Background: Pooling is a popular strategy for increasing SARS-CoV-2 testing throughput. One popular poolingscheme is Dorfman pooling: testNindividuals simultaneously. If the test is positive - retest each individual separately.However, requiring more than one positive test may lead to increased false-negative rates. Methods: We analyze the false-negative rate (i.e., the probability of a negative result for an infected individual) of Dorfman pooling via a new probabilistic model. We demonstrate that different, previously made probabilistic assumptions regarding pooling are unlikely in light of empiric data. Our model is conservative in that it ignores sample dilution effects,which can only worsen pooling performance. Results: We show that one can expect a 60-80% increase in false-negative rates under Dorfman pooling, for reasonable parameter values. Moreover, we show that the false-negative rates under Dorfman pooling increase when the prevalenc eof infection decreases. Discussion: In most pooling schemes, identifying an infected individual requires positive results in multiple testsand hence substantially increases false-negative rates. Furthermore, this phenomenon is more pronounced when infection prevalence is low - exactly when pooling is most efficient. Thus, pooling presents an inherent trade-off: it is most efficientwhen it is least accurate. The deterioration of false-negative rates and the aforementioned trade-off are inherent problems of pooling schemes and should be kept in mind by practitioners and policy makers.
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