The inherent problem of pooling: increased false-negative rates

Background: Pooling is a popular strategy for increasing SARS-CoV-2 testing throughput. A common pooling scheme is Dorfman pooling: test N individuals simultaneously. If the first test is positive - retest each individual. Methods: Using a probabilistic model, we analyze the false-negative rate (i.e., the probability of a negative result for an infected individual) of Dorfman pooling. 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. On average, when separate testing misses, e.g., ten infected individuals - Dorfman pooling misses more than sixteen. Discussion: In most pooling schemes, identifying an infected individual requires positive results in multiple tests and hence substantially increases false-negative rates. It is an inherent shortcoming of pooling schemes and should be kept in mind by policy makers.