Group Testing Case Identification with Biomarker Information

Screening procedures for infectious diseases, such as HIV, often involve pooling individual specimens together and testing the pools. For diseases with low prevalence, group testing (or pooled testing) can be used to classify individuals as diseased or not while providing considerable cost savings when compared to testing specimens individually. The pooling literature is replete with group testing case identification algorithms including Dorfman testing, higher-stage hierarchical procedures, and array testing. Although these algorithms are usually evaluated on the basis of the expected number of tests and classification accuracy, most evaluations in the literature do not account for the continuous nature of the testing responses and thus invoke potentially restrictive assumptions to characterize an algorithm's performance. Commonly used case identification algorithms in group testing are considered and are evaluated by taking a different approach. Instead of treating testing responses as binary random variables (i.e., diseased/not), evaluations are made by exploiting an assay's underlying continuous biomarker distributions for positive and negative individuals. In doing so, a general framework to describe the operating characteristics of group testing case identification algorithms is provided when these distributions are known. The methodology is illustrated using two HIV testing examples taken from the pooling literature.