Positively Correlated Samples Save Pooled Testing Costs
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The group testing approach that can achieve significant cost reduction over the individual testing approach has received a lot of interest lately for massive testing of COVID-19. Traditionally, the samples mixed in a group are assumed to be independent and identically distributed Bernoulli random variables. However, this may not be the case for a contagious disease like COVID-19, as people within a family tend to infect each other. As such, samples in a family are likely to be positively correlated. By exploiting positive correlation, we show by rigorous mathematical proof that further cost reduction can be achieved by using the simple Dorfman two-stage method. One important extension is to consider pooled testing with a social graph, where an edge in the social graph connects frequent social contacts between two persons. For pooled testing with a social graph, we propose a hierarchical agglomerative algorithm and show that such an algorithm can lead to significant cost reduction (roughly 20 two-stage algorithm is used.
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