Informative Retesting.

In situations where individuals are screened for an infectious disease or other binary characteristic and where resources for testing are limited, group testing can offer substantial benefits. Group testing, where subjects are tested in groups (pools) initially, has been successfully applied to problems in blood bank screening, public health, drug discovery, genetics, and many other areas. In these applications, often the goal is to identify each individual as positive or negative using initial group tests and subsequent retests of individuals within positive groups. Many group testing identification procedures have been proposed; however, the vast majority of them fail to incorporate heterogeneity among the individuals being screened. In this paper, we present a new approach to identify positive individuals when covariate information is available on each. This covariate information is used to structure how retesting is implemented within positive groups; therefore, we call this new approach "informative retesting." We derive closed-form expressions and implementation algorithms for the probability mass functions for the number of tests needed to decode positive groups. These informative retesting procedures are illustrated through a number of examples and are applied to chlamydia and gonorrhea testing in Nebraska for the Infertility Prevention Project. Overall, our work shows compelling evidence that informative retesting can dramatically decrease the number of tests while providing accuracy similar to established non-informative retesting procedures.