectious agents in donated blood. IIE Trans. 46(11):1147–1168.Crossref, Google Scholar
• Black MS, Bilder CR, Tebbs JM (2012) Group testing in heterogeneous populations by using halving algorithms. J. Roy. Statist. Soc. Ser. C: Appl. Statist. 61(2):277–290.Crossref, Google Scholar
• Blass A, Gurevich Y (2002) The logic in computer science column pairwise testing. Bull. EATCS 78:100–132.Google Scholar
• Burden RL, Faires JD (1985) 2.1 the bisection algorithm. Numerical Analysis, 3rd ed. (Prindle, Weber, and Schmidt, Boston), 46–52.Google Scholar
• Centers for Disease Control and Prevention (2014) Summary of notifiable diseases—United States. Accessed August 1, 2018, https://www.cdc.gov/mmwr/preview/mmwrhtml/mm6153a1.htm.Google Scholar
• Centers for Disease Control and Prevention (2015) Diagnoses of HIV infection in the United States and dependent areas. Accessed July 1, 2017, https://www.cdc.gov/hiv/pdf/library/reports/surveillance/cdc-hiv-surveillance-report-2015-vol-27.pdf.Google Scholar
• Centers for Disease Control and Prevention (2019a) West Nile virus. Accessed February 1, 2019, https://www.cdc.gov/westnile/index.html.Google Scholar
• Centers for Disease Control and Prevention (2019b) West Nile virus—Final cumulative maps & data for 1999–2018. Accessed February 1, 2019, https://www.cdc.gov/westnile/statsmaps/cumMapsData.html.Google Scholar
• Corless RM, Gonnet GH, Hare DE, Jeffrey DJ, Knuth DE (1996) On the Lambert W function. Adv. Comput. Math. 5(1):329–359.Crossref, Google Scholar
• Dauphin G, Zientara S (2007) West Nile virus: Recent trends in diagnosis and vaccine development. Vaccine 25(30):5563–5576.Crossref, Google Scholar
• Dorfman R (1943) The detection of defective members of large populations. Ann. Math. Statist. 14(4):436–440.Crossref, Google Scholar
• El-Amine H, Bish EK, Bish DR (2017) Robust postdonation blood screening under prevalence rate uncertainty. Oper. Res. 66(1):1–17.Link, Google Scholar
• European Centre for Disease Prevention and Control. Vector-borne diseases. Accessed October 1, 2018, https://ecdc.europa.eu/en/climate-change/climate-change-europe/vector-borne-diseases.Google Scholar
• Graff LE, Roeloffs R (1972) Group testing in the presence of test error; an extension of the Dorfman procedure. Technometrics 14(1):113–122.Crossref, Google Scholar
• Howard J (2018) Rates of three STDs in US reach record high, CDC says. CNN (August 28), https://www.cnn.com/2018/08/28/health/std-rates-united-states-2018-bn/index.html.Google Scholar
• Hwang FK (1975) A generalized binomial group testing problem. J. Amer. Statist. Assoc. 70(352):923–926.Crossref, Google Scholar
• Johnson NL, Kotz S, Wu XZ (1991) Inspection Errors for Attributes in Quality Control, Monographs on Statistics and Applied Probability, vol. 44 (CRC Press, Boca Raton, FL).Crossref, Google Scholar
• Kim HY, Hudgens MG, Dreyfuss JM, Westreich DJ, Pilcher CD (2007) Comparison of group testing algorithms for case identification in the presence of test error. Biometrics 63(4):1152–1163.Crossref, Google Scholar
• Korves CT, Goldie SJ, Murray MB (2006) Cost-effectiveness of alternative blood-screening strategies for West Nile virus in the United States. PLoS Med. 3(2):e21.Crossref, Google Scholar
• Lewis JL, Lockary VM, Kobic S (2012) Cost savings and increased efficiency using a stratified specimen pooling strategy for Chlamydia trachomatis and Neisseria gonorrhoeae. Sexually Transmitted Diseases 39(1):46–48.Crossref, Google Scholar
• McMahan CS, Tebbs JM, Bilder CR (2012) Informative Dorfman screening. Biometrics 68(1):287–296.Crossref, Google Scholar
• Natarajan K, Shi D, Toh KC (2013) A probabilistic model for minmax regret in combinatorial optimization. Oper. Res. 62(1):160–181.Link, Google Scholar
• North Carolina State Laboratory of Public Health. Virology/serology: Chlamydia/gonorrhea. Accessed November 1, 2016, http://slph.ncpublichealth.com/virology-serology/chlamydia/default.asp.Google Scholar
• Perakis G, Roels G (2008) Regret in the newsvendor model with partial information. Oper. Res. 56(1):188–203.Link, Google Scholar
• Petersen LR, Carson PJ, Biggerstaff BJ, Custer B, Borchardt SM, Busch MP (2012) Estimated cumulative incidence of West Nile virus infection in US adults, 1999–2010. Epidemiology Infection 141(3):591–595.Crossref, Google Scholar
• Pfleiderer C, Blümel J, Schmidt M, Roth WK, Houfar MK, Eckert J, Chudy M, Menichetti E, Lechner S, Nübling CM (2008) West Nile virus and blood product safety in Germany. J. Medical Virology 80(3):557–563.Crossref, Google Scholar
• Rios M, Daniel S, Chancey C, Hewlett IK, Stramer SL (2007) West Nile virus adheres to human red blood cells in whole blood. Clinical Infectious Disease 45(2):181–186.Crossref, Google Scholar
• Samuels SM (1978) The exact solution to the two-stage group-testing problem. Technometrics 20(4):497–500.Crossref, Google Scholar
• Saraniti BA (2006) Optimal pooled testing. Health Care Management Sci. 9(2):143–149.Crossref, Google Scholar
• Shipitsyna E, Shalepo K, Savicheva A, Unemo M, Domeika M (2007) Pooling samples: The key to sensitive, specific and cost-effective genetic diagnosis of chlamydia trachomatis in low-resource countries. Acta Dermato-Venereologica 87(2):140–143.Crossref, Google Scholar
• Sobel M, Groll PA (1959) Group testing to eliminate efficiently all defectives in a binomial sample. Bell System Tech. J. 38(5):1179–1252.Crossref, Google Scholar
• Stramer SL, Fang CT, Foster GA, Wagner AG, Brodsky JP, Dodd RY (2005) West Nile virus among blood donors in the United States, 2003 and 2004. New England J. Medicine 353(5):451–459.Crossref, Google Scholar
• Wein LM, Zenios SA (1996) Pooled testing for HIV screening: Capturing the dilution effect. Oper. Res. 44(4):543–569.Link, Google Scholar
• World Health Organization (2017) Vector-borne diseases. Accessed September 1, 2018, http://www.who.int/news-room/fact-sheets/detail/vector-borne-diseases.Google Scholar