The Statistics of Noisy One-Stage Group Testing in Outbreaks

In one-stage or non-adaptive group testing, instead of testing every sample unit individually, they are split, bundled in pools, and simultaneously tested. The results are then decoded to infer the states of the individual items. This combines advantages of adaptive pooled testing, i. e. saving resources and higher throughput, with those of individual testing, e. g. short detection time and lean laboratory organisation, and might be suitable for screening during outbreaks. We study the COMP and NCOMP decoding algorithms for non-adaptive pooling strategies based on maximally disjunct pooling matrices with constant row and column sums in the linear prevalence regime and in the presence of noisy measurements motivated by PCR tests. We calculate sensitivity, specificity, the probabilities of Type I and II errors, and the expected number of items with a positive result as well as the expected number of false positives and false negatives. We further provide estimates on the variance of the number of positive and false positive results. We conduct a thorough discussion of the calculations and bounds derived. Altogether, the article provides blueprints for screening strategies and tools to help decision makers to appropriately tune them in an outbreak.