Operating characteristics of group testing algorithms for case identification in the presence of test error

Pooling of specimens to increase efficiency of screening individuals for rare diseases has a long history, dating back to screening for syphilis in military inductees in the 1940s. Subsequently, specimen pooling has been applied to screening for many other infectious diseases and has also found broader application in entomology, screening for genetic mutations and many other areas. Currently the North Carolina Department of Public Health and investigators from the University of North Carolina at Chapel Hill have developed quick, cost effective methods to screen over 120,000 people annually for recent HIV infection using highly sensitive, automated specimen pooling algorithms as part of the Screening and Tracing Active Transmission (STAT) program. In this dissertation, we research group testing methodology to help optimize the pooling algorithm used in the STAT program and to assist in extending this innovative approach to other settings or detection of other infectious diseases where the overriding issues are identical but the specific conditions (e.g., disease prevalence) vary considerably. This dissertation is comprised of three papers. In the first paper, we derive and compare the operating characteristics of hierarchical and two-dimensional 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). In the second paper, we extend two-dimensional array to three-dimensional array-based algorithms when there exist test errors. Efficiency and pooling measurement error rates of three-dimensional array-based algorithms are compared with hierarchical and two-dimensional array-based algorithms in the presence of test error. In both the first and second papers, the methodology is illustrated by comparing different pooling algorithms for the detection of individuals recently infected with HIV in North Carolina and Malawi. In the third paper, the optimal configuration of a two-dimensional array-based pooling algorithm is considered. We derive p*, the highest prevalence, where pooling with this algorithm is better than individual testing. For the given prevalence less than p*, we determine the optimal algorithm configuration which minimizes the expected number of tests per specimen