Group testing, where groups of individual specimens are composited to test for a binary outcome (e.g., positive or negative status for an infectious disease), is a procedure used to reduce the costs of screening large numbers of individuals. Applications of group testing include Bovine Viral Diarrhea virus detection in cattle herds (Peck 2006), blood donation screening (Dodd et al. 2002), discovery of chemical compounds to use in new drugs (Remlinger et al. 2006), and opportunistic testing of individuals for chlamydia (Mund et al. 2008). In its simplest form, group testing works by pooling a number of individual specimens into a single group. If the group tests negative, all individuals within it are diagnosed as being negative. If the group tests positive, retesting is needed to decode the positive individuals from the negative individuals. Traditionally, group testing research has assumed each individual to have the same probability of positivity when developing testing algorithms. However, this assumption is often unrealistic, especially when known risk factors can be used to measure distinct probabilities of positivity for each individual. With this as motivation, we propose new retesting procedures that take advantage of the heterogeneity among individuals as measured by their probability of positivity. These proposals work in one or more of the following ways: 1) Retest individuals with higher probabilities first, 2) Select group sizes based on the individual probabilities, and 3) Organize the initial testing to reduce the number of retests that may be needed. We show that our proposals can significantly reduce the number of tests required while maintaining similar accuracy levels as standard group testing procedures.
Dodd, R., Notari, E., and Stramer, S. (2002). Current prevalence and incidence of infectious disease markers and estimated window-period risk in the American Red Cross donor population. Transfusion, 42, 975-979.
Mund, M., Sander, G., Potthoff, P., Schicht, H., and Matthias, K. (2008). Introduction of Chlamydia trachomatis screening for young women in Germany. Journal der Deutschen Dermatologischen Gesellschaft, 6, 1032-1037.
Peck, C. (2006). Going after BVD. Beef, 42, 34-44.
Remlinger, K., Hughes-Oliver, J., Young, S., and Lam, R. (2006). Statistical design of pools using optimal coverage and minimal collision. Technometrics, 48, 133-143.
Keywords: Binary response; Classification; Pooled testing; Screening
Biography: Chris Bilder is an Associate Professor in the Department of Statistics at the University of Nebraska-Lincoln. Chris and his co-author Josh Tebbs of the University of South Carolina have been examining ways to improve group testing procedures for the last four years as part of a grant from the National Institutes of Health.