Optimal group testing strategy for the mass screening of SARS-CoV-2

We analyze the group testing strategy that maximizes the efficiency of the SARS-CoV-2 screening test while ensuring its effectiveness, where the effectiveness of group testing guarantees that negative results from pooled samples can be considered presumptive negative. Two aspects of test efficiency are considered, one concerning the maximization of the welfare throughput and the other concerning the maximization of the identification rate (namely, identifying as many infected individuals as possible). We show that compared with individual testing, group testing leads to a higher probability of false negative results but a lower probability of false positive results. To ensure the test effectiveness, both the group size and the prevalence of SARS-CoV-2 must be below certain respective thresholds. To achieve test efficiency that concerns either the welfare throughput maximization or the identification rate maximization, the optimal group size is jointly determined by the test accuracy parameters, the infection prevalence rate, and the relative importance of identifying infected subjects. We also show that the optimal group size that maximizes the welfare throughput is weakly smaller than the one that maximizes the identification rate.