Biometrics 63, 1152–1163 December 2007 DOI: 10.1111/j.1541-0420.2007.00817.x Comparison of Group Testing Algorithms for Case Identification in the Presence of Test Error Hae-Young Kim, 1 Michael G. Hudgens, 1, ∗ Jonathan M. Dreyfuss, 2 Daniel J. Westreich, 3 and Christopher D. Pilcher 4 Department of Biostatistics, School of Public Health, University of North Carolina at Chapel Hill, 3107-E McGavran-Greenberg Hall, Chapel Hill, North Carolina 27599, U.S.A. Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, North Carolina 27599, U.S.A. Department of Epidemiology, University of North Carolina at Chapel Hill, North Carolina 27599, U.S.A. HIV/AIDS Division, University of California-San Francisco, San Francisco, California 94110, U.S.A. ∗ email: mhudgens@bios.unc.edu Summary. We derive and compare the operating characteristics of hierarchical and square array-based testing algorithms for case identification in the presence of testing error. The operating characteristics investigated include efficiency (i.e., expected number of tests per specimen) and error rates (i.e., sensitivity, specificity, positive and negative predictive values, per-family error rate, and per-comparison error rate). The methodology is illustrated by comparing different pooling algorithms for the detection of individuals recently infected with HIV in North Carolina and Malawi. Key words: Array; Group testing; Hierarchical; HIV; Per-comparison error rate; Per-family error rate; Predictive value; Sensitivity; Specificity. 1. Introduction Pooling of specimens to increase efficiency of screening in- dividuals for rare diseases has a long history, dating back to screening for syphilis in military inductees in the 1940s (Dorfman, 1943). Subsequently, specimen pooling or group testing has been applied to screening for many other in- fectious diseases (Kacena et al., 1998; Quinn et al., 2000; Centers for Disease Control and Prevention, 2003) and has also found broader application in entomology (Venette, Moon, and Hutchinson, 2002), screening for genetic mutations (Gastwirth, 2000), the blood bank and pharmaceutical indus- tries (Jones and Zhigljavsky, 2001), and many other areas. In the context of infectious diseases, group testing is typically used for (i) case identification, i.e., detecting all individuals having the disease of interest and (ii) prevalence estimation, i.e., estimating the proportion of individuals in the population having a particular disease. This article is motivated by examples of the former. For instance, currently the North Carolina Department of Pub- lic Health and investigators from the University of North Carolina (UNC) at Chapel Hill employ specimen pooling as part of the Screening and Tracing Active Transmission (STAT) program to detect individuals recently infected with HIV (Pilcher et al., 2002, 2005). Likewise, the newly created Center for HIV/AIDS Vaccine Immunology plans to employ similar testing procedures as part of a global attempt to iden- tify acute infections (NIAID Office of Communications and Public Liaison, 2005). This specimen pooling strategy has also been used to identify recent HIV infections in antibody negative males attending STD clinics in Malawi. In these ap- plications, the problem is how to detect very rare cases of HIV infection that elude detection by routine, standard anti- body testing assays (Pilcher et al., 2005) because they are in the pre-antibody “acute” phase of infection. The PCR-based nucleic acid amplification tests (NAATs) that detect these persons are highly sensitive but (compared to antibody tests) are expensive, time consuming, and have inadequate speci- ficity (Daar et al., 2001; Hecht et al., 2002). In this case, group testing is used to enhance testing efficiency and accuracy of high throughput screening for rare cases of acute HIV. Case identification (or classification) was the original mo- tivation behind group testing, as proposed by Dorfman (1943). Dorfman’s algorithm entailed pooling together bio- logical specimens from several individuals and testing these pools of specimens rather than testing each individual speci- men. If a pool tested negative, all specimens in that pool were declared negative. Otherwise, further testing was required to identify positive specimens. Dorfman’s original algorithm re- quired simply testing all individual specimens within positive pools. This pooling procedure is appealing in that, for diseases 1152 C  2007, The International Biometric Society