An accurate model for SARS-CoV-2 pooled RT-PCR test errors

Pooling is a method of simultaneously testing multiple samples for the presence of pathogens. Pooling of SARS-CoV-2 tests is increasing in popularity, due to its high testing throughput. A popular pooling scheme is Dorfman pooling: test N individuals simultaneously, if the test is positive, each individual is then tested separately; otherwise, all are declared negative. Most analyses of the error rates of pooling schemes assume that including more than a single infected sample in a pooled test does not increase the probability of a positive outcome. We challenge this assumption with experimental data and suggest a novel and parsimonious probabilistic model for the outcomes of pooled tests. As an application, we analyse the false-negative rate (i.e. the probability of a negative result for an infected individual) of Dorfman pooling. We show that the false-negative rates under Dorfman pooling increase when the prevalence of infection decreases. However, low infection prevalence is exactly the condition when Dorfman pooling achieves highest throughput efficiency. We therefore urge the cautious use of pooling and development of pooling schemes that consider correctly accounting for tests' error rates.