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%-35%) compared to random pooling when the Dorfman two-stage algorithm is used.

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正相关样本节省合并测试成本

与个人测试方法相比，可以显着降低成本的团体测试方法最近在 COVID-19 的大规模测试中引起了很多兴趣。传统上，混合在一组中的样本被假定为独立同分布的伯努利随机变量。但是，对于像 COVID-19 这样的传染病，情况可能并非如此，因为家庭中的人往往会相互感染。因此，一个家庭中的样本很可能是正相关的。通过利用正相关，我们通过严格的数学证明表明，使用简单的 Dorfman 两阶段方法可以进一步降低成本。一个重要的扩展是考虑使用社交图进行池化测试，其中社交图中的一条边连接两个人之间频繁的社交联系。