Multistage Group Testing Research Articles

Multi-Stage Group Testing Improves Efficiency of Large-Scale COVID-19 Screening

BackgroundSARS-CoV-2 test kits are in critical shortage in many countries. This limits large-scale population testing and hinders the effort to identify and isolate infected individuals. ObjectiveHerein, we developed and evaluated multi-stage group testing schemes that test samples in groups of various pool sizes in multiple stages. Through this approach, groups of negative samples can be eliminated with a single test, avoiding the need for individual testing and achieving considerable savings of resources. Study designWe designed and parameterized various multi-stage testing schemes and compared their efficiency at different prevalence rates using computer simulations. ResultsWe found that three-stage testing schemes with pool sizes of maximum 16 samples can test up to three and seven times as many individuals with the same number of test kits for prevalence rates of around 5% and 1%, respectively. We propose an adaptive approach, where the optimal testing scheme is selected based on the expected prevalence rate. ConclusionThese group testing schemes could lead to a major reduction in the number of testing kits required and help improve large-scale population testing in general and in the context of the current COVID-19 pandemic.

Two New Perspectives on Multi-Stage Group Testing

The group testing problem asks to find d≪n defective elements out of n elements, by testing subsets (pools) for the presence of defectives. In the strict model of group testing, the goal is to identify all defectives if at most d defectives exist, and otherwise to report that more than d defectives are present. If tests are time-consuming, they should be performed in a small constant number s of stages of parallel tests. It is known that a test number O(dlogn), which is optimal up to a constant factor, can be achieved already in s=2 stages. Here we study two aspects of group testing that have not found major attention before. (1) Asymptotic bounds on the test number do not yet lead to optimal strategies for specific n,d,s. Especially for small n we show that randomized strategies significantly save tests on average, compared to worst-case deterministic results. Moreover, the only type of randomness needed is a random permutation of the elements. We solve the problem of constructing optimal randomized strategies for strict group testing completely for the case when d=1 and s≤2. A byproduct of our analysis is that optimal deterministic strategies for strict group testing for d=1 need at most 2 stages. (2) Usually, an element may participate in several pools within a stage. However, when the elements are indivisible objects, every element can belong to at most one pool at the same time. For group testing with disjoint simultaneous pools we show that Θ(sd(n/d)1/s) tests are sufficient and necessary. While the strategy is simple, the challenge is to derive tight lower bounds for different s and different ranges of d versus n.

Group testing procedures with incomplete identification and unreliable testing results

We consider multistage group testing with incomplete identification and unreliability features. The objective is to find a cost-efficient group testing policy to select a prespecified number of non-defective items from some population in the presence of false-positive and false-negative test results, subject to reliability and other constraints. To confirm the status of tested groups, various sequential retesting procedures are suggested. We also extend the model to include the possibility of inconclusive test results. We derive all relevant cost functionals in analytically closed form. Numerical examples are also given. Copyright © 2006 John Wiley & Sons, Ltd.

Multistage Group Testing Procedure (Group Screening)

Due to a slight loss of sensitivity, that is a slightly higher chance to falsely declare a positive individual as negative, the group testing methodology has not been adopted as a standard procedure to screen blood donors. In multistage group testing schemes, as more stages are posed with the aim of reducing the expected number of tests, sensitivity is lost in the process. This article proposes a multistage group testing procedure that, when applied in a low prevalence population with slightly accurate kits, it improves the sensitivity.