An Accurate Model for SARS-CoV-2 Pooled RT-PCR Test Errors

PCR testing is an important tool to mitigate outbreaks of infectious diseases. One way of increasing testing throughput is by simultaneously testing multiple samples for the presence of a pathogen, a technique known as pooling. During the current COVID-19 pandemic, rapidly testing individuals for the presence of SARS-CoV-2 is conducted in large amounts. Since testing is often a bottleneck in mitigating the spread of SARS-CoV-2, pooling is increasing in popularity. 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 probabilistic model for the outcomes of pooled tests. As an application, we analyze the false-negative rates of one common pooling scheme known as Dorfman pooling. We show that the false-negative rates of Dorfman pooling increase when the prevalence of infection decreases. However, low infection prevalence is exactly the condition under which Dorfman pooling achieves highest throughput. We therefore implore the cautious use of pooling and development of pooling schemes that consider correctly accounting for tests error rates.